A-9 Answers to Selected Exercises (c) 13.21 min; The times differ by 0.38 min. 73. 74 students per year; Enrollment at the University of the Ozarks increased by an average of 74 students per year during this period. 75. 2 77. -5 mg per hr 79. 48 ft per sec 81. (a) C1x2 = 10x + 500 (b) R1x2 = 35x (c) P1x2 = 25x - 500 (d) 20 units; do not produce 83. (a) C1x2 = 400x + 1650 (b) R1x2 = 305x (c) P1x2 = -95x - 1650 (d) R1x2 6C1x2 for all positive x; do not produce, impossible to make a profit 85. 25 units; $6000 87. 3 88. 3 89. the same 90. 110 91. 2110 92. 3110 93. The sum is 3110, which is equal to the answer in Exercise 92. 94. B; C; A; C 95. The midpoint is 13, 32, which is the same as the middle entry in the table. 96. 7.5 Chapter 2 Quiz [2.1] 1. 141 2. 2010: 7.07 million; 2014: 6.63 million 3. y x (–1, 3) (1, 3) (0, 4) (2, 0) (–2, 0) y = –x2 + 4 0 31. A 33. D 27. x y –2 2x + 4 = 0 0 5-26; 1-∞, ∞2 29. x y 5 –x + 5 = 0 0 556; 1-∞, ∞2 35. y = 3x + 4 −10 −10 10 10 37. 3x + 4y = 6 −10 −10 10 10 39. A, C, D, E 41. 2 5 43. -2 45. 0 47. 0 49. undefined 51. (a) m= 3 (b) x y (–1, 2) (0, 5) y = 3x + 5 0 53. (a) m= - 3 2 (b) x y (0, 0) (2, –3) 2y = –3x 55. (a) m= 5 2 (b) x y (2, 0) (0, –5) 5x – 2y = 10 0 59. x y (6, –5) (3, –4) 2 0 61. x y (3, 4) (– , 4) 1 2 0 57. x y 1 1 (–1, 3) (1, 6) 0 63. x y 0 3 (– , 3) 5 2 (– , –2) 5 2 65. -$4000 per year; The value of the machine is decreasing $4000 each year during these years. 67. 0% per year (or no change); The percent of pay raise is not changing—it is 3% each year during these years. 69. -76.4 thousand per year; The number of high school dropouts decreased by an average of 76.4 thousand per year from 1980 to 2016. 71. (a) The slope -0.01717 indicates that the average rate of change per year of the winning time for the 5000-m run is 0.01717 min less. The slope is negative because the times are generally decreasing as time progresses. (b) The Olympics were not held during World Wars I and II. [2.2] 4. (4, 0) (–4, 0) x2 + y2 = 16 y x (0, 4) 0 (0, –4) 5. radius: 117; center: 12, -42 [2.3] 6. 2 7. domain: 1-∞, ∞2; range: 30, ∞2 8. (a) 1-∞, -32 (b) 1-3, ∞2 (c) none [2.4] 9. (a) 3 2 (b) 0 (c) undefined 10. 2452 people per day 2.5 Exercises 1. 4; 3 3. x 5. - 6 7 7. D 9. C 11. 2x + y = 5 13. 3x + 2y = -7 15. x = -8 17. y = -8 19. x - 4y = -13 21. y = 2 3 x - 2 23. x = -6 (cannot be written in slope-intercept form) 25. y = 4 27. y = 5x + 15 29. y = -4x - 3 31. y = 3 2 33. 1-2, 02; does not; undefined; A0, 1 2B ; does not; 0 35. slope: 3; y-intercept: 10, -12 x y 2 1 y = 3x – 1 0 37. slope: 4; y-intercept: 10, -72 x y –3 –7 7 4 4x – y = 7 0 39. slope: - 3 4 ; y-intercept: 10, 02 x y 4 –3 4y = –3x 0 41. slope: - 1 2 ; y-intercept: 10, -22 x y –4 –2 x + 2y = –4 0
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