349

Answers to Chapter 4 Exercises Exercise Set 4.1 1. –6 2. 7 3. 53 4. 49 5. –180 6. –225 7. 120 8. 135 9. –375 10. 300 11. –270 12. 675 13. 16 14. –16 15. 105 16. 165 17. –285 18. –1035

19. !25

69 20. 4

21. undefined 22. 5

2

23. !15

4 24. undefined

25. X = 31 26. Y = !4 27. Y = !91 28. X = !13 29. W = !9261 30. W = !576 31. W = 176 32. W = 216

33. M = !1

48 34. M = !

7

72

35. M = !7

192 36. M = !

17

240

37. Q = 0 38. Q = 0 39. Q is undefined 40. Q is undefined

41. !5

3 42. 2

43. 1 44. 6

45. !31

6 46. !

11

6

47. !23

36 48. !

23

18

350

49. !3

2 50. !

5

3

51. !1

7 52. !

8

25

53. 7

30 54. !

5

3

55. P = 48 56. P = 64 57. P = 26.6 58. P = 36.6

59. P = 281

2 60. P = 22

5

6

61. A = 50.24 62. A = 452.16 63. A = 4.5216 64. A = 7.065 65. S = 125.6 66. S = 150.72 67. A = 84 68. A = 180 69. A = 36.55 70. A = 66.04

71. A = 312

3 72. A = 26

1

4

73. A = 1,632.96 74. A ≈ 2,809.86 75. A ≈ 3,401.22 76. A = 16,105.1 77. A ≈ 50,569.47 78. A ≈ 291,911.39 79. A ≈ $10,766.95 80. A ≈ $18,726.11 81. C = 194.05 82. C = 425.6 83. B = 72.85 84. B = 128.05 85. V ≈ 2482.7 cubic inches 86. V ≈ 8908.66 cubic inches 87. C = 15° 88. C = 30° 89. C = –40° 90. C = –25° 91. F = 86° 92. F = 113° 93. F = –4° 94. F = –40°

95. P = 512019683

! 0.2601 96. P = 15128

! 0.1172

97. P = 7

32! 0.2188 98. P = 448

6561! 0.0683

99. P ≈ $6,304.83 100. P ≈ $4,961.36 101. F ≈ $13,728.59 102. F ≈ $29,242.38 103. F ≈ $66,666.94 104. F ≈ $139,314.61

351

Exercise Set 4.2 3. !72x 4. !78x 5. 91x 6. 132x 7. 8x +14 8. 15x + 25 9. !11x !11 10. !14x !18 11. 13x !14 12. !7x ! 7 13. 63x

2 14. 156x2 15. !48y

2 16. 210a2

17. 8y 18. 12y 19. !20y 20. !21y

21. !8

15a2 22. !

1

4x2

23. 25

36x2 24. 9

16b2

25. Associative property of addition 26. Commutative property of addition 27. Identity property of multiplication 28. Associative property of addition 29. Commutative property of multiplication 30. Inverse property of multiplication 31. Zero factor property 32. Multiplication property of zero 33. Commutative property of addition 34. Identity property of multiplication 35. Inverse property of addition 36. Distributive property 37. Distributive property 38. Commutative property of multiplication 39. Multiplication property of 0 40. Zero factor property 41. Inverse property of multiplication 42. Inverse property of addition 43. Associative property of multiplication 44. Identity property of addition 45. Identity property of addition 46. Associative property of multiplication 47. !8x 48. !33x 49. !13x

2 50. !21x3

51. !24x2y3 52. !59x

3y4

53. !20x3y2 54. !33x

3y2

55. !11a3b2+ 8a

2b3 56. !8a

2b3! 8a

3b2

57. !2x2! 5x + 7 58. !7x

2+ 4x ! 5

59. !4x2+ 4x ! 7 60. !12x

2! 9x ! 7

61. !7a !15ab ! 5b 62. !13a + 6ab + 4b 63. !11a ! 7ab ! 4b 64. !20a !12ab + 2b 65. !21uv ! 6v

2 66. !3u2! 22uv +10v

2 67. 9u

2!16uv + 2v

2 68. !8u2!13uv

69. !0.54x ! 3.37y 70. !3.13x ! 8.36y

352

71. !1

20x !

3

2y 72. !

8

21x +

1

12y

73. 1

12x !

1

6xy !

3

2y 74. !

7

6x !

4

3xy +

7

12y

75. 5.6x2! 4.77xy !12.1y

2 76. !2.9x2!10.18xy + 0.92y

2 77. 12x2 !16x ! 48 78. 35x

2! 42x ! 91

79. !30a2! 60a + 75 80. 36a

2!117a +198

81. 9x2! 8x +10 82. 9x

2! 5x +

20

3

83. !6y2+ 3y !

27

4 84. !

10

3y2+5

2y ! 5

85. 21.2x2! 26.8x ! 38.4 86. 29.6x

2! 44.8x ! 67.2

87. !43x2+ 29.5x ! 42.3 88. !27.2x

2! 53.6x + 76

89. 20x2! 40xy ! 45x 90. 96x

2!108xy !156x

91. !24xy + 30y2+ 54y 92. !96xy +156y

2+132y

93. !18x + 20y 94. !17x +14y 95. a +10b 96. 2a ! 27b 97. !11x

2+10x 98. !37x

2+ 36x

99. 16y2 + 9y 100. !24y2 ! 38y 101. !8y2 +14y ! 2 102. 15x2 ! 23x +14 103. 6x2 ! 9x + 29 104. 2x2 + 8x ! 50 105. !0.3x ! 0.8y 106. 4.1x ! 2.7y 107. !5.09a + 9.68b 108. !16.8a +19.83b

109. ! 83x +

4

3y 110. ! 1

6x +

7

20y

111. 112

x !11

40y 112. 23

90x !

1

3y

Exercise Set 4.3 1. x = !8 2. x = !6 3. x = 3 4. x = 5 5. y = !9 6. y = !13 7. a = !7 8. a = !5 9. v = !4 10. v = !5 11. b = 4 12. b = 5 13. x = !7 14. x = !10

353

15. x = !5 16. x = !5

17. x = !1

6 18. x = !

5

12

19. x = !1

2 20. x = !

1

4

21. y = !2.03 22. y = !4.32 23. t = !3.43 24. t = !2.28 25. x = !7 26. x = !16 27. y = !15 28. y = 12 29. s = 8 30. s = 11

31. t = !5

2 32. t = !

11

2

33. b = !9

2 34. b = !

14

3

35. a =9

2 36. a =

1

3

37. x = !18 38. x = 18 39. x = 12 40. x = !12

41. y =9

10 42. y =

5

3

43. a = !2

3 44. a =

4

3

45. x = !15 46. x = !28 47. x = 54 48. x = 36 49. x = !12.5 50. x = !22.8 51. y = !5.4 52. y = !16.9 53. x = 6 54. x = 5 55. y = 5 56. y = 5 57. a = !3 58. a = !5 59. b = !5 60. b = !4 61. s = 5 62. s = !4 63. t = 4 64. t = 6

65. u =7

3 66. u =

5

4

67. v = !7

2 68. v = !

8

3

69. x =1

2 70. x =

4

3

354

71. y = !3

2 72. y = !

1

4

73. x = 6 74. x = !10 75. y = 12 76. y = 12 77. a = 8 78. a = 30 79. x = !8 80. x = !21 81. y = !16 82. y = 30 83. a = 8 84. a = 12 85. b = !20 86. b = !30 87. x = –20 88. x = –11 89. x = 11.8 90. x = 6

91. x = !9

2 92. x = 3

93. y = 4 94. y = 2

95. a = 2 96. a =7

2

97. b =13

4 98. b =

17

2

99. s =10

9 100. s = 2

101. t = 177

102. t = 65

Exercise Set 4.4 1. x = 3 2. x = 3 3. x = !4 4. x = !8 5. y = !7 6. y = !7 7. y = !3 8. y = !3 9. a = !5 10. a = !5

11. a = 5 12. a =7

2

13. b =8

3 14. b =

5

2

15. any number solution 16. no solution 17. no solution 18. any number solution

19. s = !1 20. s = !3

2

355

21. t = 11 22. t = !4

23. t =5

2 24. t =

18

5

25. x =9

8 26. x =

3

4

27. y =6

5 28. y = 3

29. s =15

8 30. s =

25

2

31. t = !13

4 32. t = 3

33. a = !7

2 34. a = !

13

4

35. b = !3 36. b = 3

37. r = !9

2 38. r = !

11

4

39. t = 7,000 40. t = 10,000 41. x = 24 42. x = !1 43. y = 3 44. y = !2

45. a = !4 46. a = !15

2

47. b = !8

9 48. b = !

5

2

49. s = !6

11 50. s =

13

12

51. any number solution 52. no solution 53. no solution 54. any number solution

55. v =9

2 56. v = !

9

5

57. w = 2 58. w = !5 59. x = !5 60. x = !16 61. r = !4 62. r = 4 63. no solution 64. any number solution

65. a =7

8 66. a = !1

67. b = 11 68. b =1

6

356

69. v = !6 70. v =14

13

71. s =15

8 72. s = 0

73. g =9

13 74. p = !

13

4

75. x = !3

10 76. y = !

3

4

Exercise Set 4.5 1. 8 and 26 2. 11 and 38 3. 14 and 38 4. 15 and 39 5. –7 and – 39 6. –12 and –66 7. –25 and –162 8. –15 and –85 9. –8 10. –10 11. –6 12. –12 13. 21 in. and 27 in. 14. 32 in. and 40 in. 15. 20 in. and 40 in. 16. 15 in. and 45 in. 17. width = 6 in., length = 15 in. 18. width = 7 in., length = 15 in. 19. width = 5 m, length = 8 m 20. width = 7 m, length = 12 m 21. width = 6 ft, length = 15 ft 22. width = 9 ft, length = 21 ft 23. width = 8 ft, length = 20 ft 24. width = 8 ft, length = 28 ft 25. width = 7 m, length = 20 m 26. width = 8 m, length = 21 m 27. width = 10 ft, length = 12 ft 28. width = 21 in., length = 23 in. 29. width = 21 m, length = 22 m 30. width = 49 ft, length = 50 ft 31. 55°, 60°, 65° 32. 54°, 62°, 64° 33. 30°, 60°, 90° 34. 18°, 54°, 108° 35. 70°, 70° 36. 45°, 45° 37. 59°, 60°, 61° 38. 50°, 60°, 70° 39. Kyle is 16, Travis is 12 40. Brett is 18, Lia is 13 41. Marble is 25, Frank is 15 42. Jack is 24, Jill is 16 43. Jeremy is 30, Julia is 12 44. Janice is 30, Frank is 12 45. Don is 40, Darlene is 15 46. Fran is 10, Martha is 4 47. Lia is 15 48. Brett is 20 49. Louis is 17 50. Daniel is 13 51. 200 child tickets; 400 adult tickets 52. 250 student tickets; 150 general tickets 53. 800 $25 tickets; 1,200 $40 tickets 54. 1,400 $40 tickets; 1,100 $75 tickets 55. 12,000 $30 tickets; 4,000 $40 tickets 56. 10,000 $75 tickets; 5,000 $100 tickets 57. 60,000 people 58. 70,000 people

357

59. 17 $1 bills, 13 $5 bills 60. 12 $1 bills, 8 $5 bills 61. 13 nickels, 12 dimes 62. 17 nickels, 13 dimes 63. 22 nickels, 8 quarters 64. 27 nickels, 13 quarters 65. 12 $1 bills, 8 $5 bills, 4 $10 bills 66. 14 $1 chips, 8 $5 chips, 8 $10 chips 67. 10 pennies, 8 nickels, 7 quarters 68. 11 pennies, 11 nickels, 8 quarters 69. 12 11 oz cans, 12 15 oz cans, 6 25 oz cans 70. 12 $2.50 pairs, 10 $4 pairs, 8 $6 pairs Chapter 4 Review Exercises 1. 54 2. –240

3. 136 4. 8

3

5. X = 43 6. W = –36

7. Y = !31

600 8. Q is undefined

9. 3

2 10. 6

1

12

11. 4

9 12. 308

111

13. P = 15.4 14. A = 200.96 15. S = 188.4 16. A = 135 17. A ≈ 5,918.41 18. A = $4875 19. C = –25° 20. F ≈ $572,066.54 21. !14x ! 5 22. !156b

2

23. !1

5a2 24. 25

36y2

25. Inverse property of addition 26. Multiplication property of zero 27. Associative property of multiplication 28. Inverse property of multiplication 29. Distributive property 30. Identity property of addition 31. !14y

2 32. !64x2y3

33. !2x ! 6y 34. !18a2b3+ 7a

3b2

35. !5x2! 3x + 4 36. !19a ! 4ab + 2b

37. !10u2!16uv ! 9v

2 38. !5

12x !

3

4xy !

5

6y

39. 42x2! 63x ! 91 40. !30a

2+ 40a + 80

41. 8.5y2! 4y !17.5 42. 35x

2! 60xy ! 40x

2y +10x

43. 53a ! 91b 44. !5y2+ 9y + 8

358

45. 1.4x ! 2y 46. 1

45a !

3

44b

47. x = !13 48. v = !9 49. b = 7 50. y = !9

51. x = 9 52. t = !20

3

53. y = !39 54. a =3

4

55. x = !4 56. a = !5 57. t = 6 58. y = 6 59. a = !12 60. b = 36 61. x = !9 62. y = 14

63. a =14

3 64. b =

13

7

65. x = !5 66. y = 2 67. s = 3 68. t = 4

69. x = 1 70. t = !15

2

71. s = !7 72. y = !7

73. x = 7 74. y =5

18

75. s = !9 76. no solution

77. u = 0 78. v = !4

3

79. 12 and 21 80. –12 81. 2 ft and 3 ft 82. width = 15 m; length = 27 m 83. width = 47 in.; length = 49 in. 84. 67°, 67° 85. Jenny is 9, Frank is 5 86. Travis is 12 87. 180 adult tickets, 120 student tickets 88. 7,000 $60 tickets; 3,000 $75 tickets 89. 24 nickels, 12 quarters 90. 10 $1 chips, 20 $5 chips, 20 $10 chips