Algebra 2 Work Book Answers 2hee

Algebra 2: All-In-One Answers (continued)

Chapter 1

23. 186 24. 25 25. 0 26. -25 27. a + (a - b) + c + b +(a - 2c)+ b + c + (a - b); 4a

Practice 1-1

Guided Problem Solving 1-2

1. -4.2 2. 4 3. 7 4. 1 5. 2 6. 1.8 7. 6 8. 0.01 9. 3

All rights reserved.

6

10. = 11. 12. = 13. 14. 15. 16. 17. integer, rational, real 18. whole, integer, rational, real 19. irrational, real 20. rational, real 21. natural, whole, integer, rational, real 22. rational, real 23. irrational, real 24. integer, rational, real 25. Comm. Prop. of Add. 26. Identity Prop. of Add. 27. Assoc. Prop. of Add. 28. Inv. Prop. of Mult. 29. Dist. Prop. 30. Comm. Prop. of Mult. 31. Identity Prop. of Mult. 32. Inv. Prop. of Mult. 33. Inv. Prop. of Add. 34. Assoc. Prop. of Mult. 35–38. 3 2 1 0.5 2 3

2

1

0

1

2

3

39. 2 1 ; 2 2 40. -3; 1 41. 2 5 ; 9 42. 4; 2 1

10a. about 198 million eligible voters 10b. about 100 million voters

Practice 1-3 1. h 5 3V2 pr

3 4 9 5 2 5 43. N: natural 44. H: rational; L: rational; n: natural 45. t: rational; n: natural

2S 2. r 5 L L


4. x 5 9 g 2 3; no restrictions

h 3. w 5 S 2 1h

be many valid counterexamples for each statement.

4 c(a 1 b) 5. x 5 b 2 a ; a 2 b

3. Answers may vary. Sample: 4 is a whole number, but its reciprocal 1 is not a whole number. 4. Answers may vary. 4

6. x = t 3 - 3; t 2 0 7. $20 and $35 8. 2.5 in., 6 in., 6.5 in. 9. 41, 42, 43 10. 0 11. 1 12. 6 13. -1 14. 2 74 15. 1

1. An example that makes the statement false. 2. There may

© Pearson Education, Inc., publishing as Pearson Prentice Hall.

1. The number of eligible voters in millions in the United States from 1960 to 2000 2. The number of years since 1960 3. 28; about 180 million voters 4. 52, 60 5. about 242 million voters; about 263 million voters 6. -0.003y + 0.61 7. -0.0078y2 + 1.265y + 65.27 8. 20; about 87 million voters 9. Answers may vary. Sample: Answers are reasonable. Year Eligible Voters 1988 180 million 2012 242 million 2020 263 million

Sample: 7 is a natural number, but its opposite -7 is not a natural number. 5. Answers may vary. Sample: 0 is a whole number, and since -0 = 0, the opposite of 0 is a whole number. 6. Answers may vary. Sample: The integer -1 has -1 as its reciprocal, so -1 is an integer whose reciprocal is an integer. 7. Answers may vary. Sample: !2 and - !2 are irrational numbers, but their product -2 is a rational number. 8. Answers may vary. They should be similar to counterexamples in (3) - (7). 9a. Answers may vary. Sample: 2 and 5 are whole numbers but 2 - 5 = -3, which is not a whole number. 9b. Answers may vary. Sample: 5 is an integer, but its opposite -5 is not a whole number. 9c. Answers may vary. Sample: 3 is a whole number but 32 = 9, which is not an even number. 9d. Answers may vary. Sample: -1 is an integer, but not a whole number. 9e. Answers may vary. Sample: 4 is a whole number and !4 is 2, which is not an irrational number.

Practice 1-2 1. 7x 2. 14t - 5 3. -11a + b - 1 4. 2i + 7j 5. 12xy 6. 13x2 + 5x 7. 4m - 6 8. 1 a 1 1 b 9. 32 t2 1 2t 3 9 2 10. -a - 5 11. -8n - 16m 12. x2 - 2xy + y2 13a. 54 in.2 13b. 13.5 m2 14. $10.06 15. 85 16. 26 17. -42 18. -1421 19. 10 20. 1 21. 32 22. 13

All-In-One Answers

16. 19 17. 15 18. Mike’s bus: 35 mi/h; Adam’s bus: 55 mi/h 2 19. slower train: 50 mi/h; faster train: 100 mi/h 20. 81, 83, 85, and 87 21. length: 17 cm; width: 12 cm

Guided Problem Solving 1-3 1. $5000 2. $2000; $3000 3. 6%; 8% 4. P = 2000, r = 0.06, t = 1 5. $2120 6. P = 3000, r = 0.08, t = 1 7. $3240 8. $360 9. $746.40 10. Answers may vary. Sample: I = P(1 + r)t - P; Answers . 11. $26; $52.86

Practice 1-4 1. t -5 654321 0 1 2 3 4 2. m 8 0 1 2 3 4 5 6 7 8 9 10 3. x -2 654321 0 1 2 3 4

Algebra 2

75

Algebra 2: All-In-One Answers

(continued) 16. x -1 or x 3

4. a 2 72 7

2

54321 0 1 2 3 4 5

654321 0 1 2 3 4

17. x -1 and x 2, or -1 x 2 54321 0 1 2 3 4 5

6. x 2 12 1

2 54321 0 1 2 3 4 5

18. at least $4500 19. less than 35 ft 20. more than 15 years old 21. at least 1072 questionnaires 22. between 10.3 lb and 12.8 lb 23. at least 7.75 in. and at most 8.25 in. 24. between 4 h and 4.8 h, or between 4 h and 4 h 48 min


7. x 12 642 0 2 4 6 8 10 12 14 8. x 3 8 3 8

54321 0 1 2 3 4 5 9. x -16 18 16 14 12 10 8 6 10. -3 x 2 54321 0 1 2 3 4 5 11. x 2 or x 8 0 1 2 3 4 5 6 7 8 9 10 12. x -3 and x 6, or -3 x 6 4321 0 1 2 3 4 5 6 13. x 1 or x 2 54321 0 1 2 3 4 5 14. -3 x 5 4321 0 1 2 3 4 5 6

1. between $700,000 and $750,000 2. $496,000 3. 700,000 x + 496,000 750,000 4. 204,000 x 254,000 5. between $204,000 and $254,000 6. $204,000 + $496,000 = $700,000; $254,000 + $496,000 = $750,000 7. between 18 hr and 25 hr

Practice 1-5 1. ∆h - 8.3« 2 2. ∆a« 2.5 3. ∆x - 27.5« 5.5 4. x -17 or x 7 17 7 20

10

0

10

20

30

5. k -16 and k 22, or -16 k 22 16 22 20

10

0

10

20

30

6. all real numbers 54321 0 1 2 3 4 5 7. t -2 and t 12, or -2 t 12 42 0 2 4 6 8 10 12 14 16 8. x 2 2 or x 2 3 2

3 54321 0 1 2 3 4 5

15. -2 x -1 54321 0 1 2 3 4 5

76

Algebra 2


987654321 0 1

All-In-One Answers


5. x -8


(continued)

9. b 2 32 and b 12 , or 2 23 b 12 3

1 2

2

54321 0 1 2 3 4 5 10. w 2 2 or w 2 3

7. Answers may vary.; The experimental probability is expected to be close to the theoretical probability 5 5 0.3125 < 0.31, or 31% 16 8. Answers may vary.; The experimental probability is expected to be close to the theoretical probability 1 5 0.015625 < 0.02, or 2% 64 1 5 0.03125 < 0.03, or 3% 9. 144p < 0.09, or 9% 10. 32 5000

2

3


54321 0 1 2 3 4 5



11. all real numbers 54321 0 1 2 3 4 5 12. u -3 or u 3 54321 0 1 2 3 4 5

1. 1, 2, 3, 4, 5, 6 2. Answers may vary. Sample: (3,2) 3. (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6) 4. 36 5. 1 6. 1 7. 6 8. 1 6 36 9. Answers may vary. Experimental probabilities should be close to theoretical probabilities. 10a. (H,H,H), (H,H,T), (H,T,H), (T,H,H), (T,T,H), (T,H,T), (H,T,T), (T,T,T) 10b. 8 10c. 1 10d. 3 8 8

13. -7, 7 14. no solution 15. 2 16. -27, 3 17. -21, 21

1A: Graphic Organizer

18. 2 11 , 1 19. no solution 20. 2 20 , 4 21. -3, 3 7 5 1 22. -4, 2 23. 2 24. no solution 25. ∆x - 4.2« 0.01; 4.19 x 4.21 26. ∆x - 3.5« 0.002; 3.498 x 3.502 27. ∆x - 10« 1 ; 9 11 x 10 1 12 12 12 28. ∆T - 76« 11; 65 T 87 29. ∆w - 40« 0.25; 39.75 w 40.25 30. ∆d - 13.75« 11.25; 2.5 d 25

1. Tools of Algebra 2. Answers may vary. Sample: properties

Guided Problem Solving 1-5 1. Find a value for b that makes the equation true. 2. distance 3. |4 - 8b| = -12 4. no 5. no solution 6. For any value of b, the left side of the equality is negative. 7. no solution

of real numbers, solving equations, solving inequalities, probability 3. Check students’ work.

1B: Reading Comprehension 1. temperature scales 2. degrees of temperature 3. 18 years 4. degree 5. 32° (the freezing point of pure water) 6. Fahrenheit used a mixture of salt and ice; Celsius used the freezing point of pure water. 7. Answers may vary. Sample: No. There were 96 degrees between 0° F and normal body temperature. There are almost the same number of degrees between the freezing and boiling points of water. Since the difference between the high and low temperatures on the Celsius scale is greater, Celsius degrees must be significantly greater than Fahrenheit degrees. 8. b

1C: Reading/Writing Math Symbols Practice 1-6 1a. 1 , or 20% 1b. 2 , or 40% 1c. 3 , or 60% 5

5

5

1d. 4 , or 80% 2a. 8 < 0.42, or 42% 2b. 4 < 0.21,

19 19 5 7 2 or 21% 2c. < 0.11, or 11% 2d. < 0.37, or 37% 19 19 3a. 12 , or 50% 3b. 31 < 0.33, or 33% 3c. 61 < 0.17, or 17% 3d. 56 < 0.83, or 83% 4a. {$6, $11, $15, $21, $25, $30}; 6 outcomes 4b. 61 < 0.17, or 17% 4c. 0 4d. 13 < 0.33, or 33% 47 < 0.67, or 67% 5. 13 < 0.54, or 54% 6. 70 24

All-In-One Answers

1. 5 multiplied by 9 or 5 times 9 2. 1, 2, 3 and the pattern continues in the same way. 3. 12 divided by 0.4 4. the square root of 7 5. |–3| 6. x 8 or x 7. w = 29 8 5 8. x 9. "5 10. 2, 4, 6, . . .

1D: Visual Vocabulary Practice 1. variable 2. term 3. coefficient 4. opposite 5. absolute value 6. compound inequality 7. multiplicative inverse 8. algebraic expression 9. experimental probability

Algebra 2

77

(continued) 10.

Opposite: The additive inverse of any number, a, is -a. Reciprocal: The multiplicative inverse of any nonzero number, a, is a1. Absolute value of a real number: The distance from a real number to zero on the number line. Variable expression: An expression that contains one or more variables. Solution of an equation: A number that makes the equation true.

2 x 2

1. -8; 2 12 ; 17; 37 2. 1 2 ; 1 1 ; 0; 21 1 3. 7.8; 3.3; -7.2; -19.2 6

3

3

4. not a function 5. not a function 6. function 7. 10

; domain: {1, 2, 3, 5}; range: e 22, 3 , 3 1 , 9 f 4 2

y

6 2 2

8.

4

; domain: {-3, 0, 1}; range: {-2, 4, 5}

6

2

3

3

4

15.

; function

1 0 1 2 3

0 1 4 9

16. 1 17. 3 18. 2 19. 10 3 7

Guided Problem Solving 2-1 1. The radius. 2. 10.5 cm 3. v(r) = 4/3pr3 4. 10.5 or 10.5 cm 5. cm3 6. about 4849 cm3 7. 4849 = 43pr3; r 10.5 8. v(s) = s3; 1520.875 cm3

2 1 1 9. y 2 1 5 2 13 (x 2 0) 10. y 2 3 5 2 2 ax 2 2 b 11. y 1 2 5 2(x 1 3)

12.

x

O

2

1. 2 2. 5 3. 23 4. 2 21 5. 32 6. 2 7. 31 8. 2 72 5

y

2

2

Practice 2-2

x

O

1

5

Chapter 2 Practice 2-1

2

11. not a function 12. function 13. not a function 14. ; not a function

1. multiplicative inverse 2. solution 3. algebraic expression 4. additive inverse 5. theoretical probability 6–8. Answers may vary. Samples given. 6. The of a number is the distance between that number and zero on a number line.

O 2

1F: Vocabulary Review

7. The additive inverse of a number is its . 8. The is the multiplicative inverse of a number.

; domain: {0.5}; range: {-1, 0, 1, 3}

y


1E: Vocabulary Check

2

13.

y

y O

4

x 2

4

2 2

9.

; domain: {-1, 2, 3}; range: {2}

y 2 x 2

O

2

x O

2

14.

4

4 6

y

2

2 x 2

O

2

2

78

Algebra 2

All-In-One Answers




(continued)

15. 4x + y = 10 16. 2x - 5y = -17 17. y = -4


18. 3 ; (0, -3); (4, 0) 19. 0; (0, -2); none

1. 392 mi 2. 14 gallons 3. k = 28 4. y = 28x 5. 103.6 mi 6. 417.9 gallons 7. $0.056 8a. y = 28x; 392 = 28 3 14 mi 8b. 103.6 = 28x; x = 3.7 8c. y = 28 3 417.9; y ≈ 11,700 9a. y = 58x 9b. 145 mi 9c. 75 gallons

4

20. 4 ; (0, 7); a2 35 , 0b 21. undefined; none; (5, 0) 4

5

22. y = 2x + 5;

23. y 5 53 x 2 43 ;

y

y

2

Practice 2-4

2 x

2

O

x 2

2


2

O

2

2

24. x = -3;

9 8 7 6 5 4 3 2 1

25. y = 1; y

y

2

2 x

2

1. y = 0.6x - 2.1 2. y = -2.04x + 7.548 3. y = 1.2x + 200; $214.40 4. y = 58x; 464 words 5. y = 146x + 5000; 6460 subscribers 6. 10 ;

O

x 2

2

O

2

2

y

x

O

2

1 2 3 4 5 6 7 8 9 10

yes; using (3, 3.1) and (7, 5.2): y = 0.525x + 1.525 7. 10 ; no 9 8 7 6 5 4 3 2 1

Guided Problem Solving 2-2 1. a 32, 212 b , a223, 13 b 2. The slope of the line through the points 3. slope = (x2 2 x1) 4. a223, 13 b 2 1 © Pearson Education, Inc., publishing as Pearson Prentice Hall.

(y 2 y )

1 2 (21)

5. slope = 3 2 32 23 2 2

5 7. 2 5 8. 3 6. 2 13 13

O

y

x 1 2 3 4 5 6 7 8 9 10

8.

Practice 2-3

4

9 1. 2 32 ; 2 2 2. 6; 18 3. 9 ; 27 4. yes; 4 5. yes; -1.2

2

9

16 16

6. yes; -4 7. no 8. yes; 3 9. no 10. yes; 3 11. no 5

x 2

O

12. no 13. yes; 3; y = 3x 14. yes; 21 ; y 5 12 x 15. no

2

16. y 5 13 x 17. y = -6x 18. y = -18x 19. y 5 3 x 7

4

20. y 5 23 x 21. y 5 2 35 x 22. y 5 52 x 23. y = 55x 6 24. 10 25. 2 16 26. 11 27. 5 3 3

34

29. 46.08 in.

28. y = 0.06x; 22 min

2

yes; using (-1, -1.8) and (1, 1.9): y = 1.85x + 0.05 9. ; no y 6 5 4 3 2 1 x O

All-In-One Answers

;

y

1

2

3

Algebra 2

79

Algebra 2: All-In-One Answers 10a.

(continued) 11.

y

20 18 16 14 12 10 8

12.

y 4

2

O

y

6

x 2

4

2 2 4

x O

x

13.

10b. using (9.4, 11.2) and (15.1, 19.1): y = 1.39x - 1.83 10c. about 15.5% 10d. yes

14.

y

2 4

x

2 O 2

x

1. Equation 2. Yes 3. y

y

2

2


6

O

2

4

4

40 Fat (g)

15.

16.

y

30

x

4

20

y 4

2

10

x

x O

200 300 400 500 600 700 Calories

17.

4. slope = 0.076 5. y = 0.076x - 10.04 6. about 15 g 7. Yes, it is a good fit. 8. about 606 Calories

O

18.

y

4

x 2 x 2

O

y 4

2

O

2

20.

2

4

O

10.

y

4

x 2

y

21.

2 x x 4

2

O

4

2

O 2

O

2

2

4

4 2

2

2

2

9.

2

y

x

x

O 2

6

y

2

x 4

4

19.

2 2

y 2

2

1. E 2. C 3. A 4. F 5. B 6. D 7. 8. y

O

4

2

4

Practice 2-5

2

2

2 2

O

y x O

2

4

2 4

80

Algebra 2


8 10 12 14 16 18 20

4

All-In-One Answers


O

2


(continued) 3. vertical;

Guided Problem Solving 2-5 1. Graph the two equations. 2. Compare the graphs. Look for similarities and differences. 3a. y 2 3 5 P 12x 2 6 P

O

2

2

x

2

1x 2 6 5 2(y 2 3) 2

2

O

2

2

4

5.–6.

y 6 2 12 8


y x

2

3b. 2y 2 3 5 P 12x 1 6 P 4. 12x 2 6 5 y 2 3,

4

2

5. combined;

6. horizontal;

y

O 4

8

x 12

y

4

4

2

2

6

x O

1 x 1 6 5 –y – 3, 1x 1 6 5 y 1 3 2 2

different vertices, and one points up while the other points down. 8. Test points should result in true statements. 9. y 5 4 3 2 1 x 54321 1 2 3 4 5 1 2 3 4 5

2

4

11. y = ∆x + 3« - 2 12. y 5 2u x u 1 3

5

13. y 15. y 17. y 19. y 21. y

= ∆x« - 3 14. y = ∆x - 1« = ∆x + 2« + 1 16. y = -∆x« + 2 = -∆x + 2« 18. y = -∆x - 1« - 2 = 3∆x« - 4 20. y =

1 ∆x - 2« 2

= 2∆x + 3« - 1

22.

y 2 x 2

O

2

2

Practice 2-6 1. horizontal;

2. horizontal; y

23.

y

4

4

2

2

O

All-In-One Answers

x

4

2

O

y 2 x

x 2

O

4

9. y = -∆x - 1« + 3 10. y 5 2` x 2 12 ` 2 23

The graphs have the same size and shape. They have different vertices, and one points up while the other points down.

4

2

x

7. y = ∆x + 2« + 1 8. y = ∆x - 4«

7. The graphs have the same size and shape. They have


4. combined; y

2

O

2

2

Algebra 2

81

17.

y

18.

y 2

2

2 x

x 2

y

O

2

2

O

x 2

2

2

2

19.


2

2

20.

y

y 2

2

1. A translation shifts a graph horizontally, vertically, or both. 2. years 3. x-axis 4. horizontal 5. left 6. horizontal 7. The graphs and answers agree. 8. Vertical; the graph is

O

x

x 2

shifted up

O

2

2

O

2

2

2

Practice 2-7 1. y x - 2 2. x - 2y 4 3. y - 2x 4 4. y -2 5. x 2 6. -2x - 3y 6 7. 3x - y 3 8. y - 3x 3 9. 10. y y 2

21.

2

2

2

O

O

x 2

2

2

x

2

2 x

2

O

y

2

x 2

22.

y

2

2

12.

y

23.

24.

y

y 2

y

2

2

2

2

2

2

2

O

2

2

2

14.

y

25.

26.

y

y 2

y

x

2 2

2 x 2

O 2

2

x

x 2

2

O 2

27.

O

28.

y

16.

y

y

x O

x 2

2

82

Algebra 2

2

x 2

O 2

2

2

y

2 O

O 2

2

2

15.

2

2

4

13.

O 2

2

x O

x

x

x O

2

2

2

11.

O

2

2

x 2

O

2

2

2

29a. x + y 150, where x represents the number of tuna sandwiches and y represents the number of ham sandwiches

All-In-One Answers


24.

(continued)




(continued)

29b. 200 y

2D: Visual Vocabulary Practice 1. Constant of variation 2. Slope 3. Scatter plot 4. Translation 5. Standard form of a linear equation 6. Absolute value function 7. Trend line 8. Slope-intercept form 9. Point-slope form

150 100 50 x O

50

100 150 200

29c. Yes; the sum of 90 and 80 is more than 150. 30a. 150x + 200y 1800, where x represents the number of $150 models and y represents the number of $200 models


30b. 16 y 12 8

2E: Vocabulary Check Relation: A set of pairs of input and output values. Domain: The set of all inputs, or x-coordinates, of the ordered pairs of a relation. Range: The set of all outputs, or y-coordinates, of the ordered pairs of a relation. Function: A relation in which each element of the domain is paired with exactly one element of the range. x-intercept: The point at which a line crosses the x-axis (or the x-coordinate of that point).

2F: Vocabulary Review Puzzle

4

1

x O

4

8

12

16

30c. at least four $150 models


4

T

R

2

D

R

O

E

M

L

A

N

5

S

L

A

I

L

T

N

O

I

P

O

E

N


1. Functions, Equations, and Graphs 2. Answers may vary. Sample: linear equations, direct variation, absolute value functions and graphs, two-variable inequalities 3. Check students’ work.

2B: Reading Comprehension 1. graph paper, pencil, a ruler, and colored pencils or pens 2. plot; make; classify 3. points plotted on the same graph as the line 4. three lists of points; one for above, one for on, and one for below the line 5. a phrase that is one of the 3 choices: on the line, above the line, and below the line. 6. Step IV asks about the equation while Step III asks about an inequality.

2C: Reading/Writing Math Symbols 1. The theoretical probability of 3 occurring is 1 in 6. 2. the theoretical probability of not taking Spanish 3. a function f of x 4. f of 5, or the value of function f when 5 is the value of the variable 5. The function A (or

F U

T

O

I

N C T

6

L

I

N

E

G

E

A

R

O 7

1. dashed 2. to the right or above 3. x = -3 4. not part 5. > 6. x -3 7. 0 -3; Yes 8. x 2


3

R

A

N

Chapter 3 Practice 3-1 1. Independent 2. Inconsistent 3. Dependent 4. Independent 5. Dependent 6. Independent 7. Independent 8. Inconsistent 9. Independent 10. Inconsistent 11. Independent 12. Dependent 13a. Income: y = 2000x - 500, where x = 1 represents May; Expenses: y = -2600x + 24000, where x = 1 represents May 13b. October (the sixth month) 14. (6, 4) 15. (5, 2) 16. (12, 1) 17. (2, 1) 18. (1, -2) 19. (2, 3) 20. (-4, 0) 21. (-1, 3) 22. a 23 , 24b 23. (-8, -1) 24. (2, 2) 25. (5, 1)

Guided Problem Solving 3-1 1. 6; 80 2. 4; 100 3. The number of flyers addressed after x minutes 4. y = 6x + 80 5. y = 4x + 100

Area) of s (or the side of a square) is equal to s2 (or the z length of the side squared). 6. x2 2 0 7. z : 7 or 7 4 5 x or 4 : 10 = x : 18 10. g(7) 8. P(red) 9. 10 18

All-In-One Answers

Algebra 2

83

Algebra 2: All-In-One Answers 6. 140

(continued)

Practice 3-3

y

1.

120 100

642 2 4 6

80

2.

y

6 4

6 4 x

O

6

4 6

2 2 4 6

y x O 2 4 6

60

20

4

O

x

O 642 2

x 2 4 6 8 1012

4.

y

2 4

y 8 6 4 2O x 642 2 4 6 4

7. (10, 140) 8. 10 minutes 9. Yes; y = 6(10) + 80 = 140 and y = 4(10) + 100 = 140

5.

10. y = 3x + 5; y = 2x + 20; 80 70 60 50 40 30 20 10

y

6.

y

After 15 minutes, the numbers of newspapers is the same at 50.

6 4

2 O

2

2

x 5

10

15

7.

6 4

20

Practice 3-2

x

O 42 2

1. (6, 4) 2. (4, 1) 3. (5, 2) 4. (1, 2) 5. (4, 3) 6. a5, 2 1 b

8.

y

8

2 4

y x

O 42 2 4 6

x 2


8

8

4

y 6 4 2O x 42 2 4 6 8 2

5

7. (1, 1) 8. (2, -2) 9. (5, -2) 10. C = 525 + 150p; I = 325p; three performances 11. (2, 3) 12. (4, 6) 13. (0, 3) 14. (-3, 5) 15. (4, 1) 16. (6, 3) 17. (2, -2) 18. (3, 0) 19. (-4, -4) 20. 8r + 1g = 4.60,

6

6

9.

6r + 3g = 4.80, where r represents number of oranges and g represents number of grapefruits; oranges = $.50, grapefruits = $.60 21. (1, 4) 22. (-2, 3) 23. (0, 3) 24. (1, -2) 25. e (x, y): y 5 2 15 x 1 15 f 26. (-4, 5)

10. y

y 2

2 x

2

O

x O

2

2

4

6

2

27. (-3, 2) 28. No solution 29. (2.25, 0)

Guided Problem Solving 3-2 1. $40,000 plus $2800 per performance 2. $3675 3. y = 40,000 + 2800x 4. y = 3675x 5. 40,000 + 2800x = 3675x 6. x ≈ 45.7 7. 46 performances 8. Yes; y = 40,000 + 2800(46) = 168,800, y = 3675(46) = 169,050 9. 612 trips

11.

12.

y

2

2 x 2

O 2

y

2

O

x 2

2 4 6

84

Algebra 2

All-In-One Answers


3. 40


(continued)

x1y$6 2x 1 5y # 20 13a. µ , x$0 y$0 where x represents number of spiral notebooks and y represents number of three-ring notebooks 13b. y

19.

20.

y

6 4

6 4 x

O 642 4 6

4

21.

y

x O

4

22.

x O 2 4 6

y 2

2

4


642 2 4 6

2 4 6

y

x 6

Solutions correspond to points in shaded region with integer coordinates. x 1 y # 30 14a. • x $ 10 , y$5 where x represents number of campers on the low trail and y represents number of campers on the high trail 14b. y

4

2

x 2

O 2

23.

O

2

2

y 2 x 4

2

O 2

40 20 O

20


x

40

1. 7, 8, 9, 10 2. more (or greater) 3. j 0; s 0; s j;


j + s 7; j + s 10 Solutions correspond to points in shaded region with integer coordinates.

15.

6

16.

y

4. s

y 4

O 642 2

x

x

4 6

4

3 1

18.

y

6

O

y

4 O 642 2

5

4

4

6 17.

O

x 2 4 6

O 642 4 6

x 2 4 6

1

3

5

j

5. (1, 6), (1, 7), (1, 8), (1, 9), (2, 5), (2, 6), (2, 7), (2, 8), (3, 4), (3, 5), (3, 6), (3, 7), (4, 5), (4, 6) 6. Yes, substituting each combination listed in (8) into the inequalities of the system results in a true statement. 7a. x 0; y 0; x + y 5; x + y 8; x y or y x 7b. y (3, 2), (4, 1), (4, 2), (4, 3), 8 (5, 0), (5, 1), (5, 2), (5, 3), 7 (6, 0), (6, 1), (6, 2), (7, 0), 6 (7, 1), (8, 0) 5 4 3 2 1

x 1 2 3 4 5 6 7 8

All-In-One Answers

Algebra 2

85


6.

Practice 3-4 ; (2, 1)

y

(2, 2)

2 O 1 2.

(4, 1) (2, 1) 3 4 5 6

x ; (0, 4)

y 7 6 5 (0, 4) (2, 3) 3

Guided Problem Solving 3-4 1. corn muffins: 4 c; bran muffins: 2 c; baker has 16 c 2. corn muffins: 3 c; bran muffins: 3 c; baker has 15 c 3. P = 3c + 2b 4. c 0, b 0, 4c + 2b 16 (milk), 3c + 3b 15 (flour) 5. y

2 1 O (5, 0) x 1 2 3 4 5 3.

b

; (5, 0) y 7 (0, 6) 6 5 4 3 (4, 2) 2 1 O (5, 0)x 1 2 3 4 6 7

4.

7 6 5

7. (0, 10); 30 8. (4, 0); 4 9. (8, 8); 32 10a. Four loaves of Irish soda bread and two Kugelhopf cakes 10b. $14 11a. 10 qt regular, 4 qt extra-rich 11b. $132

; (2, 0)

y

(0,5) (3,2)

(0,0)

(4,0)

c

(0, 0), (0, 5), (4, 0), (3, 2) 6. At (0, 0), P = 0; At (0, 5), P = 10; At (4, 0), P = 12, At (3, 2), P = 13 maximized at (3, 2) 7. 3 trays of cranberry muffins and 2 trays of bran muffins 8. Yes, other points in the feasible region result in P 13. 9. 40 Q, 60 R

Practice 3-5 3 (0, 2) 6 ,6 1 O 5 5(2, 0) x 1 2 3 5 6 7

( )

5.

; (1, 0)

y 3 2

(0, 1) 2 ,2 3 3 (1, 0) O 1 2 3

1. From the origin, move forward three units. 2. From the origin, move right two units. 3. From the origin, move forward three units, left two units, and down 4 units. 4. From the origin, move back six units, left four units, and down one unit. 5. From the origin, move up four units. 6. From the origin, move forward one unit, right two units, and up three units. 7. From the origin, move forward three units, left one unit, and up six units. 8. From the origin, move right four units, and down one unit.

( )

86

Algebra 2


7 6 5 4

; (0, 0) y 7 6 (0, 5) 5 (1, 4) 4 3 2 1 O (2, 0) x 1 3 4 5 6 7

x

All-In-One Answers


1.

(continued)

Algebra 2: All-In-One Answers 9.

(continued) 13.

z

z

5

5 5

5

5 5 y

5

5 x

5 y 5 x

5

5

10.

14.

z

z 5


5

5

5 5

5

5 y

5 y 5 x

5 x

5

5 11.

15.

z

z


5

5 5

5

5 5 y

5

5 x

5 y 5

x 5

12.

5 16.

z

z 5

5

5

5 5

5 y 5 x

5

5 y x

5

All-In-One Answers

5

Algebra 2

87


(continued)

17. (0, 0, 0) 18. (0, 0, 1) 19. (0, 2, 0) 20. (3, 0, 0) 21. (0, 4, -2) 22. (0, -2, 3) 23. (-5, 0, 3) 24. (1, -1, -3) 25. z

28.

z 5

5

5 5 5

5

5 y 5 x

5 y

5

x

z

29.

5

26.

5

z 5 5 5

5 y


5

5 x 5

5 y 5 x

30.

z 5 5

27.

z 5

5 5

5

5 y 5 x 5

5 y 5 x

31.

z

5

10 10 10

10 y 10 x 10

88

Algebra 2

All-In-One Answers


5


(continued) 36. x + 2y = 6, x + 3z = 6, 2y + 3z = 6;

z

z

5 5

5 5

5

5 y 5 x

5

5 y 5 x

5 33.

5

z

37. x + 3y = 6, x + 2z = 6, 3y + 2z = 6;


5

z 5

5 5

5

y 5 x

5 5

5

x

34.

5

z

38. 2x + 3y = 6, 2x + z = 6, 3y + z = 6;

3 © Pearson Education, Inc., publishing as Pearson Prentice Hall.

5 y

4

z 5

y

6

5 x

6

5

35. x + y = 3, x + z = 3, y + z = 3; z 5

5 y 5 x 5

5 5

5 y 5 x 5

All-In-One Answers

Algebra 2

89

Algebra 2: All-In-One Answers 39. -4x + 2y = 8, -4x - 4z = 8, 2y - 4z = 8;

(continued) 42. 7x - 3y = 21, 7x + 7z = 21, -3y + 7z = 21;

z

z

5

5 5

5

5

5

y

5 y

5

5 x

5 x 5

40. 4x - 2y = 12, 4x + 6z = 12, -2y + 6z = 12;

43. 4x - 3y = -12, 4x + 6z = -12, -3y + 6z = -12;

z

z 5

5

5

5 5

5 y

5 5 x


5

5 y 5 x 5

Guided Problem Solving 3-5 1. y and z 2. x and z 3. x and y 4. x-intercept: (6, 0, 0); y-intercept: (0, 6, 0); z-intercept: (0, 0, -3) 5. x + y = 6 6. x - 2z = 6 7. y - 2z = 6 8. z

z 5

6y

5

6

3

x

5

5 y 5 x

9. The results are the same. 10. z

xy-trace: 4x + 9y = -36; xz-trace: 4x - 9z = -36; yz-trace: 9y - 9z = -36

5 y x

90

Algebra 2

All-In-One Answers


41. 6x - 3y = 6, 6x + z = 6, -3y + z = 6;


(continued)

Practice 3-6


1. No unique solution 2. (4, 0, -1) 3. (3, 3, 3) 4. No solution 5. (-1, 1, -1) 6. (4, 1, 3) 7. (5, -1, -2) 8. (-3, -2, -1) 9. (2, -2, 2) 10. (2, -1, -3) 11. (-2, 0, 5) 12. (4, -1, -2) 13. (1, 1, 2) 14. (3, 1, -6)

Linear system: This is a set of two or more linear equations that use the same variables. Dependent system: This is a system that does not have a unique solution. Linear programming: A technique that identifies the minimum or maximum value of some quantity. This quantity is modeled with an objective function. Limits on the variables in the objective function are constraints, written as linear inequalities. Objective function: In linear programming, this is a model of the quantity that you want to make as larger or as small as possible. Trace: This is a set of ordered pairs that results from substituting 0 for one of the variables in the equation of a plane.

15. a21, 4, 1 b 16. a 2 , 2 1 , 1 1 b 17. (-2, -1, -2) 2

3

2

2

18. (-1, -3, -4) 19. (0, 5, 0) 20. (8, -1, -2) 21. (1, 2, 3) 22. (2, -3, -2) 23. No unique solution 24. (1, 1, 1)


25. µ

x 1 y 1 z 5 22 3x 1 2y 1 z 5 9

, 1 y 2 z 5 10 2 where x represents the first number, y represents the second number, and z represents the third number; 3, 5, -10 x 1 5y 1 10z 5 96 26. • x 1 1 5 y 1 z , x 1 y 1 z 5 23 where x represents the number of $1 bills, y represents the number of $5 bills, and z represents the number of $10 bills; Eleven $1 bills, seven $5 bills, five $10 bills

Guided Problem Solving 3-6 1. weight of tail, weight of head, and weight of body 2. 9 lb 3. t = 9 4. h = t + 12b 5. b = h + t 6. (h, b, t) = (27, 36, 9) 7. 72 lb (27 + 36 + 9) 8. Yes, the


three weights satisfy each of the statements in the original problem. 9. 11 hours (mathematics 1 hr, history report 4 hr, speech 6 hr)

3A: Graphic Organizer 1. Linear Systems 2. Answers may vary. Sample: graphing systems of equations, solving systems algebraically, systems of inequalities, graphs in three dimensions 3. Check students’ work.

3B: Reading Comprehension 1. alphabetical order 2. where to find the word in the text 3. It repeats the word being defined. 4. an example of what is being defined 5. See if it is defined in the glossary. If not, look it up in a dictionary. 6. a

3C: Reading/Writing Math Symbols 1. The most commonly used letter is f, but accept all reasonable responses. 2. The most commonly used letters are x and y, but accept all reasonable responses. 3. m 4. w 5. l 6. the measure of angle A, usually in degrees 7. P(7)

3D: Visual Vocabulary Practice/High-Use Academic Words

3F: Vocabulary Review Puzzle 1. consistent 2. dependent 3. equivalent 4. inconsistent 5. independent 6. three E T D E P E N D E N T T

E D N E P E P P E N N S

O R D E R E D T E E C T

E E R H T C E D T H Q N

I R D N F S N S R T E I

H S E P I E I H A R S A

I Q D N P S O S E E N R

P E I E N A D O N D H T

A N D O P A L N I O E S

D N C N O Q E D L R C N

I N E L B I S A E F P O

I E Q U I V A L E N T C

Chapter 4 Practice 4-1 1. 3 1; -3 2. 3 4; 5 3. 2 3; 12 4. 3 3; q 5. 3 2; 4 6. 1 4; -4 7. c

17.6 8.3 5.4 8.7 4.0 6.6 3.5 d 9.5 5.1 4.5 6.4 2.6 5.1 2.7 8. 2 7 9. 9.5; percent unemployment in construction in June, 1996 10. 6.6; percent unemployment in services in June, 1992 11. Answers may vary. 3900 3300 Sample: M 5 £ 400 150 § 12. 3 2 100 50 13. number of days lost to strikes per 1,000 employees in Greece in the given years 14. number of days lost to strikes per 1,000 employees in the United States from 1990 to 1994

1. Define 2. Evaluate 3. Approximate 4. Interpret 5. Model 6. Set 7. Compare 8. Property 9. Test

All-In-One Answers

Algebra 2

91


(continued)



1. table 2. matrix 3. weeks 4. Estimates may vary. Sample:

1. 2, 3 2. 2

Types of CD Rock R&B Rap Classical

Wk 1 165 100 96 98

Wk2 150 94 90 97

Wk3 200 110 110 97

Wk4 180 98 100 102

Plastic Rubber 500 700 ; R B 3– color 1300 1900

3. Plant 1: 1– color

Plastic Rubber Plant 2: 1– color 400 1200 R B 1600 3– color 600

5.

Vanilla Chocolate Strawberry

8b.

Day 1 50 175 25

Day 2 75 125 50

Day 3 25 150 25

Day 1 Day 2 Day 3 Vanilla 50 75 25 Chocolate C175 125 150S Strawberry 25 50 25

Columns represent the days of Labor Day Weekend and rows are the flavors of ice cream.

Practice 4-2 1. a = 5; b 5 2 7 ; c = 12; d = 7 2. c 5 5 ; y = -7; 2 3 x = 4; z 5 7 ; a = -3; b = 0 3. x = 3; z = -2 2 37 56 23 58 0 76 93 82 4. M 5 ≥ ¥;F 5 ≥ ¥ 87 102 0 34 6 27 18 29 14 22 293 26 22 3 ¥ 6. c d 5. M 2 F 5 ≥ 87 68 2 0 212 22 8 25 26 22 2 27 12 § 8. £ 26 5 § 9. £ 24 § 7. £ 3 28 4 212 218 24 22 23 8 11 227 101 22 21 24 d 10. £ 13 14 § 11. £ 219 93 21 § 12. c 0 4 4 11 28 21 20

13. c

0 24 3 d 14. not equal; dimensions are different 24 22 5

Plastic Rubber Plant 2: 1– color 1200 3600 R B 3– color 1800 4800

5. c


8a. Flavor

Plastic Rubber 4. Plant 1: 1– color 1000 1400 ; R B 3– color 2600 3800

2200 22200 d 800 21000

6. Plant 1; 800 7. Plant 2; 2200 8. The answers check. Big

Small 270 ; R B 60 108

9a. Carrier A: Envelopes 120 Boxes

Big Small Carrier B: Envelopes 160 300 R B 25 100 Boxes

9b. c

240 230 d ; B; A 35 8

Practice 4-3

1. product undefined 2. c

6 22 4 d 3. c 6 0 23 4 21 1 4. difference undefined 5. c d 6. c 3 1 3

1 d 7 21 d 22

0 2 7. product undefined 8. £ 22 1 § 9. product undefined 21 0 16 3 23 21 10. c d 11. c d 2 22 4 20

12. product undefined 13. c

7 3 2 0 d 14. c d 0 2 0 2 0 0.4

15. product undefined 16. £ 20.4 0.2 § 20.2

17. ≥

3 23 21 4 4 4 1 21 2 2

1

¥ 18. c

0

0.5 20.5 22.5 d 2.5 22.5 25.5

15. equal; dimensions and corresponding elements are equal

92

Algebra 2

All-In-One Answers


Week 1 Week 2 Week 3 Week 4 Rock 165 150 200 180 R&B 100 94 110 98 T D Rap 96 90 110 100 Classical 98 97 97 102 6. Columns represent the weeks in August and rows are the type of CDs sold. 7. The new bar graph should be the same as the one given.


(continued) 12.

19. product undefined 20. product undefined

72 4 5 23. 2 3 2; c d 24. £ 60 5 4 0 213 19 28 25. £ 224 42 214 § 26. 25 8 23


y

6

4 x

x 6

24 72 § 212

O

6

4

6

11 10 21 1 1 c d 27. £ 11 10 § 26 5 5 11 10

23 8 14 14 12 51 24 28. £ 16 8 8 10 § 29. c d 30. D T 117 55 5 22 18 18 20 14 3 2 2 31. C 20 S 4 3

O

4

4

14.

15.

y

y

4

4 x

4

8 3

x 4

4

O 4

16.

O

4

4

y 4 x 4

Guided Problem Solving 4-3 150 130 160 5. £ 125 130 175 § 6. 3 3 7. 1 3 60 52 80 Thurs Fri Sat 8. Revenue [2100 1950 2570] 9. The answers check. Cost

10. Summer 1,270,000 Winter

B

R 1,010,000

Practice 4-4 1. c

44 44 233 5 5 22 d d 2. c 22 222 0 6 2 4 6 6 24.5 6 6 21 d d 4. c 3. c 3 23 0 24 28 26 2 22 0 2 22 0 5. c d 6. c d 4 4 23 24 24 3 22 2 0 3 3 24 1 1 26 7. c d 8. c d 9. c d 4 4 23 0 24 22 3 21 1 2 2 21.5 4 4 23 10. c d 11. c d 1 21 0 22 2 0

4

17. 17 c

21 0 214 0 3 0 d 5 c 214 27 0 7 22 21 2 0 22 0 0 0 18. c d 1 c d 5 0 22 0 22 22 22 0 21 2 0 22 0 2 19. c dc d 5 c 21 0 0 22 0 22 0

22 0 d 0 1 2 0 22 c d 22 24 22 0 d 2

Guided Problem Solving 4-4 1. 5 2. 1 3. subtract 5 from each x-coordinate 4. add 1 to each y-coordinate 5. c

25 25 25 25 28 28 23 23 d 6. c d 1 1 1 1 21 23 21 23 7. Yes, the graphs the answers.

8. c

All-In-One Answers

O 4

1. no 2. yes 3. [7 6 5] 4. 1 3


13.

y

1 2 3 4 71 34 21. 3 3 4; £ 2 4 6 8 § 22. 2 3 2; c d 49 56 3 6 9 12

7 2 8 d 26 28 0

Algebra 2

93


(continued)

Practice 4-5


2

0 1 21 3 ¥ 3. c d 4. c d 21 2 1 22 1 2

1 21 6 6 23 4 25 7 d 6. c d 7. ≥ ¥ 5. c 1 21 3 24 1 1 8 8 8. No inverse; the determinant of the matrix is zero. 22

2 3 22 10 5

1

§ 10. ≥ ¥ 9. £ 3 21 2 2 2 5 23 2

11. no inverse, cannot be solved 12. c d 13. c d 1 2

3 4 14. -1 15. -21 16. 14 17. -29 18. 9 19. 36 20. yes 21. yes 22. yes

a determinant.

3. (a1b2c3 + a2b3c1 + a3b1c2) - (a1b3c2 + a2b1c3 + a3b2c1) 4. -30 5. Yes, the determinant is the same. 6. 52

Practice 4-7 1. (0.251, 0.3, 0.07) 2. (0.7, -0.3, -0.2) 3. (1, 5, -5) 4. (2, 1) 5. (2, 1, -9) 6. (3, 2) 7. (-5, 15, 21) 8. (-1, 0) 9. (0, 6, 2.8) 10. (-2, -1) 11. (-1, 7, -3) 12. (4, 2, -8) coefficient

variable

constant

6 9 13. c d 4 13

x c d y

=

c

36 d 2

14. c

x c d y

=

c

29 d 24

3 24 d 0 7


4 0 21 x 9 15. £ 12 2 0§ £y§ = £ 17 § 1 21 12 z 3 x1 y 5 548,303 16. e ; 0.2553415x 1 0.1167209y 5 110,017 (331,975.0482, 216,327.9518); about 331,975 doctors

1. subtract c

17. e

2 7 d from both sides of the equation 23 4 4 7 4 25 dX 5 c d 4. 1 2. A-1 3. c 1 2 1 21 2 27 1 23 d 6. c d 5. c 21 4 0 1 7. Yes, the equation is true. 5 1 d 8. c 2 22

Practice 4-6 3 10 6 3 21 21 3 2§ 1. £ 21 25 23 § 2. £ 26 22 27 24 4 22 21 29 11 19 3. £ 1 21 22 § 4. no inverse 5 26 210 0.65 21.45 20.2 5. £ 20.8 1.4 0.4 § 6. no inverse 0.4 20.2 20.2

x1 y5 50 ; (20, 30); 425x 1 550y 5 25,000 20 one-bedroom and 30 two-bedroom apartments

3 , 233 b 19. a8, 4 b 20. no unique solution 18. a 17 3 17 21. (4, –32) 22. det A = 10, has a unique solution 23. det A = 0, no unique solution 24. det A = -5, has a unique solution

Guided Problem Solving 4-7 1. l = 2w 2. 840 ft 3. c

2 21 0 dX 5 c d 4. 6 2 2 840 1 3

1 6

5. C 1 1S 6. c d 280 23 3 140

7. width = 140 ft, length = 280 ft 8. The answers check. 9. 6 yards; 14 yards

Practice 4-8

9. £ 25 § 10. £ 1 § 11. no inverse, cannot be solved

4x 2 2y 5 3 12x 1 6y 5 24 2. e 6x 1 11y 5 9 2x 5 2 22x 1 9y 2 2z 5 20 3. • 3x 2 y 1 2z 5 29 4. (2, -3) 5. (6, 2) 6x 1 5y 1 5z 5 24 6. (-3, 2) 7. (0.9, 0.08, 0.3) 8. (0.25, 0.75, 0.5) 9. (3, 1, -2)

12. 39 13. -47 14. -7 15. 9 16. 26 17. -42 18. no 19. yes

10. c

20.6 0 20.2 20.4 20.4 20.1 7. £ 0 20.5 0 § 8. £ 0.2 0.5 0.2 § 20.4 0 0.2 20.1 0.2 20.1

94

4

23

3

22

Algebra 2


1. £ 1 § 2. ≥ 1 2 21

1. No, the determinant is a number. 2. Any square matrix has

1 2

1. e

23 4 28 1 3 230 ` d 11. c ` d 2 28 16 4 1 1

All-In-One Answers


1 2

1 1


(continued)

1 24 1 29 2 23 † 9 § 13. (-6, -8, 14) 14. (9, -3, -6) 4 0 2 24 15. (7, 1, 0) 16. (2, 6, -4) 17. (-1, 7, 0.5) 18. (-4, 3, 9) 19. (5, 8, -2) 20. (1, 7, -9) 21. (-2, 3, 5)

12. £ 3



1. 5 erasers and 2 pencils 2. 7 erasers and 5 pencils 3. 5e + 2p = 0.23; 7e + 5p = 0.41 5 2 0.23 2 5 0.23 ` 5 11 5. ` ` 5 0.33 6. ` ` 5 0.44 4. ` 0.41 5 7 0.41 7 5 7. e = 0.03, p = 0.04; one eraser is $0.03 and one pencil is $0.04 8. Yes, the prices match. 9. adult: $8; child: $5.50

4A: Graphic Organizer 1. Matrices 2. Answers may vary. Sample: organizing data into matrices, matrix multiplication, geometric transformations with matrices, inverse matrices and systems 3. Check students’ work.

4B: Reading Comprehension 1. They are to be taken together as a system. 2. 4 inequalities 3. 6 elements 4. 2 rows 5. 3 columns 6. 2 by 3 or 2 3 3 7. -1 8. b

4C: Reading/Writing Math Symbols


4 3 b 6. "a 1 b 1. exponent 2. base 3. amn 4. a3 5. " 7. a2 + b2

4D: Visual Vocabulary Practice 1. matrix 2. zero matrix 3. matrix addition 4. dilation 5. matrix multiplication 6. scalar multiplication 7. matrix element 8. matrix equation 9. rotation

4E: Vocabulary Check Square matrix: A matrix with equal numbers of columns and rows.

Determinant: A real number ad – bc of a 2 2 matrix c

a b d. c d

Coefficient matrix: When representing a system of equations with a matrix equation, this is the matrix containing the coefficients of the system. Variable matrix: When representing a system of equations with a matrix equation, this is the matrix containing the variables of the system. Constant matrix: When representing a system of equations with a matrix equation, this is the matrix containing the constants of the system.

All-In-One Answers

4F: Vocabulary Review 3 2 5 1. Answers may vary. Sample: £ 7 22 8 § 4 21 12 2. Answers may vary, but must have 3 rows and 2 columns. 3. 9 4. Answers may vary. 11 7 21 0 10 7 Sample: c d 1 c d 5 c d 26 21 2 5 24 4 5. Answers may vary, but the two must be identical in every way. 6. Answers may vary and can be of any dimensions, but every element is zero.

Chapter 5 Practice 5-1 1. ƒ(x) = x2 2. ƒ(x) = x2 + 4x + 8 3. ƒ(x) = -2x2 + 12 4. ƒ(x) = 2x2 - 1 5. ƒ(x) = x2 + 6x + 9 6. ƒ(x) = x2 - 4x + 7 7. (0, 1); x = 0 8. (3, 0); x = 3 9. (-1, -2); x = -1 10. quadratic; quad: x2; lin: 2x; const: -8 11. quadratic; quad: 3x2; lin: 15x; const: none 12. linear; quad: none; lin: -25x; const: none 13. linear; quad: none; lin: 22x; const: -14 14. quadratic; quad: 3x2; lin: -4x; const: 8 15. quadratic; quad: 3x2; lin: -6x; const: -7 16. quadratic; quad: 3x2; lin: none; const: -12 17. quadratic; quad: 2x2; lin: x; const: -6 18. linear; quad: none; lin: 3x; const: -5 19. P9(0, 4), Q9(3, 1) 20. P9(-2, -2), Q9(-5, -5) 21. P9(2, 2), Q9(-1, -1) 22a. h = -16t2 + 272t 22b. 372 feet

Guided Problem Solving 5-1 1. 1974 2. (0, 10), (4, 15), (7, 18), (9, 20), (14, 25), (21, 32), (27, 34), (28, 37) 3. y = -0.0112x2 + 1.24x + 9.97 4. Answers may vary. Sample: Domain: whole numbers from 0 to 50, Range: whole numbers from 0 to 44. 5. x = 18; year 1992 6. Answers may vary. Sample: The maximum value of the function is about (55, 44), so the first-class postage never reaches 50¢. The quadratic model is useful over a limited number of years, but because it increases and then decreases, it does not model the data after 2021. 7. The quadratic model is useful over a limited number of years, but because it increases and then decreases, it does not model the data after 2021. 8. The answers are verified by the graph. 9a. y = -0.016x2 + 3.99x - 41.94 9b. Answers may vary. Sample: Domain: real numbers from 0 to 100, Range: whole numbers from 0 to 200. 9c. 51 °F 9d. 118 °F; The sales may not follow this pattern when the temperature gets so hot people do not leave their airconditioned homes.

Algebra 2

95


6.

Practice 5-2 1.

2

(1 ,4)

4

O

4

7. ; min. (-1, -5)

y

x

x 2

y

O

2

2

O

2

4

4

( 1 , 92 )

(1,5) ; max. a 2 , 4 b 3 3

y

(

2

2,4 3 3

8.

O

2

)

O

2

8

9.

(1, 9) ; min. (2, -16)

y x O

2 2

2

16

4

(2, 16)

2 (2, 3)

5. 4

( 12 , 54 )

10.

6 5 4

; max. a2 1 , 5 b 2 4

y

2 1

2 x

2

O 2

321

2

12.

321 Algebra 2

11.

y

y

3

x

O 1 2 3

6 5 4 3 2 1

96

4

8

x

4

4

; min. (2, -3)

y

O

2

4

2

4.

; min. (1, -9)

y x

x 2

4

2

2

3.

; min. a1, 2 9 b 2


2.

(0, 3)

4

1O

1 1 2 3 4 5

13.

y

4 3 2 1 x

O 1 2 3

321 1 2

x 1

3

y

x

O 1 2 3

All-In-One Answers


2

O

4

x

2

2 x

2

; min. (0, -3)

y

2

; max. (1, 4)

y

6

(continued)


4 3 2 1


1 1 2

15.

y

6 4 O 8 42

x

O 1 2

4 5

29.

y

2

24.

x 3

27.

2 4 6 (0, 6) 8

10 1 2 5. y 5 2 x 1 10 6. Yes, the graph verifies the model. 10 7. y 5 2 1 x 2 1 40 250

c

y 4 2 O x 8642 2 4 2 4

x 1

(1, 7)

y x4 3 O x 3 3 6 9 12 15 3 6 9 12 15 (4, 16)

26.

y x 1 10 (1, 8) 6 4 2 O x 8642 2 4 2

28.

All-In-One Answers

x 4 6 x0

1. 10 ft 2. 10 ft 3. (0, 10), (10, 0) 4. a = 2 1 , c = 10

18. $3.25 19. 81.125 ft; 156.25 ft 20. 20 fixtures per day 21. 22. y y 6 1 Ox1 x (4, 4) 4 2 1 2 4 1 x O 2 2 4 6 8 10 3 4 4 (1, 4) 6 5 x4

25.

y 4 2 O


; $6

1 2 3 4 5 6 7 8

y 3 2 1 O x 5 3 1 1 1 2 (3, 2) 3

64

x

4 6

16. 1.2 s; 24 ft 17. p 2500 2000 1500 1000 500 O

23.


(continued)

Practice 5-3 1. y = x2 - 5 2. y = x2 + 2 3. y = (x - 2)2 4. y = -2x2 + 4 5. y = 2(x - 3)2 + 2 6. y = -2(x + 3)2 + 5 7. 8. y y 10 1O x 8 1 1 2 3 4 5 6 1 (6, 6) 4 x6 2 2O 3 x (2, 3) 4 2 2 4 6 8 10 2 5 x2 9.

8

y 6 3 x 129 3 O 6 3 6 9 12 (3, 13) x 3

11.

x 1

12.

y x 1 3 2 1O 4 2 (1, 1) 2 3

14.

x

y

x O 1 2

y 6 (2, 4) 4 x x 2 2 O 8642 2 4 2

x1 13.

4 3

4321 1 (1, 2)2

y 3 (1, 3) 2 1O x 21 3 4 1 1

y 4 (0, 3) x 0 2 1 O x 321 1 2 3 1 2

10.

y x1 4 3 2 1O x 21 3 4 1 (1, 1) 2

y x 6 8 6 4 2O x 8 42 2 2 (6, 2) 4

Algebra 2

97

15.

y 2 1O x 5 3 1 1 1 2 3 (3, 3) 4 x 3

16.

x 1 y 2O x 8642 2 2 (1, 5)

18.

17.

8 10

y

(continued)

x2

4 3 2 1O (2, 0) x 1 1 2 3 4 5 1

3 2

y x

O 21 1 2 3

1 2 3 4 (1, 2) x1

19. y = (x + 2)2 - 4 20. y = 2(x + 2)2 - 5 21. y = -2(x + 2)2 + 8 22. y = -(x - 2)2 + 8 2

23. y = (x - 2)2 - 8 24. y 5 ax 1 52 b 2 25 4 2

95 25. y = 2(x - 0)2 - 6 26. y 5 23ax 1 16 b 2 12 2

27. y 5 ax 1 72 b 2 45 28. y = (x + 4)2 - 13 4 2

29. y 5 2ax 1 32 b 1 11 30. y = (x + 2)2 - 7 2

28. (x + 4)(x + 1) 29. (x - 22)(x + 1) 30. (x + 5)(x + 8) 31. (2x + 1)(x - 3) 32. (x + 11)(x - 1) 33. (x - 12)(x - 2) 34. (x + 2)(5x - 6) 35. (x + 1)(2x - 7) 36. (x + 5)(2x + 3) 37. (x - 3)(3x + 2) 38. (x + 3)(3x + 7) 39. (x + 8)(x - 3) 40. (x + 36)(x - 2) 41. x(x - 11) 42. 3x(x + 7) 43. (x + 2)(x + 6) 44. (x - 6)(x - 4) 45. (x + 10)(x - 3) 46. (x - 14)(x + 12) 47. (x - 9)(x + 8) 48. (2x + 5)(2x - 5) 49. (x + 11)(x - 11) 50. (x + 16)(x + 1) 51. (5x - 1)(2x - 3) 52. (2x + 3)(2x + 3) 53. (2x - 5)(2x + 3) 54. (3x + 2)(3x - 2) 55. (x + 10)(x - 4) 56. 2(x + 2)(x - 2) 57. (x + 11)(x + 7) 58. 2(x + 7)(x - 7) 59. (x + 14)(x + 7) 60. (x + 6)(x + 14) 61. (3x + 2)(3x + 8) 62. (2x + 3)(4x - 9) 63. (x - 9)(x + 6) 64. (x + 13)(x - 13) 65. (5x + 3)(5x - 3) 66. 7(x2 + 7) 67. 2(x - 7)(x + 2) 68. (x + 6)(x + 2) 69. (x + 5)(x - 7) 70. (x + 9)(x - 7) 71. (5x + 1)(4x - 3) 72. (2x - 1)(6x + 5) 73. (4x + 3)(x - 2) 74. (4x - 3)(2x + 7) 75. 3(x + 7)(x - 8)



Guided Problem Solving 5-4 1. x + y 2. y 3. (x + y)2 4. y2 5. (x + y)2 - y2 6. x(x + 2y) 7. The expressions are correct. For example, 4(4 + 2 2) = 32 and 62- 22 = 32. 8. (x + y)2 - 4y2; (x - y)(x + 3y)

31. (2, -4); 8 32. (-6, 5); -7 33. (1, -1); 1

Practice 5-5

38. (-5, -3); -53 39. (-2, 5); -15

1. 20, -2 2. 0, 27 3. 0, 3 4. 7, -1 5. 7, -7 6. -1


7. 1, -1 8. 4, -1 9. -4, -5 10. -9, 216 11. 1, -11

1. price of a bagel in dollars 2. bakery’s daily profit in dollars 3. The domain is all nonnegative numbers. 4. x cannot be negative because that would mean the bakery pays people to take the bagels. 5. $277.50; $210.00 6. (0.55, 300) 7. $.55 8. $300 9. The graph verifies the answers. 10a. The domain is all nonnegative numbers. x cannot be negative because that would mean the theater pays people to see a movie. 10b. 140, 74.375 or about 74 10c. $6.50 10d. 150

Practice 5-4 1. (x + 2)2 2. (x - 5)(x - 2) 3. (x + 8)(x - 1) 4. x(x - 6) 5. (2x - 1)(x - 4) 6. (x + 7)(x - 5) 7. (x + 5)(x + 1) 8. (x + 3)(x - 3) 9. (x - 16)(x + 3) 10. (x + 2)(x - 2) 11. x(4x + 1) 12. (x - 25)(x - 4) 13. (x - 3)(x + 2) 14. (3x + 1)(3x - 1) 15. x(3x - 2) 16. (x + 8)(x - 8) 17. (x + 5)(x - 5) 18. (x + 9)(x - 9) 19. (x + 6)(x - 6) 20. (x + 10)(x - 10) 21. (x + 1)(x - 1) 22. (2x + 1)(2x - 1) 23. 4(x + 3)(x - 3) 24. (3x + 2)(3x - 2) 25. (x - 8)(x + 1) 26. (x + 9)(x + 4) 27. (x - 3)(x - 2)

98

Algebra 2

12. 0, 23 13. 2, 225 14. 1, 214 15. 1, 1 16. -1, 213

5 1 1 1 1 17. 2, 22 18. 2 , 3 19. -1, 2 20. -2, 31 21. 4, 2 22. -6, -1 23. 0, -3 24. 21 , 5 25. 2, 31 26. 12 , 1 27. 2, 232 28. 12, -12 29. 21 , 1 30. -1, 22 31. -1, 17 5 1 34. -1, 21 35. -9, -1 32. 1, 2 33. 1, 11 7 36. 6.24, -2.24 37. 7, 1 38. 4, -4 39. -2, -4 40. 3, 1 41. -2, 232 42. 12 , 32 43. 221 , 235 44. 1, 21 4 4 9

45. 212 , 21 46. -2, 241 5

47. 2, 23 48. -1, 254

1 49. -1, 219 50. -4, 212 51. -2, -1 52. -1, 11

53. 12 , 212 54. 0, 2 55. 3 , 23 56. 21 , -6 57. 12 , 14 5 5 58. -11, -1 59. 2, 61 60. 11, -11 61. 3, 241 62. 212 , 214 63. -8, -1 64. -2, -6 65. 4, -10 66. 2, -2 67. 3, -2

All-In-One Answers


34. (-4, -3); 23 35. (1, 2); 3 36. (2, 4); -8 37. (5, 1); 101 3


(continued)

68. 1.65, -3.65 69. 3.46, -3.46 70. 0.9, -2.23

18. y = -2(x - 1)2 + 5; (1, 5)

71. 3.87, -3.87 72. 9 , 2 9 73. -1, -4 74. -4, -9 75. 3, 2

19. y 5 ax 1 52 b 2 5; a252 , 25b

4

4

2

2

Guided Problem Solving 5-5 1. 24 ft by 16 ft 2. 384 ft2 3. 276 ft2 4. length: (2x + 24), width: (2x + 16) 5. (2x + 24)(2x + 16) - 384 = 276 6. x = -23 or x = 3 7. 3 ft 8. Yes, the area of the border is 276 ft2. 9. 5 ft


2

23. y 5 3ax 1 32 b 2 43 ; a232 , 234 b 24. 26 4 4"2 25. 12 4

Practice 5-6 1. 2i, -4 + 2i, 12 - 14i 2. 1 + i, 1 + 3i, -7 + 7i 3. -2 - 3i 4. 4 - i 5. -2i 6. 1 + i 7. 6i 8. -5 + 2i 9. 2 - 3i 10. -4 11. 2 12. 13 13. "2 14. "5 15. 5 16. "29 17. "13 18. "5 19. 3"2 20. 3 21. 2 22. "17 23. 3"5 24. "10 25. 4 26. 2"10 27. 2i"22 28. -6i 29. 2 30. 0 31. 4 - 5i 32. -5 - 3i 33. 26 34. 21 + 27i 35. 18 - 46i 36. -7 + 24i 37. 13 38. 8 39. -9 + 7i 40. -1 + 6i 41. 4i"3 42. 10i"3 43. 5i"3 44. 2 + 4i 45. 15 - 8i 46. 18 - 26i 47. 22 - 4i 48. 2 - 16i 49. 265 50. -2 + 8i 51. -5 + 16i 52. 169 53. 11 - 2i 54. 10 - 10i 55. -144 - 130i 56. 2i"11 57. 23i"7 58. 2i"2 59. -7 + 22i 60. 6 + 6i 61. 3 - 4i 62. 7 + 6i 63. 7 64. 5 + 12i 65. 2 + 8i 66. -3 + 14i 67. 26 68. 44i"5 69. 410i 70. 42i"5 71. 42i"3 © Pearson Education, Inc., publishing as Pearson Prentice Hall.

20. y 5 22ax 2 52 b 1 23 ; a 52 , 32 b 21. y = 6(x - 1)2 - 5; (1, -5) 22. y = -2(x - 2)2 - 1; (2, -1)

72. 45i 73. 46i"2 74. 420i 75. 4 12 i 76. 4i"5

77. 45i 78. 43i 79. 4i"10 x2 +

"5 "3 "10 i"14 27. 12 4 2 28. 1 4 2 29. 4 4 30. 1 4 2 5 5

31. 0, -11 32. 7, -2 33. 21 , -1 34. 232 4 35. 22 4

38. 1, -3 39. 27 4 42. 232 4

- 9i2

x2 -

9i2

1. Yes 2. 3. 3ix - 3ix or 4. x2 + 9 5. 25 6. ±5 7. Yes, - 5 and 5 check and are both solutions. 8. x = ±7

Practice 5-7 1. 9 2. 49 3. 36 4. 94 5. 16 6. 64 7. 441 8. 1 4 4 2 9. y = (x + 2) - 10; (-2, -10) 10. y = (x - 3)2 - 3; (3, -3) 11. y = 4(x + 1)2 - 8; (-1, -8) 2

12. y 5 4ax 1 12 b ; a212 , 0b 13. y = 2(x + 1)2 - 7; (-1, -7)

"23 2

"106 "5 36. 2 3 4 i"3 37. 241 4 4 2 2 2

"97 "37 40. 32 4 2 41. 1 4 i"2 2

"17 "41 3"5 43. 272 4 2 44. 238 4 8 2

"65 "19 45. 1 4 i"6 46. 54 4 4 47. 23 4 2 48. 0, 3 2

"11 49. 0, 8 50. 2 1 4 i"11 51. 212 4 2 4 4

52. 254 4 55. 67 4

"37 i"15 53. 256 4 6 54. 2, -1 4

"145 "17 "13 56. 232 4 2 57. 272 4 2 6

58. 0, 52 59. 0, -14 60. 21 4

Guided Problem Solving 5-6 a2 + b2

"21 26. 22 4 "3 2

62. 212 4

"14 61. 1, 254 2

"21 "17 63. 4, -1 64. 21 4 2 65. -1, 34 6

66. 2, -4 67. 3 1

5" 15 "13 68. 2 4 "5 69. 232 4 2 3

"41 "53 70. 2 3 4 i"15 71. 232 4 2 72. 272 4 2 2 2

73. 232 4

"29 74. 3 4 "7 2

Guided Problem Solving 5-7 1. height in feet 2. horizontal distance from the base of the left side of the arch in feet

3. 600

y

2

14. y 5 23 ax 1 32 b 1 31 ; a223 , 13 b 2

15. y 5 23ax 2 12 b 2 41 ; a 12 , 214 b 16. y = (x + 1)2; (-1, 0) 17. y = -5(x - 1)2 + 6; (1, 6)

All-In-One Answers

300

x O

300 500

Algebra 2

99


(continued)

4. (315, 630) 5. The domain is real numbers from 0 to 630 and the range is real numbers from 0 to 630. The distances and heights must be nonnegative real numbers. 6. 630 ft 2 (x 2 315) 2 1 630; Yes, 7. 630 ft 8. vertex form: y 5 2315 the answers .

9a.

Guided Problem Solving 5-8 1. the year 1985 2. the amount of carbon monoxide released in a year in millions of tons

3.

y 200

y 60

100

50 40 30

x

20 10

x 200

vertex (100, 50) 9b. 50 ft 9c. 200 ft

Practice 5-8 1. 200; 2 real 2. 60; 2 real 3. 576; 2 real 4. 0; 1 real 5. 9; 2 real 6. -7; 2 imaginary 7. -7; 2 imaginary 8. 61; 2 real 9. -31; 2 imaginary 10. 9; 2 real 11. 0; 1 real 12. -8; 2 imaginary 13. 225; 2 real 14. -44; 2 imaginary 23 4 i"31 15. 0; 1 real 16. -3 17. 7, 8 18. 23 , 1 19. 4 20. 32 , 4 21. 254 , 1 22. -3, -5 23. 5

24.

31.

23 4 2i"3 3

23 4 "3 29 4 "133 32. -10, -8 33. 34. 4 4 3i 2 2

35. -4, 34 36. 38.

21 4 i"2 3

21 4 i"79 3 4 "17 25. 6, -2 26. 27. 2, 12 8 2

28. 23 4 "13 29. 1 4 2i 30.

5 4 i"119 22 4 i"11 37. 3 6

3 4 i"47 21 4 i"59 39. 21 4 2i 40. 4 10 5

21 4 " 61 41. 10

30

40

50

1 4 i"34 42. 43. 1 4 i"2 5

3 4 i" 183 5 4 i"71 45. 46. -5, -1 47. 4, 2 4 8 48. 3 4 "3 49. No; When p = 4000, the discriminant is negative, so there are no real solutions. 50. 3, -1

44.

6 4 "15 ; 1.41, 0.30 7 25 4 3"5 54. ; 0.17, -1.17 55. -1, 21 56. 1 , 24 4 2 3 10

51. -1, -4 52. 4, -2 53.

y = 100 is when less than 100 million tons were released. 5. 0.0721x2 - 2.8867x + 117.061 < 100 6. Subtract 100 from each side. Then use the quadratic formula to solve. 7. Answers may vary. 8. The results are the same. 9a. Wherever y 5 22x2 1 100x 1 4000 is above y = 4500 is when profit was greater than $4500. 9b. Solve -2x2 + 100x + 4000 4500 by first subtracting 4500 from each side. Then use the quadratic formula to solve.

5A: Graphic Organizer 1. Quadratic Equations and Functions 2. Answers may vary. Sample: properties of parabolas, transforming parabolas, quadratic equations, completing the square 3. Check students’ work. Chapter: Quadratic Equations and Functions; Modeling Data with Quadratic Functions: using quadratic functions to model data; Properties of Parabolas: identifying properties of parabolas; Transforming Parabolas: translating parabolas in the coordinate plane; Factoring Quadratic Expressions: factoring quadratic expressions; Quadratic Equations: working with quadratic equations; Complex Numbers: defining and understanding complex numbers; Completing the Square: factoring quadratic expressions by completing the square; The Quadratic Formula: using the quadratic formula to solve quadratic equations

5B: Reading Comprehension 1. factoring 2. ax2 + bx + c = 0 where a 2 0 3. because you need factors that have product ac and sum b 4. (2x - 5) 5. Answers may vary. Sample: a(b + c) = ab + ac 6. Answers may vary. Sample: If two quantities have a product of zero, then one of them must be zero. 7. Answers may vary. Sample: The Zero-Product Property states that one quantity must be zero. This means that one solution or the other gives zero. “And” would mean both solutions satisfy the equation at the same time. 8. b.

57. -3, 2 58. 16, -3 59. 0, 252 60. 62.

23 4 "21 ; 0.79, -3.79 61. 2 4 "3; 3.73, 0.27 2 1 4 2" 2 ; 1.28, -0.61 63. 7, -5 64. -5, -2 3

100

Algebra 2


100

20

4. Wherever y = 0.0721x2 - 2.8867x + 117.061 is below

All-In-One Answers


10


(continued)



1. Answers may vary. Sample: (2, 3) means 2 units to the right along the x-axis and then 3 units up along the y-axis. (3, 2) means 3 units to the right along the x-axis and then 2 units up along the y-axis. The x distance is always listed first. y (2, 3) 2

(3, 2) x

2

O

2

2

1

V

E

R

2

T

E

X

N

O

3

R 4 5 6

F

B

P A

I

T

T

O

M

I

A

L

N

N C

S

R

D

R

M

A

I

A R

B

A

D

O

L


L

1 2 3 2. Answers may vary. Sample: c d is a 2 3 3 matrix 4 5 6 with 2 rows and 3 columns. 1 2 £ 3 4 § is a 3 3 2 matrix with 3 rows and 2 columns. 5 6 3. 12 4 3 means 12 divided by 3, which equals 4, while 3 4 12 means 3 divided by 12, which equals one-fourth. 4. 15 - 5 means to subtract 5 from 15 to get 10, while 5 - 15 means 5 minus 15, which is -10. 5. No; by the Symmetric Property of Equality, a = b means b = a.


5D: Visual Vocabulary Practice 1. absolute value of a complex number 2. parabola 3. difference of two squares 4. imaginary number 5. Quadratic Formula 6. vertex form of a quadratic function 7. standard form of a quadratic equation 8. complex number plane 9. perfect square trinomial

5E: Vocabulary Check Quadratic function: A function that can be written in the form f(x) 5 ax2 1 bx 1 c , where a 0. Its graph is a parabola. Axis of symmetry: The line that divides a parabola into two parts that are mirror images. Vertex of a parabola: The point at which the parabola intersects the axis of symmetry. Factoring: Rewriting an expression as the product of its factors. Greatest common factor (GCF) of an expression: The common factor of each term of the expression that has the greatest coefficient and the greatest exponent.

A

Chapter 6 Practice 6-1 1. y = -0.0439814815x3 + 0.6507936508x2 - 2.935185185x + 24.84126984; 21.098 2. y = 0.0130787037x3 -

0.1743055556x2 + 0.7951058201x + 3.125396825; 4.6362 3. 5x + 2; linear binomial 4. -3; constant monomial 5. 6x4 - 1; quartic binomial 6. 5s4 - 2s + 1; quartic trinomial 7. 2m2; quadratic monomial 8. -4x3 + x2 + 3x; cubic trinomial 9. 2x2 - 1; quadratic binomial 10. -3m3 + 5m2; cubic binomial 11. -7x2 + 5x; quadratic binomial 12. 3x3; cubic monomial 13. -x3 + 2; cubic binomial 14. -x; linear monomial 15. a5 + a4 + a3; quintic trinomial 16. x2 - 25; quadratic binomial 17. p2 - 5p + 6; quadratic trinomial 18. 9c4; quartic monomial 19. b - 3; linear binomial 20. 12x - 6; linear binomial 21. s2 1 32 ; quadratic binomial 22. 21 x4 1 x 2 54 ; quartic trinomial 23. 21 z5 1 1; quintic binomial 24. 3x + 5 units 3 25. 0.0008797x3 + 0.2229900x2 - 3.1465532x + 29.0544437; about $1203.18 26. 0.0000006x3 - 0.0005101x2 + 0.1270416x + 2.0612682; about 12 yr

Guided Problem Solving 6-1 1. h = 10 cm 2. They are the same. 3. pr2h 4. V 5 10pr2 5. 34pr3 6. V 5 23pr3 7. V 5 23pr3 1 10pr2 8. Answers may vary. 9. 12pr2 1 48r

Practice 6-2 1. 5, multiplicity 3 2. 0; 8, multiplicity 2 3. 2; -7, multiplicity 3 4. 0, multiplicity 2; 4, multiplicity 2 5. -3, 0, 3 6. 252 ; 3, multiplicity 2 7. y = 2x3 - x2 - 50x + 25

All-In-One Answers

Algebra 2

101

(continued)

8. y = -2x3 + 15x2 - 22x - 15 9. V = x3 + 54x2 + 936x + 5184 10. y = x3 - 6x2 + 5x + 12 11. y = x3 - 4x2 + 5x - 2 12. y = x4 - 2x3 - 15x2 13. y = x3 + 6x2 + 12x + 8 14. x3 - 2x2 + x 15. x3 + 7x2 + 15x + 9 16. 2x4 + 23x3 + 60x2 - 125x - 500 17. y = 2x(x + 2)(x + 3) 18. y = x2(x + 2)(x - 3) 19. y = -3x(x - 3)2 20. -1, 1, 3; y 2

Guided Problem Solving 6-3 1. x + 3 2. 3x3 1 10x2 2 x 2 12 3. 0 4. -3 5. 23k 3 10 21 212 6. 0 7. yes 3

(1, 0) x 2 (3, 0)

O

29 23 1 24

12 0

8. (x + 3)(3x2 + x - 4) + 0 = 3x3 + 10x2 - x - 12 9. 3(-3)3 + 10(-3)2 - (-3) - 12 = 0 10. no

2

Practice 6-4 21. -2, 3;

2 4

4. 2(x - 5)(x2 + 5x + 25); 5,

O

y (3, 0) x 2

25 4 5i"3 2

5. 4(x - 2)(x2 + 2x + 4); 2, 21 4 i"3 1 4 i"3 6. (3x + 1)(9x2 - 3x + 1); 213 , 6

6

22. -5, 0, 2;

7. (4x - 1)(16x2 + 4x + 1); 41 ,

y

8. (x - 3)(x2 + 3x + 9); 3,

10 (5, 0) (0, 0) 4 O

(2, 0) 4

x

23. rel. max.: 4.06; rel. min.: -8.21; zeros: 0, 2, 5 24. rel. max.: 16.9; rel. min.: -5.05; zeros: -3, 1, 3 25. x(x + 2)(x - 8) 26. x(x + 3)(x + 4) 27. x(x - 3)(x - 5) 28a. V = x2(20 - x) 28b. about 1185 in. 3

Guided Problem Solving 6-2 1. 4 ft 2. The volume will be twice as much. 3. x ft 4. 60 ft3 5. 120 ft3 6. V(x) 5 (x 1 5)(x 1 4)(x 1 3) 7. 1 8. 1 ft 9. Answers may vary. 10. 2 in.

Practice 6-3 1. yes 2. yes 3. no 4. yes 5. x2 - 3x + 2 6. x2 + 3x - 7, R 5 7. -2x2 + 9x + 5 8. x2 + 6x + 9 9. x2 - x + 8, R -12 10. x2 - 7, R -10 11. x3 + x, R 1 12. x3 + 2x2 + 6 13. x3 - x2 + x + 11, R 32 14. 2x3 + 15x2 - 125 15. -1 16. -13 17. 0 18. 39

Algebra 2

21 4 i"3 8

23 4 3i"3 2 9. (x + 1)(x - 1)(x + 2)(x - 2); -2, -1, 1, 2

20

102

23 4 3i"3 4

2. (x + 4)(x2 - 4x + 16); -4, 2 4 2i"3 3 4 3i"3 3. 2(x + 3)(x2 - 3x + 9); -3, 2

(2, 0) 2

1. (2x - 3)(4x2 + 6x + 9); 23 ,

10. (x + 1)(x - 1)(x2 - 11); -1, 1, 2"11, "11 11. (x2 - 2)(x2 - 8); 2"2, "2, 2"8, "8 12. (x + 2)2(x - 2)2; -2, 2 13. (x2 - 7)(x2 - 2); 2"7, "7, 2"2, "2 14. (x2 + 4)(x2 + 9); -2i, 2i, -3i, 3i 15. (x + 1)(x - 1)(x + 3)(x - 3); -1, 1, -3, 3 16. (x + 1)(x - 1)(x2 + 4); -1, 1, -2i, 2i 17. 5.52% 18. -2, 2, -0.71, 0.71 19. 0.06, 15.94 20. 0 21. -0.59, 0, 0.42 22. -0.67, 0, 1.4 23. -9, 0, 9 24. (n - 1)n(n + 1) = -336; -8, -7, -6 25. (x - 5)(x2 + 5x + 25) 26. (x2 - 3)(x2 - 5) 27. (x + 1)(x - 1)(x2 + 2) 28. (x + 1)(x2 - x + 1) 29. (x2 - 6)(x2 + 4) 30. (x2 + 1)(x2 + 9) 31. (x + 3)(x2 - 3x + 9) 32. (x2 - 2)(x2 + 9) 21 4 i"3 33. 0, 1, 34. 21, 1, 2"6, "6 2

35. 2"14, "14, 2i, i 36. 2i"2, i"2, 22i"2, 2i"2 37. -3, 3, -3i, 3i 38. 2"5, "5, 2i"5, i"5 39. 0, -2, 2, 2i"3, i"3 40. 0, 2, 6

All-In-One Answers


(1, 0) 2

19. x - 16 20. 2x + 11, R 48 21. x2 + 6x + 3, R 2 22. 3x2 - 7x + 7, R -8 23. (x + 1)(x - 3)(x + 5) 24. (x - 2)(x + 3)(x - 4) 25. 2x2 - 2x - 1, R 16 26. x3 + 3x2 + 3x + 4, R 1 27. x3 + 2x2 - x, R 1 28. x4 + x3 + x2 + x + 1 29. x3 + 2x2 + x + 2, R -6 30. 3x2 - 3x + 3 31. width: x - 3; height: x - 5




(continued)

Guided Problem Solving 6-4 m3

1. 60 2. the length of the box 3. width = x - 2 4. height = x - 1 5. V(x) = x(x - 1)(x - 2) 6. x(x - 1)(x - 2) = 60 7. (5, 60). The length of the box when the volume is 60 m3. 8. 5 meters 9. 5 4 3 = 60 10. 10 years old

Practice 6-5


1. 2 2 3i, 2"7 2. 3 1 "2, 1 2 "3 3. 4i, 6 1 i 4. 5 1 "6, 22 2 "10 5. x4 - 8x3 + 21x2 - 32x + 68 6. x4 - 4x3 - x2 + 8x - 2 7. x4 + 3x2 - 54 8. x4 - 6x3 + 9x2 + 6x - 20 9. 4, 2, -1 10. 3, 1, -5 2343"5 11. -4, -3, 21 12. 7, -2, -4 13. 3; 2 14. -2, -1, 1, 2 15. 2, 2 4 i 16. -1, 3 4 i 17. 1, 2 4 3i 18. -2, 1 4 2i 19. 1, -1, 5 20. -4, 2 21. -2, 1, 3

22. 10, 21 4 i"19 23. 1, -3 24. 3, 12 , 212 234"13 25. 2, 26. -3, 23 , 214 2

Guided Problem Solving 6-6 1. three 2. three 3. 41, 42, 43, 44, 46, 49, 412, 418, 436 4. 4 5. x 2 1 9 6. 3i, -3i 7. 4, 43i 8. Answers may vary. 9. Answers may vary. 10. -1, 42i

Practice 6-7

1 1 1 2 4 1 , 4 1 , 4 1 ; -4, 21 , 1 4 6 9 9 9 12 18 36 6 6 1 1 1 2 1 29. 41, 4 2 ;-1, 22 30. 41, 42, 44, 4 2 , 4 3 , 4 3 , 4 43 , 4 41 , 1 1 1 1 4 , 4 ; none 31. 41, 4 ; ; 1 32. 41, 47, 449; none 6 12 5 5 33. x3 - 7x2 + 17x - 15 = 0 34. x3 - 5x2 + 4x - 20 = 0 35. x3 - 5x2 + 4x + 10 = 0 36. x3 + 7x2 + x + 7 = 0 37. x3 + 4x2 + 16x + 64 = 0 38. x3 - 12x2 + 49x - 78 = 0

1. combination 2. permutation 3. permutation 4. combination 5. 12 6. 66 7. 792 8. 12 9. 1 10. 15 11. 1 12. 84 13. 1 14. 252 15. 2002 16. 2,118,760 17. 40,320 18. 110 19. 17,280 20. 360 21. 479,001,600 22. 239,500,800 23. 95,040 24. 12 25. 3024 26. 455 27. 60 28. 360 29. true, comm. prop. of mult. 30. false; Let a = 2. (22)! = 24 2 4 = (2!)2 31. false, Let a = 2 and b = 3. 2 ? 3! = 12 2 720 = (2 ? 3)! 32. true; identity prop. of add. 33. false; Let a = 2 and b = 3. (2 + 3)! = 120 2 8 = 2! + 3! 34. false; Let a = 2. (2!)! = 2 2 4 = (2!)2



27. 41, 43, 45, 415; none 28.41, 42, 44, 4 12 , 4 13 , 4 23 , 4 3

4 ,4 ,4 ,4 ,4 ,4 ,4


1 2 3 6 9 18 17. 5; 5, 3, or 7 7 7 7 7 7 1; 41, 45 18. 5; 5, 3, or 1; 41, 42, 43, 46, 4 1 , 4 3 , 4 1 , 4 3 , 2 2 4 4 1 3 19. 3 20. 4, -3i, 3i 21. 22, 1 4 "7 4 ,4 8 8 21 4 i"5 22. 2, 1 4 "5 23. 1, 24. -3, 1, 4 2 25. -4, 2i"7, i"7 26. -1, 21 4 i"3 27. -3, 3, -2i, 2i 2 2 28. -2, 2, 2"3, "3 29. 23 , 3 , 2i, i 30. 2"3, "3, 212 i, 12 i 43, 46, 49, 418, 4 , 4 , 4 , 4 , 4 , 4

1. two 2. four 3. 3 - i 4. 2i 5. (x - 2i)(x + 2i)(x - 3 + i)(x - 3 - i) 6. (x - 2i)(x + 2i)(x - 3 + 1)(x - 3 - i) =

(x2 + 4)(x2 - 6x + 10) = x4 - 6x3 + 14x2 - 24x + 40 7. x4 - 6x3 + 14x2 - 24x + 40 = 0 8. Check students’ work. 9. Answers may vary. 10. x4 1 10x2 1 9 5 0

Practice 6-6 1. -1, 0, 1 2. -4, 0, 4 3. 213 , 0, 12 4. 212 , 0, 13 5. -1, 21 , 0 6. -5, 0, 5 7. 2; 2 or 0; 41, 43, 4 12 , 4 32 5

8. 2; 2 or 0; 41, 42, 45, 410, 4 13 , 4 23 , 4 53 , 4 10 3 9. 4; 4, 2, or 0; 41, 45, 4 12 , 4 52 10. 3; 3 or 1; 41, 43, 49, 1 3 9 1 3 9 11. 5; 5, 3, or 1; 41, 43, 45, 2 2 2 4 4 4 1 3 5 15 1 5 1 5 415, 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 12. 3; 3 or 1; 2 2 2 2 3 3 6 6 41, 47 13. 3; 3 or 1; 41, 42, 43, 44, 46, 412 14. 4; 4, 2, or 0; 41, 42, 43, 46, 4 12 , 4 23 15. 5; 5, 3, or 1; 1 3 1 3 41, 42, 43, 46, 4 , 4 , 4 , 4 16. 6; 6, 4, 2 or 0; 41, 42, 2 2 4 4 4 ,4 ,4 ,4 ,4 ,4

All-In-One Answers

1. 2; 5; 3; 2 2. the number of different ratings possible 3. No; a particular television set will fall into one price range or the other. 4. 1 5. the Multiplication Counting Principle 6. 2 5 3 2 7. 60 8. Answers may vary. 9. 240

Practice 6-8 1. x4 + 8x3 + 24x2 + 32x + 16 2. a7 + 14a6 + 84a5 + 280a4 + 560a3 + 672a2 + 448a + 128 3. x7 + 7x6y

+ 21x5y2 + 35x4y3 + 35x3y4 + 21x2y5 + 7xy6 + y7 4. d9 - 18d8 + 144d7 - 672d6 + 2016d5 - 4032d4 + 5376d3 - 4608d2 + 2304d - 512 5. 256x8 - 3072x7 + 16128x6 - 48384x5 + 90720x4 - 108864x3 + 81648x2 - 34992x + 6561 6. x9 - 9x8 + 36x7 - 84x6 + 126x5 - 126x4 + 84x3 - 36x2 + 9x - 1 7. 64x12 - 384x10y2 + 960x8y4 - 1280x6y6 + 960x4y8 - 384x2y10 + 64y12 8. x35 + 14x30y + 84x25y2 + 280x20y3 + 560x15y4 + 672x10y5 + 448x5y6 + 128y7 9. about 1%

10a. about 99% 10b. about 95% 10c. about 5% 11. about 3% 12. about 3% 13. about 8% 14. about 0.6% 15. n3 - 9n2 + 27n - 27 16. 16n4 + 64n3 + 96n2 + 64n + 16 17. n5 - 30n4 + 360n3 - 2160n2 + 6480n - 7776 18. n6 - 6n5 + 15n4 - 20n3 + 15n2 - 6n + 1

Algebra 2

103

(continued)

3584x5 + 17920x4 + 57344x3 + 114688x2 + 131072x + 65536 29. x6 - 18x5y + 135x4y2 - 540x3y3 + 1215x2y4 - 1458xy5 + 729y6 30. x5 + 10x4 + 40x3 + 80x2 + 80x + 32 31. x10 - 5x8y2 + 10x6y4 - 10x4y6 + 5x2y8 - y10 32. y5 + 15y4 + 90y3 + 270y2 + 405y + 243 33. x12 + 18x10 + 135x8 + 540x6 + 1215x4 + 1458x2 + 729 34. x7 - 35x6 + 525x5 - 4375x4 + 21875x3 - 65625x2 + 109375x - 78125 35. x4 - 16x3y + 96x2y2 - 256xy3 + 256y4

Guided Problem Solving 6-8 1. 0.5 2. 5 3. 0.5 4. 2 5. b3g2 6. 5C3 5 10 7. 10b3g2 8. about 31% 9. 1 10. 5b4g1 11. about 16% 12. 5b1g4 13. about 16% 14. Answers may vary. 15a. 37.5% 15b. 25% 15c. 25%

6A: Graphic Organizer 1. Polynomials and Polynomial Functions 2. Answers may vary. Sample: polynomials and linear factors, dividing polynomials, solving polynomial equations, the Fundamental Theorem of Algebra 3. Check students’ work.

6B: Reading Comprehension 1. x 2. y 3. 1 unit 4. parabola 5. y-axis 6. downwards 7. (0, 0) 8. upper right 9. a

6C: Reading/Writing Math Symbols 1. subtract 2. inverse 3. zero 4. inverse; 18 5. 1 6. inverse 7. identity

6F: Vocabulary Review Puzzle 1. absolute 2. opposite 3. term 4. variable 5. evaluate 6. complex

Chapter 7 Practice 7-1 1. 12 2. -5 3. not a real number 4. 0.1 5. 0.3 6. 3 7. -3 8. 0.3 9. 6 10. -7 11. -0.4 12. 10 13. -20, 20 3 14. no real square roots 15. -100, 100 16. -0.25, 0.25 17. no real fourth roots 18. -4, 4 19. -0.1, 0.1 20. -5, 5 21. 9x2 22. 11 ∆y5« 23. 2g2 24. 5x3 25. 3xy3 3

26. x - 9 27. 5(x + 2)2 28. 4x 29. -2, 2 30. -3, 3 7 4 4 31. -0.4, 0.4 32. 27 , 7 33. 20 cm 34a. about 25.30 ft/sec 34b. about 10.48 ft/sec


1. K and L, respectively 2. length, L 3. K 5 1.35"L 4. 8 5 1.35"L; L 35 ft 5. 10 5 1.35"L; L 55 ft 6. 20 ft longer 7. The answers check. 8a. 72,000 cars 8b. 6,500 cars

Practice 7-2

3 6x2 4. 48x 5. 2xy 1. 2"6 2. 9xy2"y 3. 5yz2" 3 4 " 9x2y2 "3y " 54x3 6. 27"2y 7. 3"2x 8. 9. 3y 10. 3x

2 3 3 2 "2xy 11. 12. "6abc 13. 10 14. 54 15. 9 16. -3 4y 2bc 3 2 y z 17. 3x2"2 18. 2xy3 19. 6x"x 20. 5z"

3 4 3 21. 3k3"2 22. 22a4" 2 23. xy5"z 24. 4st3" s

3 3 4 25. 6xy" x 26. 5r"3r 27. 5uv2" u 28. "2 29. "4x

3 31. 2x 32. "12y 33. 3"3 30. k a 2 2 3

25y

6D: Visual Vocabulary Practice/High-Use Academic Words 1. symbol 2. always 3. table 4. explain 5. graph 6. formula 7. common 8. never 9. simplify

6E: Vocabulary Check Polynomial: A monomial or the sum of monomials. Degree of a polynomial: The largest degree of any term. Remainder Theorem: If a polynomial P(x) of degree n 1

34a. r 5

3 3V ; r 5 "6p2V 34b. 2.88 in. 2p Å 4p 3

Guided Problem Solving 7-2 1. distance in miles from the satellite to the center of Earth 2. 3950 mi 3. r = 3950 + 100 = 4050 4. 17,498 mi/h 5. r = 3950 + 200 = 4150 6. 17,286 mi/h 7. 212 mi/h greater 8. The answers are reasonable. 9. 0.22 gram

is divided by (x - a) where a is a constant, then the remainder is P(a). Multiplicity: The number of times the related linear factor is repeated in the factored form of the polynomial. Relative maximum: The y-value of a point on the graph of a function that is higher than other nearby points.

104

Algebra 2


19. 8a3 + 24a2 + 24a + 8 20. x8 - 4x6y2 + 6x4y4 4x2y6 + y8 21. 32x5 + 240x4y + 720x3y2 + 1080x2y3 + 810xy4 + 243y5 22. 64x12 + 192x10y2 + 240x8y4 + 160x6y6 + 60x4y8 + 12x2y10 + y12 23. x6 - 3x4y2 + 3x2y4 - y6 24. 16b4 + 32b3c + 24b2c2 + 8bc3 + c4 25. 243m5 - 810m4n + 1080m3n2 - 720m2n3 + 240mn4 - 32n5 26. x18 - 6x15y4 + 15x12y8 - 20x9y12 + 15x6y16 - 6x3y20 + y24 27. x7 + 7x6 + 21x5 + 35x4 + 35x3 + 21x2 + 7x + 1 28. x8 + 32x7 + 448x6 +

All-In-One Answers




(continued)

Practice 7-3

1. -63 2. -6 3. 73 4. 11"3 5. 5"2 + 2"3 3 3 x 7. 11"xy 8. -2 - "3 9. 10 - 5"3 6. 3"7 - 7" 22 1 14"3 3 1 "5 10. - 2 11. 12. 22"2 13. 4"2 13



4 14. 0 15. 13" 3 16. -3 - "5 17. -38 + 7"10 18. 67 - 15"7 19. 28 - 16"3 20. 9 + 2"14 21. 30 + 12"6 22. 12"7 23. 18"10 3 3 24. 41"3 - 3"6 25. 6" 3 + 4" 9 26. 105"x 27. 26y"5 28. 6y + 13"5y - 25 29. x - 3

3 "3 1. s" 2. 2A ; 2A9"3 ; #2A 3. about 8.8 in. 2 3 3"3 4. about 15.2 in. 5. Yes, the answer checks. 6a. about 10.7 in. 6b. about 11.5 in.

30.

1a. ƒ(x) = 1.8x 1b. g(x) = 0.75x 1c. g(f(150)) = $202.50 1d. No; it doesn’t matter whether you first multiply by 0.75 or by 1.8. 2. 2x2 + 4x + 2; all real numbers 3. -2x2 + 4x - 4; all real numbers 4. 8x3 - 2x2 + 12x - 3; all real numbers

Practice 7-6

3 2 x 1 2" "5 2 2"2 x 31. "2 32. x 3 33a. (900 1 300"3 1 300"6) ft or about 2154 ft

33b.

270,000 1 90,000"3 2 ft or about 212,942 ft2 2

5. 4x2 2 1 ; all real numbers 6. 2x2 - 4x + 4; all real

Guided Problem Solving 7-3 1.

1 1 Í5 2

2. subtract 3.

2 1 1 Í5

2x 1 3

4. 1 2 Í 5 5.

21 1 Í 5 2

6. 1 7. Yes, it equals the reciprocal of the golden ratio. 8. 224Í 35 1 52

Practice 7-4 1. 3 2. 81 3. 32 4. 256 5. 1 6. 4 7. -1 8. 9 9. 2 10. x 6 11. 2y2 12. 4 13. 1 14. 21 15. 49 16. 0 5


22. -27, 27 23. 64 24. 0, -1 25. no solution 26. 64 27. 23 28. 0 29. no solution 30. -2 31. 1 32. -123 33. 8 34. 12 35. 1 36. 16 37. 8 38. -6, 2 39. 2

3

3 7 31 2 17. 12x6 18. 31 19. 9ab 3 20. 16 21. b 4 22. y 40

a y y6 2 3 13 3x 1 1 23. 2 24. 8a 4 25. 26. 12x 20 27. y 9 x 21

Guided Problem Solving 7-6 1. cost in dollars to produce x violins; income in dollars from selling x violins 2. profit earned when he makes and sells x violins 3. I(x) = 5995x 4. C(x) = 1000 + 700x 5. P(x) = 5295x - 1000 6. 157,850 7. He made a profit of $157,850 when he makes and sells 30 violins. 8. The answers match. 9a. P(x) = 56x -30 9b. $13,970

3 4 3 5 x 30. " 2y 31. "a3 32. " b 28. 10.1% 29. "

3 2 4 5 12 z 34. " ab 35. " m 36. 71 37. 51 33. " "t2 "a8 3

1

1

1 2

2 numbers 7. 2x 1 3 ; all real numbers except 1 8. -4 4 4x 2 1 9. -2 10. 7 11. 23a 1 2 12. -4x + 7 5 13. 2x2 - 3x - 7 14. 17 15. 16 16. -8x + 6 17. 2 4 5 5 5 18. 23x 1 2 19. 7 20. 3x2 - 13 5 5 21. 3x3 + 2x2 - 15x - 10 22. -2x2 + 3x + 12 23a. ƒ(x) = 0.75x 23b. g(x) = x - 5 23c. g(ƒ(50)) = $32.50 23d. Yes; multiplying by 0.75 and then subtracting by 5 is different than subtracting by 5 and then multiplying by 0.75.

3

1

38. x 2 39. m 3 40. (5y) 2 41. 23y3 42. b 4 43. (26) 2 4

Practice 7-7

3

44. 36a2 45. n5 46. (5ab) 4

1.

6 4 2

Guided Problem Solving 7-4 1. 39% 2. number of years ago that the organism died T

R 5 (2.7) –8033 3. fraction of A left after T years 4. A 5. 78% 6. 61% 7. 37% 8. Yes, the answers check. 9. 81%; 65%; 12%

4 O

2.

y x 2 4 6

y 6 4 2O 642 2 2 4 6

x 6

Practice 7-5 1. 127 2. -8, 8 3. 9 4. 3 5. no solution 6. 25 7. 9 8. -14 9. 1 10. 27 11. 4, 2 12. 9 13. 7 14. 2 15. 4 16. 29,-25 17. 10 18. 16 19. 4 20. 13 21. 4 All-In-One Answers

Algebra 2

105


y

5 4 3

2O

642 2 4 6

3 2 1 32 O

x

–3

–2

–1

0

y

–2

–1

0

1

y

x x

2

4 5

O

x

6.

y x 1 2 3

2 3

4 3 2 1

2

y

2 O

O

2

2

x 1 2 3 4

26.

2

x

–3

–1

0

–2

y

0

1

2

3

y

7. y 5 4"x 2 2; no 8. y = x - 2; yes

2

9. y 5 13 x 2 1; yes 10. y 5 4"2x 2 3; no

x 2

x ; no 11. y 5 12 x 1 12 ; yes 12. y 5 4 1 2 Ä 3

17. y 5 4"x 1 4 2 4; no 18. y 5 4"4 2 x; no

19. f21(x) = 6x; The domain and range of f and f21 is the set of all real numbers; f21 is a function. 20. f21(x) 5 25x 1 10; The domain and range of f and f 21 is the set of all real numbers; f 21 is a function.

21. f21(x) 5 4"x 1 2; Domain of f = all real

numbers = range of f 21; Range of f = the set of real

O

2

2

13. y 5 4 x ; no 14. y 5 4"x 2 3; no

Ä5 4 ; no 16. y 5 4 x 1 2 ; no 15. y 5 4 x 1 Ä 6 Ä 3

27. -1 28. 3 29. 2 12 30. f21(x) 5

22.

f21 (x)

5 4"x 2 4; Domain of f = all real

numbers = range of

f 21; Range

of f = all real numbers

greater than or equal to 4 = domain of f 21; f 21 is not a function.

23. f 21 (x) 5 x 2 1 1; Domain of f = all real numbers greater than or equal to 1 = range of f 21; Range of f = all real numbers greater than or equal to 0 = domain of f 21; f 21 is a function.

x 2 635,600 ; in 2009 198,900

Guided Problem Solving 7-7 1. v is the velocity of the water in feet per second; g is the acceleration due to gravity (32 ft/s2); x is the height of the 2 2 water in feet. 2. v2; v ; v 3. 25 4. 25 ft 5. 6.25 6. 6.25 ft 2g 64 7. Yes, the answers check. 8. r 5

numbers greater than or equal to -2 = domain of f 21; f 21 is not a function.


5.

4

25.

y

S 2 1; r 8.4% ÅP

Practice 7-8 1.

y 6 4 2O x 642 2 4 6 2 4 6

2.

y 6 4 2O x 2 2 4 6 8 10 2 4 6

24. f 21 (x) 5 31 x 2; The domain and range of f and f 21 is

the set of all real numbers greater than or equal to 0; f 21 is a function.

106

Algebra 2

All-In-One Answers


3.

(continued)



5.

7.


9.

11.

13.

y 6 4 2O x 2 2 4 6 8 10 2 4 6

4.

y 6 4 2O x 2 2 4 6 8 10 2 4 6

6.

y 4 2O x 42 2 4 6 8 2 4 6 8

8.

y 6 4 2O x 2 2 4 6 8 10 2 4 6

10.

2

y 6 4 2O

14.

16.

x

1

321

18.

y

19.

6

2 3

3 2 1 21

O 2 2 4 6

y x

1

x

O 2 3 4 5

24.

y

3 2 1

x O 1 2

4321

2 3 4

2 3 4 5

y

2 3

4321

1

x O 1 2 3 4 5 6

3 2 1

x O 1 2 3 4

2 1

1

y

y

22.

y

23.

25.

2 4 6 8

5 4 3 2 1

2 3

y 6 4 2O x 2 2 4 6 8 10 2 4 6

6 4

20.

y

x O 21 1 2 3 4

x

x O 1 2 3 4 5

x O 1 1 2 3 4 5

4 3 2 1

21.

5 4 3 2 1

x

O

2 3

y 6 4 2O 4 2 4 6 2 4 6

y

2

3 2 1 6 8

4 3 2 1

x 2 4 6 8 10

17.

y 6 4 2O x 2 2 4 6 8 10 2 4 6

y 6 4 2O x 2 2 4 6 8 10 2

y 6 4 2O

2 2 4 6

4 6

12.

All-In-One Answers

15.

y 6 4 2O x 2 2 4 6 8 10 2 4 6

y 6 4 2O x 2 2 4 6 8 10 2 4 6

6

(continued)

x 1 2 3 4 5

x O 1 2

2 3 26.

y O

y

4 3 2 1

y

x O 321 1 2 3 2

Algebra 2

107


(continued) 43.

y

5 4 3 2 1

y

2 2

x O 1 1 2 3 4 5

2

O

4

x

2

2

2

28b. about 10.6 ft

r

O

2x

2


12

1. length, in feet, of the trapeze 2. time, in seconds, for a trapeze to complete one full cycle

3. 4

4 A

O

y All rights reserved.

8

2

100 200 300 29. 75 30. 7 31. no solution; 3 is extraneous 32. 2.36

O

2

2

4

x

6

33. y 5 9"x 1 2; graph of y 5 9"x shifted left

2 units 34. y 5 22"x 1 5; graph of y 5 22"x

4. 4.3; about 4.3 s 5. 6.1; about 6.1 s 6. Yes, the answers

3 3 shifted left 5 units 35. y 5 5" x 2 2; graph of y 5 5" x

shifted right 2 units 36. y 5 28"x 1 3; graph of

7a.

3 y 5 28"x shifted left 3 units 37. y 5 22" x 2 7 1 4; 3 graph of y 5 22" x shifted right 7 units and up 4 units

38. y 5 5"x 1 3 2 1; graph of y 5 5"x shifted left 40.

y

2

x 2

x

2

O

2

4

2

4

O

42.

y

2

7B: Reading Comprehension

x O 2

7b. about 9.1 nautical miles; 11.7 nautical miles

1. Radical Functions and Rational Exponents 2. Answers may vary. Sample: roots and radical expressions, binomial radical expressions, rational exponents, inverse relations and functions 3. Answers may vary. Sample: packaging, art, space travel, solar energy 4. Check students’ work.

y

2 2

6


4

41.

4

2

2

2

4

y

2 x

y

2

3 units and down 1 unit

39.

check.

2

2

O 2

2

x

1. cube 2. 12 edges 3. 8 vertices 4. sphere 5. They are not actually visible. 6. cube or polyhedron 7. inscribed 8. circumscribed 9. b

7C: Reading/Writing Math Symbols 1. f, h 2. a 3. g 4. c 5. d 6. b 7. f 8. j 9. i, k

108

Algebra 2

All-In-One Answers


28a.

44.

y


(continued) 7.

7D: Visual Vocabulary Practice 1. nth root 2. like radicals 3. composite function 4. inverse relation 5. square root equation 6. radical equation 7. square root function 8. radical function 9. inverse functions

4 2 x


2

Radicand: The number under a radical sign. Index: With a radical sign, this indicates the degree of the root. Principal root: When a number has two real roots, this is the

All rights reserved. © Pearson Education, Inc., publishing as Pearson Prentice Hall.

2 x

Rational exponent: If the nth root of a is a real number and n

n

1. index 2. inverse 3. left 4. principal 5. radical 6. rational L O N O E G R V E

I A C T E V I E T

N R N R V N N E L

D E I O V A R N A

E E O E I C O R C

X D R I H T G R I

T S D A E L A T D

E N N I E E I R A

2

m


N G R O H F N R R

E E X E G T I I R

; y=0

y

4

an expression so there are no radicals in any denominator and no denominators in any radical. m

2

6

Rationalize the denominator: Rewrite the denominator of

1 n m n m is an integer, then an 5 Í a and a 5 Í a 5 Q Í a R . If m is negative, a 0.

O

8.

positive root.

P R I N C I P A L

; y=0

y

6

O

2

9. y = 18,000(0.75)x; $5695.31 10. y = 29,000(0.88)x; $11,851.59 11. y = 1573(1.02)x; 1917 bears 12. y = 75,000(1.125)x; $2,568,247.87 13. y = 200,000(0.9925)x; 94,207 birds 14. y = 2(0.65)x 15. y = 10(0.8)x 16. y = 0.7(1.2)x 17. 1.45 18. 0.9 19. 0.6 20. 3 21. 25% decrease 22. 37.5% decrease 23. 73% increase 24. $300,000

Guided Problem Solving 8-1 1. the intensity of sunlight beneath the surface of the ocean 2. the depth beneath the ocean surface, in feet 3. percent of sunlight that reaches a depth of x feet 4. 50 5. y 5.63976205 6. about 5.6% 7. 370 8. y 0.00170898 9. about 0.0017% 10. Answers may vary. 11. about 91.8%

Practice 8-2

Chapter 8

1. 7.3891 2. 0.0821 3. 1.3956 4. 4.1133 5. $39,624.12 1

Practice 8-1 1. growth 2. decay 3. growth 4. decay 5. ;y = 0 y

8. y 5 8a 12 b

1 64.9 x

; about 2.7 mg

1 13.2 x

4

9. y 5 45a 12 b ; about 34.6 mg 10. decay 11. growth 12. decay 13a. $9948.90 13b. $19.68 14. 9.9 yr

2

15.

6

O

6. 6

16.

y

x 2

x

64.1 6. $21,557.68 7. y 5 12a 21 b ; about 5.5 mg

y

4

4

2

2

2

; y=0

y

2

O

2

x

2

O

2

x

4 2 x 2

O

2

All-In-One Answers

Algebra 2

109


2

O

4

2

2 2

2

x

y x

4

2

O

2

2

2 O

21.

O

20.

y

2

15. log8512 = 3 16. log13169 = 2 17. log2512 = 9

2

4

19.

1 11. 2-10 = 1 9. 560 = 1 10. 12-2 = 144 1024 12. 38 = 6561 13. log981 = 2 14. log25625 = 2

y

x

2

22.

y

56. 6.3 3 10-9 57. 6.3 3 10-7 58. 2.5 3 10-6

y 2

25 1 23. log8 8 = -1 24. log111 = 0 25. log66 = 1 1 = -3 27. log 1 = 0 28. log 17 = 1 26. log6 216 17 17 29. 5 h 30. 4 31. 3 32. 2 33. 1 34. 0 35. -1 36. -2

45. 1 46. 1 47. 5 48. -2 49. -3 50. -2 51. 52 52. -2 53. 12 54. 6.3 3 10-8 55. 5.0 3 10-8 x

4

1 = -3 22. log 1 = -2 20. log100.001 = -3 21. log4 64 5

37. -3 38. 1 39. 3 40. 2 41. -1 42. 0 43. 0 44. 3

4

x

18. log41024 = 5 19. log5625 = 4

O

2

59. 2.5 3 10-5 60. 1.0 3 10-7 61. 1.3 3 10-3 62.

2 2

O

23.

2

4

x

24.

y

4

2

2

3 2 1

1 1 2 3

y

4

O

25.

2

x

2

O

26.

y O

O 1 2 3 4

1 1 2 3

3 2 1

65. 4 3 2

x O 1 2 3 4 5

x

O

1 1 2 3

x

y

y

1 2 3 4 5

y

x

O

1 1 2

1 2 3 4 5

4

2

66.

2 4

x

y

x 2

2

3 2 1

63.

y

64.

2


18.

y

67.

y

y

2 x 4

2

x

2

O

x

O O

2

2

4

2

4

4

2

Guided Problem Solving 8-2 1. to save $8000 2. 5 yr 3. a single deposit 4. continuously 5. 0.052 6. 8000 5 Pe0.052(5) 7. $6168.41 8. $6497.65, $6844.47, $7209.80, $7594.63, $8000. Answers may vary. 9. Answer may vary. 10. $2556.43

Practice 8-3

68.

69.

y

y 2

2 x 2

O 2

2

O

2

4

6x

2

1. 44 = 256 2. 70 = 1 3. 25 = 32 4. 101 = 10 1 7. 95 = 59,049 8. 172 = 289 5. 51 = 5 6. 8-2 = 64

110

Algebra 2

All-In-One Answers


17.

(continued)


(continued)

Practice 8-5

y

1. 3.58 2. 3.36 3. 1.5 4. 0.68 5. 0 6. 1.43 7. 3 8. 1.63 9. 0.5 10. 0.53 11. 7.92 12. 1.28 13. 0.93 14. -0.47 15. 2.79 16. 0.39 17. 2.52 18. 2.04 19. 33.33 20. 10 21. 334 22. 0.22 23. 40 24. 4 25. 100 26. 100 27. 25 28. 125 29. 10 30. 16.67 31. 2.26 32. 1.19 33. 0.48 34. -0.32 35. 1.48 36. 1.19 37. 3.85 38. 1.72 39. about 19 mo 40. about 27 yr 41. 3.16 42. 0.4 43. 0.04 44. 4000 45. 20 46. 497.5 47. 47.5 48. 0.03 49. 5.48 50. 0.48 51. 0.23 52. 3.30 53. 0.86 54. 0.75 55. -2.54

2 x O

2

4

6

2


Guided Problem Solving 8-3 1. log273 2. log273 = x; yes 3. 3 5 27x 4. The error is in the second line. It should read 3 5 27x . 5. 31 5 (33) x 6. 31 5 33x 7. 1 = 3x 8. log273 5 31 9. Answers may vary. 10. The error is in the third line. It should read 23 5 (22) x; the correct answer is 23.

E ? 30

log11,600 ; 5.1 10. Answers may vary. log30 11. Answers may vary. 12. after 2 hours

9. M 5 7.9 2 1 1

2 2 3 14. log7x3 15. log415x 16. log 14 17. log x 3 18. log r s1

y

t4 3 2 19. log3100xy 20. log 8 21. log 3x 22. log 64 23. log 8 24. log x11 25. log6 21 26. log 8 27. log3 2x5 7 y 1 1

1 3

x 2y 3 y 30. log t24 31. log5 4 8 2 z r t y3 32. log x + log y + log z 33. log2x - log2y - log2z 34. log 6 + 3 log x + log y 35. log 7 + 2 log (3x - 2) 36. 21 log 2 + 12 log r + 12 log s + 21 log t - 12 log 5 - 12 log w 37. log 5 + log x - log 4 - log y 38. log55 - 5 log5x, or 1 - 5 log5x 39. log 2 + 2 log x + log y - log 3 - 3 log k 40. 2 log43 + 2 log4x + 2 log4y + 2 log4z 41. Quotient Prop. 42. Power Prop. 43. Product Prop. 44. Power Prop. 45. Power Prop. 46. Power and Quotient Prop.

28. log2 x 1 29. log © Pearson Education, Inc., publishing as Pearson Prentice Hall.

7.9 3. E ? 307.9 4. E ? 30M 5. E ? 30 M 5 11,600

8. (7.9 2 M)log30 5 log11,600

1. about 377.7 decibels 2. about 2.6 decibels 3. 1.0792 4.1.2042 5. -0.2219 6. -0.0969 7. 1.8751 8. 0.5052 9. 0 10. 1.7782 11. log512 12. log65 13. log21 = 0

Guided Problem Solving 8-4 1. 1024 W/m2 2. 6.31 3 1026 W/m2 3. decibels 4. the decrease in apparent loudness 24

5. L1 5 10 log 10I

0

1026 6. L2 5 10 log 6.31 3 I 0

24

7. L1 2 L2 5 10 log 10I

0

8.

1. 7.9 2. the magnitude of the Pennsylvania earthquake 6. 307.92M 5 11,600 7. log(307.92M) 5 log11,600

Practice 8-4

10(log1024


26 2 10 log 6.31 3 10 I0

2 logI0) 2 10flog(6.31 3 1026) 2 logI0g

9. 10 log1024 2 10 log(6.31 3 1026) 10. 20 - 10 log 6.31 12 dB 11. L1 5 80dB, L2 68dB; L1 2 L2 < 80 2 68 5 12dB 12. about 15 dB All-In-One Answers

Practice 8-6 1. 40.2 days 2. 35.7 days 3. 31.8 days 4. 6.36 km/s; no 5. 22.65 6. 25.79 7. 2.71 8. 0.92 9. 1.91 10. 0.41 11. 4.69 12. -1.15 13. 0 14. 17.33 15. 2.60 16. -2.28 17. -0.02 18. 6.44 19. 1.61 20. 4 21. 21 22. no solution 23. 0.61 24. 12.37 25. 1.58 26. 29,937.07 27. -0.11 28. 633.14 29. 2.12 30. 1.85 31. 1.84 32. 3 33. 2 34. 12 35. 1.83 36. 7.36 37. -0.93 38. 48.14 39. 151.48 a z 40. 4.19 41. ln 2 42. ln 243 43. ln 4b 44. ln 3 45. ln 9x x 4 3 46. ln x y

Guided Problem Solving 8-6 1. maximum velocity of the rocket, in kilometers per second; the time in seconds that the booster rocket fires; velocity of the exhaust, in kilometers per second; the mass ratio of the rocket 2. 6.9; 50; 3.1; unknown 3. 6.9 5 20.0098(50) 1 (3.1)ln R 6.9 1 0.0098(50) 6.9 1 0.0098(50) 3.1 5 ln R 5. e 4. 5R 3.1 6. R 10.8 7. Answers may vary. 8. Answers may vary. 9. Answers may vary. 10. R 20.0

8A: Graphic Organizer 1. Exponential and Logarithmic Functions 2. Answers may vary. Sample: properties of exponential functions, logarithmic functions as inverses, properties of logarithms, natural logarithms 3. Reading Data 4. Testing Multiple Choices 5. Answers may vary. Sample: population, depreciation, medicine, investments 6. Check students’ work. Chapter: Exponential and Logarithmic Functions; Exploring Exponential Models: modeling exponential growth and decay; Properties of Exponential Functions: exploring properties of exponential functions; Logarithmic Functions as Inverses:

Algebra 2

111

(continued)

write, evaluate, and graph logarithmic functions; Properties of Logarithms: use properties of logarithms; Exponential and Logarithmic Equations: solve exponential and logarithmic equations; Natural Logarithms: evaluate natural logarithmic expressions and solve equations using natural logarithms

26. z 5 3x3 ; 9



1. the current use of logarithms 2. common and natural 3. Answers may vary. Sample: The phrase “In the twentieth century” 4. 500 5. 39 6. log 500 x = 39 7. a

1. directly 2. inversely 3. y = 8 4. the value of x when

1. 1; 13; no 2. 1; 5; no 3. (2, -3); (-3, 2); no 4. 5; -1; no 5. 64; 64; yes 6. -9, -9, 9; yes and no, -(b2) is the same as

(-b2), but it is not the same as (-b)2.

k(48) y = 12 and z = 2 5. y 5 kx 6. 8 5 7. k = 1.5 z2 (3) 2 8. y 5 1.5x 9. x = 32 10. Answers may vary. z2 11. Answers may vary. 12. a = 4

Practice 9-2

8D: Visual Vocabulary Practice 1. common logarithm 2. change of base formula 3. exponential equation 4. growth factor 5. logarithmic equation 6. continuously compounded interest 7. logarithmic function 8. decay factor 9. natural logarithmic function

3 x2 3. y 5 2 3 x2 6. y 5 2 3 x2 8. y 5 2 3 x1

1. y 5 2

9.


1 1 2. y 5 2

4 2O x 642 2 4 6 2 4 6

Asymptote: A line that a graph approaches but never reaches.

Logarithmic function: The inverse of an exponential function.

Exponential function: The general form is y = abx, where x is a real number, b 0, and b 1. Common Logarithm: A logarithm that uses base 10. Growth factor: The value b in y = abx, where b 1.

3 13 x11 3 1 6 5. y 5 2 3 2 2 4. y 5 2 x x23 4 1 2 7. y 5 2 3 2 1 x13 1 11 2 ; x = 1, y = 2 y 2

10.

; x = -1, y = 0

y

8F: Vocabulary Review 1. e 2. d 3. f 4. b 5. c 6. a 7. g 8. h

6

Chapter 9

x

O 2 4

2 4 6

Practice 9-1

36 1. 1 2. 1.2 3. 50 4. 2 5. 4.2 6. y 5 14 x 7. y 5 x 7

0.8 30 4 8. y 5 2 24 x 9. y 5 2 x 10. y 5 x or y 5 5x 8 12. y 5 3 13. y 5 6.3 or y 5 63 11. y 5 x x x

10x

3 14. y 5 2 0.3 x or y 5 2 10x 15. I varies inversely with R. 16. A varies tly with b and h. 17. h varies directly with V and inversely with B. 18. V varies directly with the cube of r. 8 ; 1 23. y 5 2 1 ; 2 1 19. 4 20. -4 21. 2 22. y 5 x x 8

11.

; x = -3, y = -3

y 12963 3 6 9 12

O

x

3

36 24. y 5 7.2 x or y 5 5x ; 0.9 25. z = 2xy; 48

112

Algebra 2



27. inverse; y 5 20 x 28. neither y 32 29. direct; y = 6x 30. direct; y = 125x 31. neither 32. inverse; y 5 15 x

All-In-One Answers




6 4

; x = 2, y = -2

y

13.

18.

8 6 4

x

O 2 4 6

(continued)

2 4 6

42 2 4 ; x = 0, y = 3

y


14.

;x y 1O x 4321 1 2 1 2 3 4 5


15.

4 3 2 1

y

16.

O

y 3 2 1O 321 1 2

; x = 2, y = 1

21.

; x = 1, y = -1

22.

; x = 0, y = 0

2

All-In-One Answers

x

x

;x y 6 4 2O x 8642 2 4 2 4 6

23.

4 2 4 6 8

= -3, y = -1

; x = 5, y = 0

y 6 4 2O 4

x

; x = 3, y = -2

y x

O 2

; x = 0, y = 0.5

3

642 2 4 6

2

; x = -1, y = 2

y

x

y

2

20.

2 3 4 5

y 2 1O 21 1 2 1 2 3 4

17.

= -1, y = -2

x

1 O 1 2

6 8

4 2O x 642 2 4 6 2

x O 1 2 3

321

x

O 2

19.

4 3 2

; x = 3, y = 1

y

2 4 6 8

Algebra 2

113


(continued)

; x = 0, y = 0

y


2

1. 10,000 mi 2. mi/gal 3. g, gallons of gasoline used to drive

O

10,000 g 5. Check student’s table. 10,000 miles 4. m 5

x

25.

;x y 4 3 2 1O x 21 1 2 3 4 1 2

= 1, y = 1

Mileage (mi/gal)

2

100 80 60 40 20

O

100 200 300 Gasoline Used (gal)

400

6. This will translate the graph 50 units to the right. 26.

; x = 0, y = 0

y

10,000

7. m 5 g 2 50 ;

2

O

2

x

2

27.

; x = 4, y = -2

y

4 2O 2 4 6 8 28.

3 2 O 1 1 2 3

100 80 60 40 20

O

x 4 6 8 10

100 200 300 Gasoline Used Later (gal)

400

8. 25 mi/gal; 28.57 mi/gal 9. Check students’ work. 10,000 10,000 m 5 20,000 or g ; The graph of g ;m 5 1 g 2 the new mileage is a strech of the graph of the old mileage by a factor of 2.

10. m 5

; x = 2, y = -0.5

y

Practice 9-3 x 1 2 3 4 5

29. 2.25 ft 30. 412.5 Hz 31. 825 Hz 32. 165 Hz 33. $7.50 34. 324 keepsakes 35. $4.50 36. $36.00

114

Mileage (mi/gal)

2

Algebra 2


2

1. -3, 4 2. 42 3. 2 4. 0, -2 5. -1 6. 0, 43 7. y = 0 8. y = 1 9. y 5 12 10. y = 2 11. y = 0 12. y = 1.5 13. 14. y y 6 6 4 4 2O 2 x x O 4 642 2 4 6 8 2 4 6 2 2 4 4 6 6

All-In-One Answers


2



17.

y 6 4 2O x 2 2 4 6 8 10 2 4 6

16.

y 6 4 2O 642 2 4 2 4 6

18.

19.

x 6 9 12

y 9 6 3O x 63 3 6 9 12 3 6 9

20.

y


y 9 6 3O

63 3 6 9

x

x 2

21.

x 2

2

O

2

2

x © Pearson Education, Inc., publishing as Pearson Prentice Hall.

5. Answers may vary. 6. 6 free throws 7. 70%; answers may vary; 100%; answers may vary 1 6 27 3 8. 21 9. 20 assignments 30 1 6 5 36 5 4 5 75%

1 1 ; x 2 0 or -2 6. 3 ; x 2 -2 4. 43 ; x 2 -5 5. x x12 5 2 ; y 2 0 or -6 8. x ; x 2 5 or -5 7. y 1 6 x15

1 8 ; x 2 7 or -5 9. x 2 3 ; x 2 6 or -6 10. x x27 x26

2x 1 1 ; x 2 -5 or 22 14. 2x 1 3 ; x 2 1 or 2 13. 3x 12 3 3 x21

2 O

WINDOW FORMAT Xmin=0 Xmax=100 X s c l =10 Ymin=.5 Ymax=1 Y s c l =.1

26 4x 2 12 11. 3x ; x 2 3 or -2 12. ; x 2 -3 or -7 x17 x23

y

2

4.

1. 2x x1 1 ; x 2 0 2. 2; x 2 232 3. 3; y 2 1 or -1

2

O

1. the player’s rate of success if she makes x more shots 2. an x-value; the number of free throws she needs to make 3. Answers may vary.

Practice 9-4

y

2 2

(continued)

2

2

22. vertical asymptote at x = -2; hole at x = 2 23. vertical asymptote at x = 1; hole at x = 0 24. vertical asymptotes at x = 1 and x = -1 25. vertical asymptote at x = -2 26. no vertical asymptotes or holes 27. vertical asymptote at x = 3; hole at x = -3 28. vertical asymptote at x = 4 29. vertical asymptotes at x 5 24 and x = 3 5 30. vertical asymptotes at x = 2 and x = -2 1 3500 , where x = number of pages; 31a. y 5 0.02x x

7 ; x 2 4 or -4 16. x 2 3 ; x 2 -3 15. x 1 4 2

17. 10; a 2 -1, 0 18. -1; x 2 22 , 0, 43 5

19. x2 - 1; x 2 -4, 2 20. x + 3; x 2 -4, -3, -1 2 7y 2 28 21. 6y 1 24 ; y 2 -5, -4 22. 3x 1 3x ; x 2 0, 45 x25

5y 2 1 10y 1 5 ; y 2 -2, -1 24. 3x 2 6 ; x 2 -1, 2 36y 1 72 14 y y 25. y 2 2 ; y 2 2, 49 26. 23 ; y 2 46 27. ; y 2 0, 47 5 2 2 16 x 1 2 x 1 28. x 2 2 ; x 2 2 , 2, 3, 5 29. 2 ; x 2 41, 43 x 29

23.

2 30. 1; x 2 -3, 0, 5 31. x2 2 5x 1 6 ; x 2 -3, -2

x 1 5x 1 6

1 ; x 2 0, 46 33. x + 8; x 2 -2, 48 34. 4 ; x, y 2 0 32. x y 3

2 16 35. 4x 3x ; x 2 0, 1 , 5, 44 36. x ; x, y 2 0 6y 3 37. 3x; x 2 0, -2 38. x ; x 2 -6, -4, 2 3 2 39. x2 2 2x 1 1 ; x 2 -7, -3, 4

x 1 14x 1 49 2 40. x 2 1 2x 1 1 ; x 2 -2, 41 x 1x22

31b. at least 2365 pages 31c. 3571 pages 31d. 7292 pages 31e. x = 0; y = 0.02

Guided Problem Solving 9-4 1. The radius and height are both r. 2. cylinder or hemisphere 3. V 5 23pr3 4. S.A. 5 3pr2 5. V 5 S.A.

All-In-One Answers

Algebra 2

2r 9

115


(continued)

V 5 4r 9. The ratio 6. V 5 pr3 7. S.A. 5 4pr2 8. S.A. for the cylindrical tank is larger. 10. The cylindrical tank has a larger volume. 11. yes; cylindrical tank holds more than a hemispherical tank; answers may vary. 12. cylindrical tank

33. no solution 34. 6 35. -5 36. -1 37. about 13 mi/h tail wind 38. about 14 mi/h head wind 39. about 1.3 days 40. Tom: 125 min, Huck: 500 min

Practice 9-5

1. 700 miles 2. 360 mi/h 3. t 5 ds 4. 35 18 h 5. faster 700 700 6. dt 1 x or 360 1 x 7. 360700 8. 1 x 360 1 360 1 x 5 3.5 35 700 or 18 1 360 1 x 5 3.5 9. 90 mi/h 10. Answers may vary. 11. 50 mi/h

2 2x 2 2 7. 3 8. 2 2 n 9. 2x 6. x 1 12 n24 9 xy3

2

5

3(3y 2 1) 7y 1 5 12y 1 5x 10. 3y 11. 12. 2 y 25 10x2y2 2 2 3 2 2x y 10x 2 26 13. 14. (x 1 5)(x 2 5)(x 1 1) 8x3y3 9y 1 4x x 2y 3 15. 16. 17. x 1 2 21x2y2 x2 2 4 (5x 1 1)(x 1 3) 18. (x 2 3)(x 1 2)(x 1 5)(x 1 1) 2(x 1 2) 7x 1 5 19. 20. 2(3x 2 1)(2x 2 3)(2x 1 3) x(x 2 3) 2 4x 1 1 36x 1 3 21. 22. 4x 2 x29 (x 1 5)(x 1 1)(x 2 2) 2 2 5x 1 6 23. 3x2 1 14 24. 5x 2 2 25x 1 31 25. 3x 21 x 15 x 2 5x 1 6 2 2 26. 5a 2 1 2a 27. 28c

a 24

2 29. 2 28. gh

6t t 2 2 25

c 29 2 1 y2 2 x 2y x12 30. 28r 31. 2 32. 3x 33. 4x 26 r 24 x 1 xy y 2 2 34. 2 x 35. 4y 36. 15 37. 2x + 3 4 2x 2 3x 2 2 3y(y 2 2) 2y 1 6xy 38. 3x 2 3 39. 40. x 5x 1 5 (y 2 6) (y 1 2) (y 2 4) 24 ohms 41b. 4 ohms 41a. 17 3

Guided Problem Solving 9-5 1. 1 unit 2. 13 unit 3. 1; 2 4. 1 2

2 2 1 5 1 1 2 5. 3 1 a b ab 2 3 4 2 6. 3; 2 7. 5 8. 3 9. 1 1 5 ab ? 1 2 1 5 a2ab 1b a 1 b a 1 b

10. Check students’ work. 11. 83

Practice 9-7 1. no 2. yes 3. yes 4. no 5. dependent 6. independent 7. independent 8. dependent 9. 20% 10a. 0.6 10b. 1 10c. 0.7 10d. 0.6 11a. 23 11b. 23 11c. 23 11d. 61 1 15. 0.16 16. 1 12. about 69.6% 13. 12.5% 14. 20 20 17. 11 18. 55% 19. 38% 12

Guided Problem Solving 9-7 1. a multiple-choice test 2. 3 3. 4 4. 1 5. 41 6. no 7. independent 8. 41; 41; 14 9. P(A) P(B) P(C) = 41 41 14 1 10. 64 11. Check students’ work. 12. 18

9A: Graphic Organizer 1. Rational Functions 2. Answers may vary. Sample: inverse variation, rational functions and their graphs, rational expressions, solving rational equations 3. Check students’ work.

9B: Reading Comprehension 1. y-axis 2. when it is the ratio of two functions, written as a fraction 3. The value 2, substituted for the variable x, results in a value of zero for the denominator, which makes the (x 2 1) function undefined. 4. x 2 2 ? 5. When the value 2 x22 1 is substituted for the variable x, the denominator is zero and the function is undefined. 6. a


1. "21 2. <2.718 3. <3.14 4. 7! means 7 factorial, or 7 3 6 3 5 3 4 3 3 3 2 3 1. 5. 3 : 5 means the ratio of 3 to 5 or 3 . 6. decimal point, read as “and,” separates units 5 and tenths 7. Multiply 7 times 9.

Practice 9-6 4 4. 2 9 5. 9 6. -2 7. -0.2 1. 43 2. 44 3. 211 4 17

9D: Visual Vocabulary Practice/High-Use Academic Words

8. -0.5 9. 3 10. -2 11. 0 12. -17 13. 12 14. 6

1. notation 2. composition 3. arrange 4. pattern 5. approach 6. equivalent 7. apply 8. exclude 9. solve

3 16. no solution 17. -9 18. 7 19. 11 20. 41 15. 16

21. 5 22. -3 23. 0 24. 219 25. -3 26. 18 27. 60 7 25 14 28. -5 29. no solution 30. 12 31. 4 32. 3

116

Algebra 2


3. (2x + 3)2(2x - 3) 4. 10x(x + 3)2(x - 3) 5. 2x

All-In-One Answers


1. 6x(x + 2)(2x - 3) 2. 6(x - 1)(x - 2)2(x + 10)



(continued) 10.


3 2 1

Branch: A piece of a discontinuous graph. Inverse variation: An equation of the form y 5 k x or

xy = k, where k 0.

P(x) Rational function: f(x) 5 , where P(x) and Q(x) are Q(x) polynomial functions and Q(x) 0. t variation: An equation of the form z = kxy, where k 0. Point of discontinuity: Occurs at x = a, if a is a real number for which the denominator of a rational function f is zero.

1 1 2 3

3

11.

3 2 1


9F: Vocabulary Review Puzzle 1. simplest form 2. complex 3. extraneous solution 4. discontinuity 5. independent 6. branch 7. rational 8. dependent 9. combined 10. mutually exclusive

O 1

x

hyperbola; x-axis, y-axis; {x∆x # -3 or x $ 3}, all real numbers

x


x

circle; all lines through center; {x∆-3 # x # 3}, {y∆-3 # y # 3}

3

y

O 1 2

Chapter 10 12.

Practice 10-1 1. (0, 0); (43, 0), (0, 43); {x∆-3 # x # 3}, {y∆-3 # y # 3} 2. (0, 0); (43, 0); {x∆x # -3 or x $ 3}, all real numbers 3. (0, 0); (41, 0), (0, 43); {x∆-1 # x # 1}, {y∆-3 # y # 3} 4. (0, 0); (43, 0), (0, 41); {x∆-3 # x # 3}, {y∆-1 # y # 1} 5. (0, 0); (43, 0), (0, 42); {x∆-3 # x # 3}, {y∆-2 # y # 2} 6. (0, 0); (45, 0), (0, 45); {x∆-5 # x # 5}, {y∆-5 # y # 5} 7. ellipse; y

3 2


21 1 2 3

x


y

x

O

32

x-axis, y-axis; {x∆-2 # x # 2}, {y∆-1 # y # 1}

6 4 2 6

13.

21 1 2

2 3

3 1 32 1

y

x

O

ellipse; x-axis, y-axis; {x∆-1 # x # 1}, {y∆-2 # y # 2}

14.

3 2 1

1 2 3

32

y

2 1 3

1 1 2

2

6

O 1 2

y

x

O 2 3

circle; all lines through center; {x∆2"2 # x # "2}, {y∆2"2 # y # "2}

2 3

3 9.

O

y

2 1

2 3

8.

2 2 4 6

y

x

O 1

All-In-One Answers

3


15.

3 1 3

1 1

y

x

O 1

3


3

Algebra 2

117

3 2

y

x

O

32

ellipse; x-axis, y-axis; {x∆2"2 # x # "2}, {y∆-1 # y # 1}

22.

6 4 2 642 2 4 6

2 3 2 3

17.

3 2 1 321 1 2 3 18.

3 2 1 321 1 2 3 19.

3 2 1 321 1 2 3 20.

6 4 2 642 2 4 6 21.

6 4 2 6

118

2 2 4 6

y

x

O

hyperbola; x-axis, y-axis; {x∆x # 2"2 or x $ "2}, all real numbers

23.

6 4 2 642 2 4 6

1 2 3

24.

y

x

O 1 2 3

y

x

O

hyperbola; x-axis, y-axis; all real numbers, {y∆y # -1 or y $ 1}

hyperbola; x-axis, y-axis; {x∆x # 2"5 or x $ "5}, all real numbers


x


2 4 6

y

O 2 4 6

circle;

y

all lines through center;

2 3 2 3 25.

9 6 3

26.

6 2 6

2 4 6

2 2

x

O 2 3

{x∆213 # x # 13 },

{y∆213 # y # 13 }

x


x


x


y

963 3 6 9

x

O

O

2 3

1 2 3

y

x


y

3 6 9

y

O 2

6

6 y

x

O 2

Algebra 2

6


27.

6 4

y

O

64


16.

(continued)

4 6 4 6

All-In-One Answers




6 4 2 64

x

3 2 1 321 1 2 3


642

y

x

O




642 2 4 6 37.

3

x


1 3

2 4 6

y

321 1 2 3

x


x


x


x


x

42 2 4 39.

3 y

x

O 1 2 3

All-In-One Answers

y

O 2 4 6

y

O 2 4 6

y

O 1

3

y

4 2


6 3 2 1

O

3

2 4 6

33.

1 1

38.

O

642

6 4 2

2 4 6 8

y

642 2 4 6

36.

x

O

8

6

6 4 2 642 2 4 6

y

8642 2 4

32.

x


y

2 4 6

35.

1 2 3

8 6 4 2

6 4 2

6 4 2 4 6

30.

31.

34.

4 6

2 4 6

29.


y

(continued)


1 321 1 2 3

O 2 4

y

x

O 1 2 3


Algebra 2

119

Algebra 2: All-In-One Answers 3 1 21 1

y

x

O


1 2

321 1 2 42.

x

O 1 2 3

32

1 2 3

ellipse; x-axis, y-axis; {x∆2"2 # x # "2}, {y∆22"3 # y # 22"3}

1 , 0b ; x 5 2 1 1 b; y 5 1 13. a0, 2 12 14. a 20 20 12 1 , 0b ; x 5 1 15. a0, 22 34 b; y 5 23 41 16. a2 12 12 1 , 0b ; x 5 2 1 17. (2, -3); x = -2 18. a 32 32 1 b; y 5 2 1 19. (0, 2); y = -2 20. a0, 32 32

y

2 1

6. left 7. right 8. downward 9. (0, -8); y = 8 3 3 1 , 0b ; x 5 2 1 11. a 4 , 0b ; x 5 2 4 12. a 48 48

y

2 1

1. left 2. downward 3. left 4. upward 5. upward 1 b; y = 1 10. a0, 2 32 32

3 41.

Practice 10-2

x

O


1 2 3

1 x2 23. x 5 2 1 y 2 21. x = 2 81 y 2 22. y = 16 12 1 x2 1 x2 24. y 5 2 16 25. y 5 2 12 26. x 5 1y2 8


40.

(continued)

1 y2 27. y 5 1 x2 28. x 5 1 y2 29. x 5 2 24 12 12 1 y2 1 x2 32. y 5 1 x2 30. x 5 2 20 31. y 5 20 28 1 x2 34. x 5 1 y2 35. x 5 1 y2 33. y 5 32 4 24

1. the lamp 2. the very edge of the shadow 3. a plane and a double cone 4. The wall is like the plane and the lamp shade is like the double cone. 5. parabola 6. hyperbola 7. circle 8. Hold the lamp at an angle so that the light from the top of the shade gives a closed, curved oblong area of light on the wall. 9. Answers may vary. 10. Answers may vary.

1 x2 36. y 5 2 16 37. y 5 41 x2 38. x 5 2 1 y 2 12 1 y2 39. x 5 2 14 y 2 40. x 5 2 40 41. y 5 2 1 x 2 12 1 y2 43. y 5 1 x2 44. x 5 1 y2 42. x 5 20 20 12 1 x2 45b. 12.5 in. 46. y 5 1 x2 47. y = x2 45a. y 5 40 8 48. (3, -1); (3, -2); y = 0 y O

x 2

4

2 4 6

120

Algebra 2

All-In-One Answers




(continued)

49. (0, 0); a 1 , 0b ; x = - 18 8

Practice 10-3 1. (x + 5)2 + (y + 2)2 = 16 2. (x - 1)2 + (y - 4)2 = 4

y

3. (x + 2)2 + (y - 5)2 = 1 4. (x + 4)2 + (y + 1)2 = 4

2

5. (x + 3)2 + (y + 4)2 = 9 6. (x - 4)2 + (y - 6)2 = 1

x 2

O

7. x2 + y2 = 9 8. x2 + (y - 1)2 = 4 9. (x + 1)2 + y2 = 36

2

10. (x - 2)2 + y2 = 1 11. x2 + (y + 3)2 = 25

2

12. (x - 4)2 + (y + 4)2 = 2.25 13. (x + 2)2 + (y - 6)2 = 16 14. (x - 5)2 + (y + 1)2 = 1.21 15. (x - 1)2 + (y + 5)2 = 6.25

50. (-1, 1); (0, 1); x = -2


4

16. (x - 2)2 + (y - 3)2 = 14 17. (x - 4)2 + (y + 2)2 = 9 18. (x + 2)2 + (y - 5)2 = 12 19. (x - 1)2 + (y - 7)2 = 49

y

20. (x - 5)2 + (y - 5)2 = 1 21. x2 + (y - 10)2 = 25

2

22. (x + 8)2 + (y + 6)2 = 36 23. (-1, 8); 1 24. (0, -3); 3

x 2

O

25. (-3, -1); "2 26. (6, 0); "5 27. (6, 9); 2 28. (0, 0); 12

2

2

29.

12 8 4



1. meters 2. speed of the wave, in meters per second 1 3. (0, 0) 4. a = 10 ; upward 5. c = 2.5 6. (0, 2.5), y = -2.5 7. Answers may vary. Sample (10, 10), (0, 0), (-10, 10) 8. d 12

31.

s

8 4

6

8

d 33.

16 12 8 4

4

84

2 16 12 8 4

0

4

8

12

t 16

x 4 8 12

12 8 4

x 4 8 12 16

20 12 4

y

O x 4

8 12 34.

y

8 4 16 8

O

x 4 8 12 16

35.

16 8 8 12

36.

y

8 4 x

O 4 8

y x

O 4 8

8 12 16

8 12 8 4

All-In-One Answers

O

32.

y O

y

8 12 16

8 12 16

6

O

1284

8 12 8 4

9. Check students’ work. 10.

8 4

O x 20 12 4 4

6 6 O

30.

y

84

y O

x 4 8 12 16

8 12 16

Algebra 2

121

(continued) 9. Q 46"2, 0 R ;

1. the center and the radius of the circle 2. no 3. (x2 2 6x) 1 (y2 2 2y) 5 24 4. (x2 2 6x 1 9) 1 y2 2 2y 5 24 1 9 5. (x2 2 6x 1 9) 1 (y2 2 2y 1 1) 5 24 1 9 1 1 2 6. (x 2 3) 2 1 (y 2 1) 2 5 Í 6 7. (x 2 h) 2 1 (y 2 k) 2 5 r2 8. 3; 1; "6 9. The center is (3, 1). 10. The radius is "6. 11. Answers may vary. 12. (2, 3), 4

Practice 10-4 1. Q 0, 43"5 R ;

9 6 3 9 63

x 3 6 9

6 9

9 63

y

x

O 3 6 9

6 42

9 6 3 9 63

y

x

O 2 4 6

12 8 4 1284

2 4 6

y 3 x

O

6 42

y

x

O 2 4 6

4 6

Algebra 2

6 4 2 6 42

x

O 2 4 6

O

x 3

17. Q 4"65, 0 R ;

63 x

O 2 4 6

6 9

3 21

y

x

O 1 2 3

1O 21 1 2 1

x

16. Q 0, 4"11 R ;

y

y

4 2O x 642 2 4 6 2 4 18. Q 0, 42"6 R ;

y

O 3 6

y

3

2 3

y

3 2 1

3

O 1 2

9 6

x 4 8 12

14. Q 4"5, 0 R ;

y

3 2

x 4 8 12

O

2 3

15. Q 4"15, 0 R ;

8. Q 0, 4"21 R ;

6 4 2

y

2 1O 1 1 1 2

21

1284

y

12. Q 4"5, 0 R ;

3 6 9

y

12 8 4 8 12

13. Q 0, 4"5 R ;

8 12

7. (44, 0);

3 6 9

4 6

x

6. Q 0, 44"5 R ;

4 6

122

6 42

y

6 9

5. Q 0, 4 72 "3 R ;

6 42

6 4 2

O

x

O

11. Q 0, 44"3 R ;

4. (46, 0);

6 9

6 4 2

6 4 2

y

6 9

4 6

3. Q 0, 4"91 R ;

9 6 3

9 63

2. Q 0, 4"35 R ;

y

O

9 6 3

10. Q 43"13, 0 R ;



6

y

x

x 642

2 4 6

6

4 6

All-In-One Answers



Algebra 2: All-In-One Answers 19. Q 4"2, 0 R ;

20. Q 4"2, 0 R ;

y

3 2

3

2 3

y 2

x 2 3

4. Q 0, "19 R , Q 0, – "19 R

y

3 2

O

32

(continued)

x

O 1

1

3

2 3


3

2

y2

2

y2

5 5

3

y2

2

y2

2

y2

2

2

y2


2 y2 y2 51 5 1 33. x 1 49 100 25

y2

y2

2

x 1 5 1 35. x 1 51 34. 100 100 196 196 2 y2 y2 5 1 37. x 1 51 36 625 20.25 2 2 y2 x2 1 y 5 1 40. x2 1 y 5 1 38. x 2 1 4 5 1 39. 16 4 32 16 2

x 1 36. 400

2

y2

2

y2

2

1. Q 42"2, 0 R ;

6 4 2

y2

2

y2

2

y2

x 1 x 1 5 1 46. x 1 5 1 45. 51 44. 20 9 18 26 16 25 2 2 y2 y2 5 1 49. x 1 y 2 5 1 5 1 48. x 1 49 25 4 5 2 2 y2 y2 51 50. x 1 5 1 or x 1 2500 10,000 10,000 2500

47. x 2 1

Guided Problem Solving 10-4 1. eccentricity = ac 2. 10; 9 3. 0.9

All-In-One Answers

64 2 4 6

2. Q 0, 4"34 R ;

y

x

O 2 4 6

3. Q 4"85, 0 R ;

6 4 2 64 2 4 6

2 4 6

8 x

O 8

x

O 8

8

8 8

8

5. Q 4"10, 0 R ;

64 2 4 6

x

O

y

8

6 4 2

y

4. Q 0, 42"10 R ; y

y2

x 1 51 5 1 43. x 1 5 1 42. x 1 41. 20 4 81 121 100 36 2

x

5

Practice 10-5

29. x4 1 y2 5 1 30. x 1 4 5 1 31. x9 1 18 5 1 5

2

O

7. The shape is close to a circle; the shape is close to a line segment. 8. No; since c2 5 a2 2 b2, c a, so ac , 1. 9. Check students’ work.

2 2 x2 1 y 5 1 28. x2 1 y 5 1 27. 16 25 0.25 2.25

2

x

x

x 1 24. 29 5 1 25. x2 1 5 1 26. x 1 y2 5 1 4 10 5

x 1 32. 36

8

y

x 1 22. 81 5 1 23. x 1 51 4 16 16

2

4

5. 10; "99 9.95; 1; 0.1 6.

21. Q 0, 42"2 R ;

2 1O 1 1 1 2

8 4 O

6. Q 42"17, 0 R ;

y

x

O 2 4 6

6 4 2 64 2 4 6

y

x

O 2 4 6

Algebra 2

123

64 2 4 6

y

x

O 2 4 6

5" 5 9. a0, 4 2 b ;

6 4 2 64 2 4 6

1284 4

y

x

O 2 4 6

64 2 4 6

64

x 2 4 6

10

4 8 12

x

10

x 2 4 6

42

y

x

O 2 4

4 6

15. Q 4"26, 0 R ; 8 x

O 8 8

Algebra 2

x

6

x

x

O 6

6 6

y 9 6 3O 63 3 6 3 6 9

24. Q 0, 44"2 R ;

6 x

y

2O x 642 2 4 6 2 6

2 4 6

y

4 6

2 4 6

6

y

6 4 2O 42 2 4 2 4 6

x 642

22. Q 4"37, 0 R ;

y 6 4 2O

25. Q 0, 42"5 R ;

16. Q 4"29, 0 R ; y

64

y

4 6

23. Q 44"5, 0 R ;

14. Q 0, 45"2 R ;

6 4 2

6 4

4 6

10

y

y

x O 2 4 6

642

y 6 4 2O x 642 2 4 6 2 4 6

20. Q 4"17, 0 R ;

21. Q 42"5, 0 R ;

O

x

O

x

6 4

O

y

2 4 6

y

18. Q 0, 4"41 R ;

4 6

19. Q 0, 4"13 R ;

10

4 6

124

2 4 6

6 4 2

y

O

8

6 4 2

y

13. Q 0, 4"29 R ;

642

x

O

12. Q 0, 42"26 R ;

8 12

6 4

64 2 4 6

y

10. (0, 45);

11. Q 4"73, 0 R ;

12 8 4

6 4 2

17. Q 0, 4"10 R ;


8. Q 4"13, 0 R ;

7. (0, 45);

6 4 2

(continued)

y

2O x 642 2 4 6 2 6 26. Q 45"2, 0 R ;

y 6 4 2O x 642 2 4 6 2 4 6

All-In-One Answers



Algebra 2: All-In-One Answers 27. Q 4"29, 0 R ;

64

x

6

x O 2 4 6

642

y

x O 2 4 6

4 6

x

O 8

8

64

8

33. a0, 4 25 b; 4

x

y 6 4 2O

6

All-In-One Answers

2O x 642 2 4 6 2

6

x 64

y

6

y

2O x 642 2 4 6 2 6

45. Q 42"17, 0 R ;

6 4 2O 2 4 6

y 6 4 2O x 642 2 4 6 2 4 6

44. Q 0, 42"5 R ;

4 2O x 642 2 4 6 2 4

y

6

x

6 36. Q 4"13, 0 R ;

y

6 4 2O 2 2 2 4 6

6

y

y 6 4 2O x 642 2 4 6 2 4 6

42. Q 43"5, 0 R ;

y

2 4 6

43. Q 0, 4"29 R ;

4

6 4 2O x 642 2 4 6 2 4 6

6 4 2

x 4 6

2 4 6

y

4 6 41. Q 0, 4"17 R ;

y 6 4 2O x 642 2 4 6 2 4 6 40. Q 4"41, 0 R ;

x O 2 4 6

642

34. a0, 4 25 b ;

y

35. Q 4"13, 0 R ;

6 4

32. Q 42"5, 0 R ;

8

y

2O x 642 2 4 6 2

39. Q 0, 42"5 R ;

y 6 4 2O 2 2 2 4 6

y

38. (45, 0);

6

30. Q 4"10, 0 R ;

31. Q 4"26, 0 R ;


y

4 6

6 4 All rights reserved.

6 4 4 6

2 4 6

29. Q 0, 4"13 R ;

6

37. Q 0, 4"10 R ;

28. (0, 45);

y 6 4 2O

642

(continued)

x 4 6

64

y 6 4 2O

2 4 6

x 4 6

Algebra 2

125

(continued)

y x2 2 51 11 1.869 3 10 3.752 3 1012

y2 x2 2 51 10 3.112 3 10 3.907 3 1012 2 y2 x2 2 y 5 1 49. x2 48. 49 2 51 32 8.582 3 1010 4.812 3 1010 2 y2 y2 x2 50. x 2 2 51 5 1 51. 25 200 5.858 3 107 1.667 3 107 2 2 2 x2 2 y 5 1 53. x 2 y 51 52. 4489 5625 26,775 3975 2 2 2 x2 2 y 5 1 55. x2 2 y 5 1 56. x2 2 y 5 1 54. 64 336 36 36 64 45 2 2 2 x2 2 y 5 1 58. x2 2 y 5 1 59. x2 2 y 5 1 57. 36 9 28 80 40 2 2 2 2 x 2 y 5 1 61. x 2 y 5 1 60. 64 36 63 81 47.

Practice 10-6 1. ellipse; (-1, 2); 2"30 a21 4

5

6 4 2 64

3. 2

Q 4"10, 2 R ;

, 2b ;

y

x

O 2 4 6

3. ellipse; (-4, 0); Q 24 4 4"3, 0 R ;

x

O

12 6

6 6 9

4

x

4 2

2 (x 2 1) 2 – (y 1 1) 2 5 1 4. subtract 5. add 6. 4

7.

1

42

3

y O

x 2 4 6

8. Answers may vary. 9.

(x 1 1) 2 (y 2 2) 2 2 5 1; 4 9 4

y

2 4

2

y

x

O 1 2 3 4 5

4 2 2 4

y

x

O 2 4 6 8 10

8. circle; (0, 0); "7;

(8, 2), (-2, 2);

8 6 4 2

1

8

7. hyperbola; (3, 2); 3

3 2 1

6. hyperbola;(5,3); Q 5 4 "5, 3 R;

x

1

2 4 6

2 3

4 6 8

y O

x

O

4. circle; (4, 2); 1;

y

9 6

y

O

642

y

4 6

5. circle; (0, -3); 6; 4

6 4 2

4 6

Guided Problem Solving 10-5 2 1. down 1 unit 2. x4 2 y2 5 1

2. hyperbola; (0, 2);

y

3 2 1 x

O 2 4 6 8 10

3 1

y

x

O 1 2 3

2 3

x 4

2 O

2

2

126

Algebra 2


2

46.

All-In-One Answers



Algebra 2: All-In-One Answers 9. circle; (-1, -7); 9;

10. hyperbola; (-1, -1); Q 21 4 "34, 21 R ;

y O

3 63

4 2

x 3

(continued)

9

86

6 9 12 15

2

17. circle; (-4, -1); 4;

y x

O 4


2 1

1 x

O 2 3

1

5

13. circle; (5, -2); 6;

4 2

9 6 3 9 3

x 2 4 6

22.

y

x

O

4 2

4 6 8 10

42

x

O 4 6 8

(y 2 5) 2 (x 1 4) 2 51 2 4 5

(x 2 50) 2 y2 5 1 24. x = 1 (y + 2)2 + 1 2 2304 2 196 2 2 2 (y 2 2) (y 1 5) 2 (x 1 4) 25. x9 1 5 1 26. 1 51 4 9 4

x

O 6 9

27. (x + 1)2 + (y - 2)2 = 36 28. y = -(x + 1)2 + 5 (x 2 2) 2 (y 2 2) 2 2 51 4 5

y

30.

(x 2 2) 2 (y 1 5) 2 51 1 16 25

31.

(x 2 125) 2 y2 2 51 36 15,589

8 6

O

y

29.

8

642

4 6

20. parabola; (2, -1);

16. parabola; (-3, -2);

y

4 2

x

O

23.

x

15. parabola; (1, 2);

y

21. (x + 4)2 + (y - 5)2 = 36

14. circle; (-1, 5); 8;

6 8

64 2 4 6

y

2 4 6

1 2 3 4 5

3 4

2 4 6 8 10


x

O

15

O

6 4 2

y

y

x 2

19. parabola; (2, -1);

Q 2 4 "6, 21 R ;

2 1

6 4 2

6

12. ellipse; (2, -1);

y

y

O 10 642

4 6 8

11. circle; (2, 2); 3;

5 4

6 4

18. hyperbola; (0, 0); Q 42"2, 0 R ;

x

O

86

2 4

2 (y 1 2) 2 32. x 1 51

2.25

6.25

4

Guided Problem Solving 10-6 1. hyperbola 2. (3, -2) 3. (-3, -2) 4. 6 5. (10.2, -2) 6. 7.2 7. b2 = (7.2)2 - 62 = 15.84 8. horizontal 9.

(x 2 h) 2 a

2

2

(y 2 k) 2 b

2

5 1 10.

11. Answers may vary. 12. (y –

(x 2 3) 2 (y 1 2) 2 2 15.84 36 2) 2 2 (x 2 3) 2 5

51 1

10A: Graphic Organizer 1. Quadratic Relations 2. Answers may vary. Sample: parabolas, circles, ellipses, hyperbolas 3. Reading for Problem Solving 4. Choosing Cannot Be Determined 5. Answers may vary. Sample: design, solar energy, machinery, architecture 6. Check students’ work.

All-In-One Answers

Algebra 2

127

(continued)

10B: Reading Comprehension 1. y-axis 2. x-axis 3. upward; to the right 4. downward; to the left 5. b

10C: Reading/Writing Math Symbols 1. the set of all x such that x is a real number 2. the set of all x such that x is greater than zero 3. the set of all y such that y is less than negative 1 4. the set of all x such that x is between 5 and 9 or the set of all x such that x is greater than 5 and less than 9 5. the set of all x and y such that x is equal to y 6. the set of all x and y such that y is equal to 3 times x

10D: Visual Vocabulary Practice 1. vertices of a hyperbola 2. ellipse 3. foci of an ellipse 4. parabola 5. vertices of an ellipse 6. hyperbola 7. radius 8. circle 9. foci of a hyperbola

10E: Vocabulary Check Radius: The distance between the center of a circle and any point on the circumference.

Conic section: A curve formed by the intersection of a plane

6. a n 5 a n 2 1 1 1 where a1 = 2 ; 2 1 3

3

3

7. an = an-1 + 3 where a1 = 36; 51 8. an = an-1 - 6 where a1 = 36; 6 9. a n 5 1 a n 2 1 where a1 = 9.6; 0.3 10. an = 7n; 140 2 11. an = 6n - 4; 116 12. an = n + 4; 24 13. an = n - 2; 18 14. an = 2n + 1; 41 15. an = 0.8n; 16 16. a n 5 n ; 5 17. a n 5 1 ; 1

4 2n 40 2 1 18. a n 5 n 2 ; 19 19. multiply by 2; 32, 64, 128 3 3 20. subtract 5; 19, 14, 9 21. add 0.1; 1.2, 1.3, 1.4 22. add 7; 39, 46, 53 23. multiply by 2; 40, 80, 160 24. subtract 3; -21, -24, -27 25. explicit; 1 , 2 , 1, 4 , 5 3 3 3 3 26. explicit; -5, -2, 3, 10, 19 27. recursive; 5, 8, 17, 44, 125 28. explicit; 0, 1 , 1, 1 1 , 2 29. recursive; 5, -2, 5, -2, 5 2 2 30. recursive; -4, -8, -16, -32, -64 31a. 1, 6, 36, 216 31b. a n 5 6a n 2 1 where a1 = 1 32a. 60° 32b. a n 5 360 n 32c. No polygon has one or two angles.




of the parabola is the same distance from the focus and this line. Circle: The set of all points in a plane at a distance r from a given point. Center: The point that is the same distance from every point on the circle.

1. 2 2. 7 3. 15 4. an = an - 1 + [2n + (n - 1)] 5. 26 6. 40 7.

10F: Vocabulary Review Puzzle E

C

L

I

L

H

Y

P

E

R

A

B

O

I P

R

B

O

L

A

C A

S

A

E

L

I

C

T

R

I

X

F

O

C

U

S

U S

3

4

5

Cards Needed

2

7

15

26

40

8. Yes, the numbers of cards per level is correct. 9. Levels

1

2

3

4

5

Blocks Needed

1

3

6

10

15

1. 96 2. -406.9 3. 36.3 4. -99 5. 464 6. -231 7. 5.5 8. -10.5 9. 171 10. no 11. yes; -3 12. yes; -0.4 13. yes; 5 14. yes; -29 15. yes; 0.3 16. yes; 6 17. yes; 0.2 18. yes; 13 19. 36 20. 21 21. 31 22. 14.5 23. -42 24. -3.5 25. 0 26. -2 27. 21.5 28. -28.5 29. 227 30. 189.5 31. 4.5 32. 14.5 33. 9 34. 3 35. -1 36. -6.5

A E

2

Practice 11-2

E

R

1

A

D D

Levels

I

5

Chapter 11 Practice 11-1 1. an = an-1 + 6 where a1 = -14; 16 2. an = an-1 - 0.3 where a1 = 6; 4.5 3. an = -2an-1 where a1 = 1; -32 4. an = 3an-1 where a1 = 1; 81

37a. a n 5 a n 2 1 1 5 where a1 = 32 37b. 32, 37, 42, 47, 52 37c. a n 5 32 1 5(n 2 1) 37d. 127 people

Guided Problem Solving 11-2 1. 403, 417, 431 2. 403; 14 3. an 5 403 1 (n 2 1)(14) 4. an = 495 5. n = 8 6. 501 7. 6 min 8. 3:20 P.M. = 920; 1 min 9. 403, 417, 431, 445, 459, 473, 487, 501, …; 501 - 495 = 6 min 10. 69

5. a n 5 1 a n 2 1 where a1 = 1; 1 32 2

128

Algebra 2

All-In-One Answers


and a double cone.

Directrix: The fixed line used to define a parabola. Each point


(continued)

Practice 11-3


1. 8 2. 12 3. 4 4. 6 5. 10 6. 4.8 7. yes; 3; 243, 729 8. yes; 2; 64, 128 9. no 10. yes; -2; 64, -128 11. yes; 0.5; 0.0625, 0.03125 12. yes; 0.3; 0.81, 0.243 13. no 14. yes; -0.5; 4, -2 15. no 16. geometric; 1 , 1 17. neither; -9, -14

1. 20 2. Front row of middle section has 10 seats; each of the two side sections has 4 seats 3. Last row of middle section has 29 seats; each of the two side sections has 23 seats 4. Total seats in middle section is 390; each of the two side


9 27 18. geometric; 2, -2 19. arithmetic; 17, 22 20. arithmetic; -11, -14 21. neither; 5, -6 22. an = 3(-2)n-1; 3, -6, 12, -24, 48 23. an = 5(3)n-1; 5, 15, 45, 135, 405 24. an = -1(4)n-1; -1, -4, -16, -64, -256 25. an = -2(-3)n-1; -2, 6, -18, 54, -162 26. an = 32(-0.5)n-1; 32, -16, 8, -4, 2

27. an = 2187 a 13 b

n21

; 2187, 729, 243, 81, 27

n-1

28. an = 9(2) ; 9, 18, 36, 72, 144 29. an = -4(4)n-1; -4, -16, -64, -256, -1024 30. an = 0.1(-2)n-1; 0.1, -0.2, 0.4, -0.8, 1.6 31a. about 19.2 in. 31b. 9 mm 32a. an = 2537(1.025)n-1 32b. about 2732 33a. an = 1(1.5)n-1 33b. 1.5 in. 33c. 2.25 in. 33d. about 86.5 in.



1. geometric mean = !product of the two numbers 2. an 5 a1 ? rn21 3–6. Answers may vary: A sample is given 3. 3 and 12; 6 4. 3, 6, 12; 2 5. 768 6. 48 7. 5th term 8. The answers check. 9. Answers may vary. The answer to

20

sections has 270 5. 930 seats 6. middle section: a (n 1 9) ; n51

20

side section: a (n 1 3) 7. $46,950 8. The answers are n51

reasonable. 9. n = 24; d = 6

Practice 11-5 1. converges; yes 2. converges; yes 3. converges; yes 4. diverges; no 5. converges; yes 6. diverges; no 7. 15 8. no sum 9. 23 10. no sum 11. 16 12. 1.5 13. 600 255 14. 4000 15. arithmetic; 126 16. geometric; 1024 17. geometric; 1023 18. arithmetic; 240 19. 79.921875 20. 28,697,812 21. about 74.99 22. 40.5 23. 0.22222222 24. 6300 25. $8553.71 26. $40,928.80 27. 5000 cm 28. about 177.78 mm 29. $2,319,367.05; $4,950,000

Guided Problem Solving 11-5 1. 4 2. 4 3.

step 7 is the same since halfway from the 1st term to the 9th term is the 5th term.

Practice 11-4 1. 4; 0; 3; 6 2. 5; 3; 11; 35 3. 6; 28; 33; 183 4. 4; 13; 28; 82 5. 4; 2.5; 8.5; 22 6. 6; 2; -3; -3 7. 6; 5; 10; 45 8. 4; -4; -7; -22 9. 4; 11; 20; 62 10. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15; 64 11. 5 + 8 + 11 + 14 + 17 + 20 + 23 + 26; 124 12. 4 + 9 + 14 + 19 + 24 + 29 + 34 + 39 + 44; 216 13. 10 + 25 + 40 + 55 + 70 + 85; 285 14. 17 + 25 + 33 + 41 + 49 + 57 + 65; 287 15. 125 + 126 + 127 + 128 + 129 + 130 + 131; 896 7

5

n51 4

n51

16. a (2n 2 1) 17. a (0.3n 1 2) 6

18. a 4n 19. a (23n 1 13) n51 8

n51 7

20. a (4n 2 1) 21. a (10n 1 5) n51

n51

22. sequence; finite 23. series; infinite 24. sequence; infinite 25. series; finite 26. sequence; infinite 27. series; finite 28. -9 29. 39 30. -72 31. -51 32. 4.5 33. 60 34. 1025 stitches 35. 19 musicians; 84 musicians

All-In-One Answers

Stage 1 4

Stage 2 16

Stage 3 64

4. 4, 16, 64 5. 4 6. 4 + 16 + 64 + 256 + 1024 + 4096 7. 5460 8. formula gives 5460 also 9a. $10, $20, $40 9b. $10 + $20 + $40 + $80 + $160 9c. $310

Practice 11-6 For Exercises 1–19, answers are in units2. 1a. 0.5(3.75) + 0.5(3) + 0.5(1.75) + 0.5(0); 4.25 1b. 0.5(4) + 0.5(3.75) + 0.5(3) + 0.5(1.75); 6.25 2a. 0.5(15.5) + 0.5(14) + 0.5(11.5) + 0.5(8); 24.5 2b. 0.5(16) + 0.5(15.5) + 0.5(14) + 0.5(11.5); 28.5 3a. 0.5(1.875) + 0.5(1.5) + 0.5(0.875) + 0.5(0); 2.125 3b. 0.5(2) + 0.5(1.875) + 0.5(1.5) + 0.5(0.875); 3.125 4a. 0.5(4) + 0.5(4.25) + 0.5(5) + 0.5(6.25); 9.75 4b. 0.5(4.25) + 0.5(5) + 0.5(6.25) + 0.5(8); 11.75

Algebra 2

129


(continued)

5a. 0.5(6) + 0.5(6.5) + 0.5(8) + 0.5(10.5); 15.5 5b. 0.5(6.5) + 0.5(8) + 0.5(10.5) + 0.5(14); 19.5 6a. 0.5(2) + 0.5(2.125) + 0.5(2.5) + 0.5(3.125); 4.875 6b. 0.5(2.125) + 0.5(2.5) + 0.5(3.125) + 0.5(4); 5.875 7a. 0.5(14.25) + 0.5(12) + 0.5(8.25) + 0.5(3); 18.75 7b. 0.5(15) + 0.5(14.25) + 0.5(12) + 0.5(8.25); 24.75 8a. 0.5(2) + 0.5(2.75) + 0.5(5) + 0.5(8.75); 9.25 8b. 0.5(2.75) + 0.5(5) + 0.5(8.75) + 0.5(14); 15.25 9a. 0.5(9.75) + 0.5(9) + 0.5(7.75) + 0.5(6); 16.25 9b. 0.5(10) + 0.5(9.75) + 0.5(9) + 0.5(7.75); 18.25 10a. y 12 8

5. 3 units2 6. y 8

4 2 12

4

x

units2

7. 7.5 units2 8. The mean best approximates the area because it is between the other measures known to be larger and smaller than the actual value. 9. 75 , 147 ; 111 16 16 16

10a–b.

4

y All rights reserved.

8 x

O

6

4

10b. 5.5 10c. 9.5 10d. 7.5; the mean 11. 6.75 12. 16.5 13. 9 14. 12 15. 2.25 16. 18 17. 9 18. 6 19. 4.6 20. total feet 21. total number of computers 22. total miles 23. total gallons 24. total molecules 25. total price 26. ; 3.25 units2 y

4 2 x 1

2

3

4

area = 7 units2

4

10c.

y

2

8

x O

2

27. 12

4

6 ; 4.25 units2

y

4 2

8

x 4

1 x

4

O

4

Guided Problem Solving 11-6 1. less 2. greater 3–4. y 8

3

4

area = 15 units2 10d. mean area = 11 units2; The mean best approximates the area because it is between the other measures known to be larger and smaller than the actual value.

11A: Graphic Organizer 1. Sequences and Series 2. Answers may vary. Sample: arithmetic sequences, geometric sequences, arithmetic series, geometric series 3. Answers may vary. Sample: geometry, fund raising, design, crafts 4. Check students’ work.

4 2

130

2

4

Algebra 2

x

All-In-One Answers


4


(continued)


2a.

Rolling Two Number Cubes

1. in a geometric sequence 2. The recursive formula is

Sum

based on knowing the previous term. The explicit formula is based on knowing the ratio. 3. In an-1, n - 1 is a subscript that tells which term you are finding. In r n-1, n - 1 is the exponent that tells you how many times to use the base, r, as a factor. 4. the recursive formula 5. the explicit formula 6. a

5 or less

Greater than 5

Frequency

10

26

Probability

10 36

26 36

2b.


Sum

11C: Reading/Writing Math Symbols means “negative” and is describing a kind of number, so it is an adjective. In 7 - 5, the symbol means “subtract” or “minus” and names a binary operation, so it is a verb that describes an action. 6. Answers may vary. Sample: The letter m alone represents “line m.” The letter m in front of an angle represents “the measure of” angle A.

11D: Visual Vocabulary Practice 1. arithmetic sequence 2. circumscribed rectangles 3. arithmetic mean 4. geometric mean 5. geometric series 6. geometric sequence 7. arithmetic series 8. inscribed rectangles 9. explicit formula

Composite

Frequency

15

21

Probability

15 36

21 36

2c.

Only 1 Cube shows 2

Both cubes show same number

Cubes show different numbers, neither is 2

Frequency

10

6

20

Probability

10 36

6 36

20 36

Numbers showing

3a. Student Pizza Preferences

11E: Vocabulary Check Sequence: An ordered list of numbers. Term: Each number in a sequence. Common ratio: The ratio of consecutive of a

Sausage

56

Cheese

43

Pepperoni

39

Supreme

28

Other pizza

31

No pizza

19

geometric sequence.

3b. sausage: 25.9%, cheese: 19.9%, pepperoni: 18.1%,

Series: The sum of the of a sequence. Limit: The least and greatest integer values of n in summation

supreme: 13.0%, other pizza: 14.4%, no pizza: 8.8%; 100.1%; There is a rounding error of 0.1%.

notation.

3c.

Chapter 12

Pizza No pizza

80%

11F: Vocabulary Review 1. Answers may vary. Sample: A sequence is an ordered list of numbers; a series is the sum of the of a sequence. 2. Answers may vary. Sample: In calculating the area under part of a curve, circumscribed rectangles are partially above the curve while inscribed rectangles are completely under the curve. 3. Answers may vary. Sample: The common difference is the difference between consecutive in an arithmetic sequence. The common ratio is the ratio between consecutive in a geometric sequence. 4. Answers may vary. Sample: An arithmetic sequence is an ordered list of numbers in which the difference between consecutive is constant. A geometric sequence is an ordered list of numbers in which the ratio between consecutive is constant.

100% Probability



60% 40% 20% 0%

3d.

Outcomes

100%

Cheese

80% Probability


1. line AB 2. line segment CD 3. angle A 4. triangle XYZ 5. Answers may vary. Sample: In -5, the symbol

Prime

40%

Sausage or pepperoni Supreme or other

20%

No pizza

60%

0%

Outcomes

Practice 12-1 1a. about 0.66 1b. about 81 persons 1c. about 0.05 1d. about 0.15 1e. about 0.37

All-In-One Answers

Algebra 2

131


(continued)

3e. The sum of the probabilities of pizza categories in part d equals the probability of pizza in part c. The overall total in

4a. 45% 4b. 6% 5. M = male, F = female, C = attend concert,

both is 100.1% (0.1% rounding error). 4a. Check student’s work. 4b. Check student’s work.

N = not attend concert

C

0.45 M

Guided Problem Solving 12-1 1. the ratio of the number of times the event occurs to the number of times the event does not occur 2. A 1:4, B 2:3, C 1:3, D 1:7 3. the probability of each event 4. find the sum

0.55

0.51 0.49

of the number of times it occurred and did not occur

0.49

5. P(A) = 0.2, P(B) = 0.4, P(C) = 0.25, P(D) = 0.125 6. 0.4

0.51

F

5a. about 47% 5b. about 25%

0.2


0.1 A

B C Event

W

X Y Event

P(A and B) 5. 0.6 6. P(A) is equal to P(B) P(A|B). 7. The fact that P(A) = P(A|B) illustrates that the probability of A is the same, regardless of the occurrence of B. 1 9b. 1 8. Yes, the conclusions are the same. 9a. 26 13 9c. They are not equal. The events are dependent.

4. P(A|B) 5

Probability

7. Yes, the answers are reasonable. 8. 0.10 y 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

D

1. The occurrence of B has no effect on the probability of A. 2. P(A) = 0.60; P(B) = 0.25 3. 0.15

Practice 12-3

x Z

1. 23 2. 78 3. 3 4. 110 5. about 93.3; 97; 97 6. about 47.6; 48; 41, 49 7. about 2.6; 2.45; 2.4 8. about 15.7; 15.6; no mode 9. about 418.8; 423; no mode 10. about 1021.9; 1023; 1023 11. about 0.019; 0.019; 0.018, 0.019 12. about 26.4; 27; 29 13. about 44.8; 45; 42, 45, 49 14. about 48.1; 50.5; no mode 15. 18; 16.5; 15 16. about 1.5; 1.5; 1.3, 1.5 17. about 9.2; 9; no mode 18. about 116.2; 116; 114 19. about 4.29; 4.26; 4.25 20. about 32.4; 34; no mode 21.

Practice 12-2 1a. 8.9% 1b. 24.6% 1c. 0.2% 1d. 1.1% 1e. 6.3% 1f. 4.0% 2a. 11.7% 2b. 36.8% 2c. 21.0% 2d. 47.2% 2e. 14.4% 2f. 16.0% 2g. 48.9% 2h. 51.1% 3. about 58.2% 4. D = drizzle, F = fog without drizzle,

0

5

10 15 20 25 30 35

22.

C = cancelled game, P = played game

0.8

C

D 0.3 0.7

P C

0.3 F

1125

1250

1375

1500

40

42

44

46

48

50

52

24.

0.7 P

132

1000

23.

0.2

Algebra 2


N

0.3

10

20

30

40

50

60

All-In-One Answers


Probability

N C


(continued)

25. 174; 188 26. 346; 368 27. 94; 98 28. 22; 86 29a. about 47.4 29b. 47.9 29c. 50.8 29d. 44.1, 47.9, 50.8; Q2 Q3 Q1 38 40 42 44 46 48 50 52 54

Guided Problem Solving 12-3 1. 16 2. 1, 2, 4, 6, 7, 7, 8, 8, 9, 12, 13, 15, 16, 20, 22, 38 3. Q1 = 6.5, Q2 = median = 8.5, Q3 = 15.5, minimum = 1, maximum = 38


4. 0

10

20

30

40

5. 38 6. Q1 = 6, Q2 = median = 8, Q3 = 15, minimum = 1, maximum = 22

7.

0

10

20

random classrooms would be more accurate. 3. The pizza restaurant sells to many different groups of people. The class might not like the same kinds of pizza as the population as a whole. The poll should be of class . 4. The people eating in the restaurant probably are not indicative of the population as a whole, either geographically or economically. The poll should be a random sample of the residents, possibly a random sample from each phone exchange to include people from all the different areas of the county. 5. This excludes the people who are working during the day. ing randomly selected people, either from the phone book or voter registration lists, would be more accurate. 6. This is fairly accurate usually. 7. about 44 8. about 2500 9. about 12,346 10. about 27,778 11. 53%; 416%; 37% to 69% 12. 72%; 44%; 68% to 76% 13. 62%; 48%; 54% to 70% 14. 30%; 46%; 24% to 36% 15. 42%; 43%; 39% to 45%

Guided Problem Solving 12-5 x 4. 63% 1. 408 2. 258 3. sample proportion = n

5. margin of error = 4 1 6. 5% 7. 58% to 68% "n 8. 63%; sample proportion; yes 9a. 17.2% 9b. 12.5% 9c. 4.7% to 29.7%

30

8. The main effect of removing the outlier is a shortening of the long whisker. 9. The median decreases from 8.5 to 8. 10. Yes, the answers are correct.

Practice 12-6 1.

M 0.125

0.5

F 0.125

0.5

M 0.125

0.5

F 0.125

0.5

M 0.125

0.5

F 0.125

0.5

M 0.125

F 0.5

F 0.125

0.5 M 0.5

0.5

69

71

73

75

F

77

Practice 12-4 1. 295.7; 47.4 2. 30.3; 3.2 3. 2.4; 0.1 4. 74.3; 3.9 5. 66.8; 33.1 6. 8; 9.5; 4 7. 189; about 109.6; 114.5 8. 15; about 531.4; 6.5 9. 1.7; 2.3; 1.05 10. 4; 46.7; 2 11. 8; 100.5; 2.5 12. 5 13. 3 14a. about 3.49 14b. about 0.55 14c. 1.7 14d. 2; 1 15a. 33 15b. 18.5 15c. about 88.2 15d. about 10.5 15e. 3 15f. 2 16. +0.375 17. +2.75

Guided Problem Solving 12-4 (x 2 x) 2 1. s2 5 a n 2. s 5

2 a (x 2 x) 3. 5.5 n Å 4. 6.5, -2.5, -3.5, -1.5, -0.5, 1.5 5. 42.25, 6.25, 12.25, 2.25, 0.25, 2.25 6. 6 7. 10.9 8. 3.3 9. The values match. 10. s2 = 41,000; s = 202.5

Practice 12-5

M

0.5

0.5 F 0.5

1a. 87.5% 1b. 50% 1c. 37.5% 2. the weather outcome on a given day, acceptable weather; Check students’ work. 3. asking a person chosen at random; favoring an early curfew; Check students’ work. 4. selecting a part; part is defective; Check students’ work. 5. about 1% 6. about 0.002% 7. about 25% 8. about 38% 9. 0.5 0.4 0.3 0.2 0.1 0 0 1 2 3 4 5 Number of Successes Probability


0.5

M

11.

1. It is most likely that Sample C was largest since it has the smallest standard deviation, implying less variation than Samples A and B. 2. This sample is likely to contain a disproportionate number of readers. Selecting students in

All-In-One Answers

Algebra 2

133


8.

8.2 13.4 18.6 23.8 29 34.2 39.4

0 1 2 3 Number of Successes

Probability

11.

9.

496 556 616 676 736 796 856

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

Probability

0.5 0.4 0.3 0.2 0.1 0

x

10.

17.3 29.6 41.9 54.2 66.5 78.8 91.1

x

11. about 34% 12. about 13.5% 13. about 2.5% 14. about 68% 15. about 16% 16. about 50% 17a. about 6 students 17b. about 37 students 17c. about 156 students 18a. about 3 nails 18b. about 82 nails 18c. about 19 nails 19a. about 10% 19b. about 5 bags 19c. about 40 bags

0 1 2 3 Number of Successes

12.

x

Guided Problem Solving 12-7 1. 63 min 2. 4 min 3. 2.5% 4. 13.5% 5. 16% 6. yes 7. 59 min 8. Yes, the z-score is less than -1. 9. 81.5%

0 1 2 3 4 Number of Successes

13a. 68% 13b. 99% 13c. 97% 13d. 84% 14a. 18% 14b. 6% 14c. 56%

Guided Problem Solving 12-6 1. 99% or 0.99 2. 1% or 0.01 3. nCxpxqn2x 4. n = 10, x = 9 5. 0.0914 or 9.14% 6. n = 10, x = 7 7. 0.0001 or 0.01% 8. There is a malfunction in the machinery that must be corrected. 9. 0.0042 or 0.42%; Yes, it is between 9.14% and 0.01% 10. 0.25 or 25%

12A: Graphic Organizer 1. Probability and Statistics 2. Answers may vary. Sample: probability distributions, analyzing data, standard deviation, working with samples 3. Answers may vary. Sample: social science, genetics, market research, recycling 4. Check students’ work.

12B: Reading Comprehension 1. how probability is affected by a small number of cases 2. probability of getting heads when tossing a coin

Practice 12-7

3. 12 4. experimental probability

1. 53.3 2. 69.9 3. 36.7 4. 28.4 5.

5. 12 6. b

12C: Reading/Writing Math Symbols 59 71 83 95 107 119 131

1. Answers may vary. Sample: -8, 3 2. no 3. yes 4. Answers may vary. Sample: -8, 4 5. yes 6. no 7. the probability of event R, given event Q 8. Answers may

x

6.

vary. Sample: given that the event that follows takes place

55 70 85 100 115 130 145 7.

x

12D: Visual Vocabulary Practice 1. box-and-whisker plot 2. quartiles 3. mean 4. conditional probability 5. frequency table 6. probability distribution 7. z-score 8. interquartile range 9. standard deviation

42 48 54 60 66 72 78

134


Probability

0.5 0.4 0.3 0.2 0.1 0

Algebra 2

x

All-In-One Answers


10.

(continued)


(continued) 3.

12E: Vocabulary Check Median: The middle value in a data set. Outlier: An item of data with a substantially different value from the rest of the items in the data set. Sample: Information gathered from only part of a population. x , where x is the number of times an Sample proportion: n event occurs in a sample of size n. Margin of error: An estimate of error of a sample proportion.

135°

x

x O

O

5.

6.

y 210°

y 270°

x

x

1. mean 2. outlier 3. quartiles 4. median 5. random sample 6. mode All rights reserved.

y

100°



4.

y

O

O

Chapter 13 7.

Practice 13-1 1. not periodic 2. periodic; 2 3. periodic; 3 1 4. any two 4 points on the graph whose distance between them is one period; sample: (0, 2) and (3 1 , 2); 3 1 5. any two points on the graph 3 3 whose distance between them is one period; sample: (0, 0) and (4 1 , 0); 4 1 6. any two points on the graph whose distance 4 4 between them is one period; sample: (0, 2) and (4, 2); 4 7. 2 1 ; 1 8 3 3 1 2 8. 3; 2 9. 2; 3 10. 6; 2 8 11. 6; 1 12. 1 ; 1 13. 4; 2 4 3 4 5 2 1 1 14. 5; 1 8 15. 1 ; 2 16. 4; 2 17. 5; 1 18. 2 12 , 1 58 3 2 2

8.

y

y

330°

x

x

9.

30°

O

O

10.

y

y

x

x O

O 90°


190°

1. 0.2 s 2. 0.5 mV 3. Yes; the y-values repeat in a regular pattern. 4. 5 cycles 5. 5 units 6. 1 sec 7. 1 sec 8. 6 units 9. 3 mV 10. 1.5 mV 11. Check students’ work. 12. The 11.

period is 0.5 s and the amplitude is 1.5 mV.

12.

y

y

Practice 13-2 1.

2.

y

x

x

y

O

O 330°

150° 30°

O

x

60°

x

O

13.

14.

y

y 315°

x

x O

All-In-One Answers

45°

O

Algebra 2

135


y

"2 "2 66. (0, 1); (0, 1) 67. a 2 2 , 2 b ; (-0.71, 0.71)

y 120°

x

x O

O 180°

Guided Problem Solving 13-2 1. Quadrant I 2. negative 3. positive 4. (cos θ, sin θ) 5. cos θ = -, sin θ = + 6. -; -; +; - 7. II and III 8. II 9. If the terminal side of an angle is in Quadrants I or

18.

y

y 145°

x

x O

O 120°

19.

II, then the sine of the angle is positive; otherwise it is not. If the terminal side of an angle is in Quadrants I or IV, then the cosine of the angle is positive; otherwise it is not. 10. Check students’ work. 11. positive

Practice 13-3

20.

y

p 5p 4p p 3p p 1. 4 2. 2 3. 6 4. 6 5. p 6. 3 7. 2 10p 5p 11. 4p 12. 11p 13. 8p 14. 9 8. 3 9. 2p 10. 2p 9 9 9 18 11p 15. 9 16. 180° 17. 360° 18. 150° 19. 135° 20. 270°

y

x

21. 30° 22. 210° 23. 330° 24. 60° 25. 240° 26. 225° O

O 145°

x

355°

21. 260° 22. 300° 23. 135° 24. 215° 25. 12° 26. 345° 27. 122° 28. 124° 29. 340° 30. 61° 31. 49° 32. 322° 33. 16° 34. 150° 35. 27° 36. 30° 37. 300° 38. 80° 39. 190° 40. 10° 41. 20° 42. 98° 43. 120° 44. 46° 45. 240° 46. 100° 47. 138° 48. 30° 49. 233° 50. 17° "2 "2 51. a 2 , 2 b ; (0.71, 0.71) "2 "2 52. a 2 2 , 2 2 b ; (-0.71, -0.71)

"3 27. 315° 28. 120° 29. 20° 30. 40° 31. 2 ; 12 "2 "2 "2 "2 "3 32. 12 ; 2 33. 2 2 ; 2 2 34. 2 2 2

"3 1 "3 "3 35. 2 2 ; 12 36. 2 21; 2 2 37. 2 ; 2 2

1 "3 38. 2 2 ; 2 39. 11.0 in. 40. 39.8 cm 41. 10.5 cm 42. 92.2 cm 43. 2.1 ft 44. 15.7 m 45. about 17.8 in. 46. 1.2 m

"2 "2 53. a 2 2 , 2 b ; (-0.71, 0.71)


"3 "3 55. a 2 , 2 12 b ; (0.87, -0.5) 56. a 2 , 21 b ; (0.87, 0.5)

p 5 330p < 1036.7 mi 8. p radians 7. 3960 ? 12 12 395p p 9. 1580 ? 12 5 3 < 413.6 mi 10. C = 2π (3960)

"2 54. a 2 , 2 "2 b ; (0.71, -0.71) 2 "3 57. a 2 2 , 12 b ; (-0.87, 0.5)

"3 58. a 2 2 , 2 12 b ; (-0.87, -0.5)

"3 "3 59. a 12 , 2 2 b ; (0.5, -0.87) 60. a 12 , 2 b ; (0.5, 0.87)

"3 "3 61. a 2 12 , 2 2 b ; (-0.5, -0.87) 62. a212 , 2 b ; (-0.5, 0.87) 63. (0, -1); (0, -1) 64. (1, 0); (1, 0) 65. (1, 0); (1, 0)

136

Algebra 2


17.

"3 68. a212 , 2 b ; (-0.5, 0.87) 69. -60° 70. 120° 71. 315°

+

+

1. 24 2. 360º 3. 360 5 30 5 15 + 4. 2π radians 24 2 2p p p 5. 24 5 12 radians 6. 12 radians

24,881 24,881 mi; 1036.7 mi 11. C = 2π (1580) 9927 mi; 24 9927 413.6 mi 12. more; Check students’ work. 13. 8 o’clock 24

Practice 13-4 1. 4; 2p; y = 4 sin u 2. 1.5; p ; y = 1.5 sin 4u 2 3. 2; 3p; y = -2 sin 32 u 4. 1; 6p; y = sin 13 u 5. 2.5; p; y = -2.5 sin 2u 6. 4; p; y = -4 sin 2u

All-In-One Answers


15.

(continued)


; y = 2 sin 2u

y

2

(continued) 14. 2

y u

u O

p 2

2

8.

p

O

3p 2

2 ; y = 3 sin u

y

2

p 2

15. 2

p

3p 2

p

3p 2

y u

u O

p

2p

O

3p

2

2

9.

; y = 2 sin 4u

y

2


p 2

16. 4

y u

u O

p 4

2

10. 2

p 2

O

3p 4

p

2p

3p

p 2

p

3p 2

p 3

2p 3

p

p 2

p

3p 2

p 5

2p 5

3p 5

4 ; y = 2 sin 8u

y

17. 2

y u

u O

p 8

2

11. © Pearson Education, Inc., publishing as Pearson Prentice Hall.

2

p 4

O

3p 8

2 ; y = 1.5 sin 6u

y

18. 4

y u

u O

p 6

2

12. 2

p 3

O

p 8

4 ; y = 2.5 sin u

y

19. 4

y

u O

p

2p

u O

3p

2

13. 2

4 y

20. 4

y

u O

p

2p

2

All-In-One Answers

3p

u O 4

Algebra 2

137


(continued) 6.

y

y

2

u O

2p

p

O

u

3p

2

4

6

p

2p

3p

p 2

p

3p 2

2

4

22. about -0.1 23. about 0.2 24. about 0.2 25. 0.3 26. about 0.1 27. about 0.2 28. -0.3 29. about -0.2

7.

y

2

u


2

8.

u

Practice 13-5 2

O

y

4 u

O

p

2p

9.

3p

y

2

2

u O

2. 2

y

3p

2 u

O

2p

p

2

4

10. 4

6

y

2

u O

3. 4

y

4 u

O

p

2p

11. 4

3p

p 2

p

3p 2

2

4

6

y

4

u O

4. 2

y

4 u

O

p

2p

12. 2

3p

4

O

p

2p

4

6

3p

13. 2

p 2

p

3p 2

y u

4

O 2

138

2

2

y u

O

y u

2

5.


1.

y

4


1. the sound wave for the note A above middle C 2. 0.001; 880π 3. the amplitude 4. the number of cycles in 0 to 2π 5. period = 2p 6. 0.001 7. 2p 8. 1 9. 880π 880p 440 b 10. Answers may vary. 11. 480; 1

O

Algebra 2

All-In-One Answers


(continued) 12.

y

4

y

u O

2

4

O

6

4

4

15. 4

13.

y

4

p 2

p

3p 2

u

p 2

p

3p 2

u

p 4

p 2

3p 4

u

p 2

p

3p 2

p 4

p 2

3p 4

y

u O

2

4

6

O


4

4

14.

16. y = 6 cos 2p t 17. y = -5 cos u

4

5

y

18. y = 4 cos 2u 19. y = 3 cos 4u 20. 2p; 1; p; 0, 2p; p , 3p 21. p; 4; 0, p, 2p; p , 3p ; p , 3p , 5p , 7p 2 2

4

4

4

2 2

O

4

4

22. 2p; 5; p; 0, 2p; p , 3p 23. 0.24, 1.85, 2.34, 3.95, 4.43, 6.04 2

2

24. 2.36 25. 1.00, 3.00, 5.00 26. 1.34 27. 0.84, 5.44 28. 0

15. 4

y

29. 2.67, 5.33 30. 4.19 31. 3.14 32. y = 2p cos 2pu

u

33. y = 21 cos 2u

O 4


Guided Problem Solving 13-5 1. 7 ft 2. 5.5 ft 3. 1.5 ft 4. 12 h 22 min 5. 742 min 2p 6. y 5 1.5 cos 742 t 7. less 8. y = -0.5 9. 225.632, 516.368, 967.632, 1258.368 10. 12:17 A.M.- 7:49 A.M., 12:39 P.M.- 8:11 P.M. 11. Answers may vary. 2p 12. y 5 2 cos 720 t

Practice 13-6 1. p; p , 3p 2. 2p; p 3. 4p; 2p 4. p ; p , 3p , 5p , 7p 2 2

16. 4 O 4

17. 4

2 4 4 4 4 p p 3p 5p 7p 9 3 5 7 1 11 5. 2; 1, 3, 5 6. 1; 2 , 2 , 2 , 2 , 2 , 2 7. 2 ; 4 , 4 , 4 , 4 8. p; p , 3p 9. 1; 1 , 3 , 5 , 7 , 9 , 11 2 2 2 2 2 2 2 2

10. 4

y

y

y u O

1

2

18.

p 6

p 3

p 4

p 2

y

u p 2

4

11. 4

p

u

3p 2

O 4

y

3

4

4

O

19. 4

y

u O 4

p 2

p

All-In-One Answers

3p 2

u

u O 4

3p 4

Algebra 2

139


(continued) 28. p 29. p 30. 2p 31. undefined 32. 1 33. -1 4

y

34. undefined

O

1

2

3

u

1 4

1 2

3 4

u

35.

; 200, undefined, -2200

4 y

O 4

Xmin=0 Ymin=–300 Xmax=470 Ymax=300 Xscl=50 Yscl=100

36. 22. 4

y

p 8

O 4

23. 4

; -14.9, -31.1, -50.1

p 4

3p 8

u Xmin=0 Ymin=–300 Xmax=470 Ymax=300 Xscl=50 Yscl=100

y

37. p 6

O 4

24. 4

1 8

4

4

u

1 4

3 8

Xmin=0 Ymin=–300 Xmax=470 Ymax=300 Xscl=50 Yscl=100

u

1. θ is the measure of one of the base angles of the isosceles triangular tiles 2. 140.4 ft2

y

3. p 2

4

4

p 2


O

26.

p 3

; -50, undefined, 50

y

O

25.

p

3p 2

y 4

u

O y u O

4

3 2

3

9 2

4

4. about 1.732 in. 5. about 5.196 in.2 6. about 15.588 in.2 7. 20,217.6 in.2 8. 3891; 1297 9. 27.714; 3891; fewer. 10. 3216

Practice 13-7 1.

4

140

y

y

x O u

O

60

30

2

27.


4

p 8

Algebra 2

p 4

3p 8

2

p 2

p

3p 2

All-In-One Answers


21.


(continued) 9.

y

y

2 x

O

p 2

4

3. 2

p

x O

3p 2

p 2

2

10.

y

4

p

3p 2

y

x O

p 2

2

4. All rights reserved.

2

p

x O

3p 2

4

11.

y

2

p 2

p

3p 2

p 2

p

3p 2

p 2

p

3p 2

p 2

p

3p 2

p

3p 2

p

3p 2

y x

x O

p 2

2

5. 2

p

O

3p 2

2

12.

y

2

y x

x O

p 2

2

6. © Pearson Education, Inc., publishing as Pearson Prentice Hall.

2

p

O

3p 2

2

13.

y

4

y

x O

p 2

2

7. 4

p

O

3p 2

4

14.

y

2

y x

x O

p 2

4

8. 2

p

O

3p 2

p 2

2

15.

y

2

y x

x O 2

p 2

p

3p 2

x

O 2

p 2

16. y = sin x - 2 17. y = cos (x + p) 18. y = cos x + p 4 19. y = sin (x - 3.2) 20. 3; 2p; none; 2 units up 21. 2; 2p; p units left; none 22. 1; p; none; 1 unit up 2

23. 1; 2p; p units right; none 24. 1 ; 2p; none; 3 units down 2 3

All-In-One Answers

Algebra 2

141


(continued)

25. 1; 4p; none; 2 units down

Practice 13-8

26.

1. 0.86 2. 2 3. -1.10 4. -1 5. undefined 6. -1.07 7. 0.58 8. 14.14 9. -1.00 10. undefined 11. -1.01 2" 3 12. 1.41 13. "2; 1.41 14. undefined 15. 3 ; 1.15

y x

O

2

16. 2 17. undefined 18. - "2 ; -1.41 19. undefined 20. 1

4

2" 3 2" 3 ; 1.15 23. ; -1.15 24. 2 3 3 25. 23 26. 25 27. 10 28. - 32 7

4

2

y 2

29.

4

2 x

O

u

2

28. 4 2

O 2

y x

O 2 4

29

2

30. 2

p

3p 2

p 2

p

3p 2

p

3p 2

p

3p 2

p

3p 2

p

3p 2

y u

O 2

2

p 2

4

y

2

y

31.

4

y 2

x

O

u

2

O

30. 2

x 2

32.

4

u O

p 2

2

y x

O

y 2

4

2

31.

p 2

2

y

O

2


27.

21. undefined 22.


4

33. 2

y

4

u

4

32. -2; 2 units to the left 33. 1; 1 unit to the right 34. -1.5; 1.5 units to the left 35. 1; 1 unit to the right 36. p2 , p2 units to the right 37. -p; p units to the left

O

p 2

2

34. 4

y u

Guided Problem Solving 13-7 1. cosine graph and sine graph 2. horizontal 3. p2 units 4. right 5. positive; p2 6. sin x 5 cos (x 2 p2 ) 7. left 8. negative; -p2 9. cos x 5 sin (x 1 p2 ) 10. Answers may p vary. 11. p2 12. T 5 65 sin (12 x 1 p2 ) 1 6

142

Algebra 2

O 4

p 2

All-In-One Answers


(continued)


y 2

1. Periodic Functions and Trigonometry 2. Answers may vary. Sample: exploring periodic data, angles and the unit circle, radian measure, sine function, cosine function, tangent function 3. Check students’ work.

u O

p 2

2

36. 2

p

3p 2


y

1. converting between two units of angle measure: degrees and radians 2. the meaning of a radian: 2p radians a complete circle, or 360° 3. 30° and 60° 4. 1 5. p 6. a 2 2

u O

p 2

2


37. 2

p

3p 2

13C: Reading/Writing Math Symbols 1. p 2. pi 3. S 4. sigma 5. p 6. u 7. theta

y

13D: Visual Vocabulary Practice 1. sine function 2. secant 3. phase shift 4. cosecant 5. coterminal angles 6. cosine function 7. periodic function 8. cotangent 9. unit circle

u O

p 2

2

p

3p 2

13E: Vocabulary Check 38. 1.73 39. undefined 40. 0.36 41. -5.76 42. 1.56 43. 1.02 44. 2.75 45. -2 46a. y 10

t O

1 2

Cosine θ : The x-coordinate of the point at which the terminal side of the angle θ intersects the unit circle.

Central angle: An angle whose vertex is at the center of a circle.

Intercepted arc: The portion of a circle whose endpoints are

46b. about 14.14 ft 46c. 10 ft

on the sides of a central angle of the circle and whose remaining points lie in the interior angle. Radian: The measure of a central angle of a circle that intercepts an arc of equal length to a radius of the circle.



1. cotangent and tangent 2. y 2

1. amplitude 2. clockwise 3. cosine 4. cycle 5. period 6. sine 7. tangent


3 2

1

Periodic function: Repeats a pattern of y-values at regular intervals.

π

2π π

x

3. Domain is all real numbers except odd multiples of p2 ; range

is all real numbers; asymptotes occur every π units at x = . . . p p 3p -3p 2 , - 2 , 2 , 2 , . . . 4. Domain is all real numbers except multiples of p; range is all real numbers; asymptotes occur every π units at x = . . ., -π, 0, π, 2π, 3π... 5. The graphs have the same period and range. 6. Their asymptotes are shifted by p2 .

C L O C K W I S E

T N E G N A T D T

C R N R I C U P I

N Y D E O T W E N

E I C S I Y N R U

T D I L Z E R I O

W N P O E I E O O

E M T R W S R D Y

A M I E P S U E I

p 5p 7. x = p4 ; x = 5p 4 8. Check students’ work. 9. x = 2 ; x = 2

All-In-One Answers

Algebra 2

143


(continued) 16. d = 5.1; &F = 11.3°; &E = 78.7° 17. 771.7 ft 18. 270.9 ft 19a. 3.8° 19b. 4.8° 19c. 2.4° 3"13 19d. 5.1° 19e. 7.2° 19f. 11.2° 20a. 13 ; 0.8

1.–18. Answers will vary 19. -tan2 u 20. csc u 21. sec u 22. cos u 23. 1 24. cos2 u 25. 1 26. csc u 27. sin u 28. 1 29. sec2 u 30. csc u 31. 1 32. 1 33. -1 34. cos u

Guided Problem Solving 14-1 1. To an identity, you should transform one side of the equation until it is the same as the other side. 2

sin u ; cotu 5 cos u 3. a sinu b or sin u 2. tan u 5 cos u cos u sin u cos 2u

4. (1 2 cos 2u) a

2

b 5. sin 2u 2 sin 2u cos 2u cos 2u 6. sin 2u; sin2u cos 2u 7. tan 2u 2 sin 2u 8. Yes, it verifies. 9. sin2ucsc2u 2 sin2u 5 sin2u(csc2u 2 1) 5 sin2u(cot2u) 2 5 sin 2ua cos 2 u b 5 cos 2u sin u sin 2u

Practice 14-2 5p 7p p 4p p 5p 3p 7p 1. 4 , 4 2. 3 , 3 3. 6 , 6 4. 3 , 3 5. 0.85, 2.29 5p 7p 2p 4p p 2p 6. 3.99, 5.44 7. 6 , 6 , 3 , 3 8. 0, 3 , 3 , p p 5p p 3p 2p 4p 9. 2 , 2 , 3 , 3 10. 0.93, 5.36 11. 0, 3 , 3 , p p 5p 3p 7p 5p p 12. 0, 4 , p, 4 13. 0, 3 , 3 14. 0, 4 , p, 4 15a. 15.7° 15b. 11.5° 16. 1.19 + 2pn, 4.33 + 2pn 17. 0.85 + 2pn, 2.29 + 2pn 18. 1.81 + 2pn, 4.47 + 2pn 19. 1.10 + 2pn, 5.18 + 2pn 20. 45° + n ? 360°, 135° + n ? 360° 21. 45° + n ? 360°, 225° + n ? 360° 22. 45° + n ? 360°, 315° + n ? 360° 23. 90° + n ? 360° 24. p 25. p , 3p 2 2

20b. 32 ; 1.5 20c.

2"13 ; 0.6 20d. 2 ; 0.7 3 13

"13 "13 ; 1.2 20f. ; 1.2 21. 45° 22. 60° 23. 60° 3 3 24. 18.9° 25. 36.9° 26. 45° 27. 66.4° 28. 73.0° 29. 48.6° 30. 26.6° 31. 85.2° 32. 6.0°

20e.

Guided Problem Solving 14-3 1. 90 ft 2. 60.5 ft 3. x2 5 902 1 902 4. x 127.28 ft 6 8. θ 3.4° 5. about 67 ft 6. 6 ft 7. tan u 5 100 9. Yes, the answers are reasonable. 10. 100.6 ft

Practice 14-4 1. 14.9° 2. 15.9 3. 15.0 4. 43.9° 5. 136.6 6. 32.6° 7. 27.8° 8. 14.8 9. 11.5 10. 38.2° 11. 12.8° 12. 90.4 13. 32.0° 14. 30.0 15. 69.8 in2 16. 33.3 ft2 17. 1.7 cm2 18. 164.4 in.2 19. 1025.5 ft 20. 2542.4 yd and 1866.4 yd

Guided Problem Solving 14-4 1. triangle with two equal sides 2. 180° 3. x° 1 x° 1 85.9° 5 180° 4. x = 47.05; 47.05° 47.05° 5 sin 85.9° 5. sin 150 6. c = 204; 204 ft 7. Yes, the c answers check. 8. 31.1 yd

Practice 14-5 1. 5.3 2. 3.1 3. 43.0° 4. 12.5 5. 21.8° 6. 35.9° 7. 18.5 8. 32.5° 9. 439.3 10. 72.5° 11. 5.8 12. 3.2 13. 14.5 14. 15.2 15. 77.9 16. 18.2° 17. 66.7° 18. 102.4° 19. 28.7° 20. 73.4° 21. 70.3° 22. 28.7 mi



1. I = the current in amps 2. t = seconds I ; sin21 I ; 1 sin21 I 4. t = 0.0028 5. 0.0028 sec 3. 40 40 60p 40

1. 85 mi 2. 20 mi 3. 65 mi 4. 20 mi 5. d2 5 652 1 202 2 2(65)(20)cos10° 6. d 45.4;

1 1 0.0028 < 0.019 sec 8. Yes, check 6. t = -0.0028 7. 60 the answers. 9. 0.0045 sec; 0.0212 sec

Practice 14-3 1. 4 2. 3 3. 3 4. 43 5. 3 6. 5 7. 53 8. 4 5 5 5 4 4 4 9. d = 17; &F = 28.1°; &E = 61.9° 10. e = 1.7; &F = 30°; &E = 60° 11. d = 2.2; &F = 26.6°; &E = 63.4° 12. d = 2.2; &F = 63.4°; &E = 26.6° 13. f = 500; &F = 0.1°; &E = 89.9° 14. f = 19.4; &F = 67.6°; &E = 22.4° 15. f = 10.4; &F = 60°; &E = 30°

144

Algebra 2


Practice 14-1

about 45.4 mi 7. sin10° 5 sinx° ; x 14.4° or x 45.4 65 180° -14.4° = 165.6° 8. Turn 14.4° left. 9. 4.4° 10. Yes, the answers are reasonable. 11. 8.7 mi

Practice 14-6

2"6 2 "2 "3 "6 1 "2 1. 2 2 2. "3 3. 4. 4 4 "6 2 "2 "2 "2 5. 6. 2 7. 2 2 8. 1 9. "3 4 "3 "3 10. 2 11. 2 12. 22 2 "3

13.–16. Answers may vary 17. cot A 18. sin A

All-In-One Answers


Chapter 14


(continued)

7p 11p p 5p p 5p 19. 6 , 6 20. p 21. 4 , 4 22. 0, p, 6 , 6 , 7p 24. 0 25. No solution 26. 0, 2p , p, 4p 23. p 6 6

3 3 p , 3p p 5p " 27. 3 , 3 28. 2 2 29. 1 30. -1 31. 0 32. 2 2


Guided Problem Solving 14-6 1. 10cos(u 1 60°) 2. 10sin(u 1 60°) 3. cos(A 1 B) 5 cosAcosB 2 sinAsinB 4. 10cos(u 1 60°) =10(cosucos60° 2 sinusin60°) 5. 5cosu 2 5"3sinu 6. sin(A 1 B) 5 sinAcosB 1 cosAsinB 7. 10sin(u 1 60°) =10(sinucos60° 1 cosusin60°) 8. 5sinu 1 5"3cosu 9. (5cosu 2 5"3sinu, 5sinu 1 5"3cosu) 10. Yes, the coordinates are the same. 11. sin 3θ

Practice 14-7


5"2 5"34 "2 7"2 1. 10 2. 10 3. 7 4. 5"2 5. 7 6. 71 7. 34 "34 "34 3"34 8. 2 34 9. 2 3 10. 2 53 11. 12. 2 3 5 5 "3 "3 13.–20. Answers may vary. 21. 2 22. "3 23. 2 2 "3 24. 12 25. Undefined 26. 0 27. 2"3 28. 2 2 #2 1 "2 1 !3 29. 2"3 30. "2 1 !3 31. 2 2

#2 2 "2 1 !3 2 2 "2 1 !3 33. 2 Å 2 1 "2 1 !3 #2 1 "2 "2 2 2 "2 34. 2 35. 36. 37. 1 38. 0 2 Å 2 1 "2

32.

Guided Problem Solving 14-7 1. sin2u 5 2sinucosu 2. cos2u 5 cos2u 2 sin2u or cos2u 5 2cos2u 2 1 or cos2u 5 1 2 2sin2u 3. 2sinucosu 4. 8sinucosu 5. 8sinu 2 3 6. 8sinu 2 3 , 3p , 0.384, 2.758 8. Yes, the answers check. 7. u 5 p 2 2 9. 2cos2u 2 cosu 2 1 5 0; u 5 0, 2p , 4p 3 3

Using Inverses: evaluate inverses of trigonometric functions and solve trigonometric equations; Right Triangles and Trigonometric Ratios: find lengths of sides, and the measures of angles of right triangles; Area and the Law of Sines: find the area of any triangle and use the Law of Sines; Law of Cosines: use the Law of Cosines in finding the area of a triangle; Angle Identities: angle identities, and sum and difference identities; Double-Angle and Half-Angle Identities: double- and half-angle identities

14B: Reading Comprehension 1. early history of trigonometry 2. 150 A.D. 3. 1600 B.C. 4. Hipparchus, Ptolemy, Menelaus, Copernicus 5. astronomy 6. b

14C: Reading/Writing Math Symbols 1. 25 2. -25 3. 12 4. 14 5. 14 6. x + 5 1 2pn and 5p 1 2pn 7. p 6 6

14D: Visual Vocabulary Practice 1. cosine 2. secant 3. cotangent 4. trigonometric identity 5. Law of Sines 6. Transitive Property of Equality 7. Law of Cosines 8. cosecant 9. sine function

14E: Vocabulary Check Trigonometric identity: A trigonometric equation that is true for all values except those for which an expression on either side of the equal sign is undefined. Radian: The measure of a central angle of a circle that intercepts an arc equal in length to a radius of the circle. Function: A relation in which each element of the domain is paired with exactly one element of the range. Tangent function: A function that matches the measure θ of an angle in standard position with the y-coordinate of the point at which the line containing the terminal side of a central angle of the unit circle intersects the tangent line x = 1. Trigonometric ratios for a right triangle: The six different ratios of the sides of a right triangle.

14F: Vocabulary Review 1. h, i 2. e 3. c, g 4. d, f 5. b 6. a 7. m 8. k 9. j 10. l

14A: Graphic Organizer 1. Trigonometric Identities and Equations 2. Answers may vary. Sample: trigonometric identities, solving trigonometric equations using inverses, right triangles and trigonometric ratios, area and the laws of sines, the law of cosines 3. Answers may vary. Sample: physics, construction, surveying, sailing 4. Check students’ work. Chapter: Trigonometric Identities and Equations; Trigonometric Identities: trigonometric identities; Solving Trigonometric Equations

All-In-One Answers

Algebra 2

145

Algebra 2 Work Book Answers 2hee

Overview 3e4r5l

More details w3441

Related Documents 3m3m1z

Algebra 2 Work Book Answers 2hee

Answers Book 2.pdf 3h1x5e

Key To Algebra Book 2 5a3k3r

Work And Power Practice 2 Answers 6t6b28

Algebra 2 2i4k3y

Algebra 2 2i4k3y

More Documents from "Denise" 476z6m

Exhaust Gas Recirculation System Pdf 3x2u4k

Algebra 2 Work Book Answers 2hee

Benguet Corp Vs Cbaa g262f

Experience Certificate Format Letter Pdf 3l4r18

6l6m1j

Communication Technology Update And Fundamentals Pdf 35272a