42. According to the model in Exercise 41, what was the number of cell phone subscribers (in millions) in 2007? 43. What is the net worth of a family with $2,250,000 in assets and $125,000 in liabilities? 44. What is the net worth of a family with $76,500 in assets and $234,500 in liabilities? 45. The volume of a cylinder is given by πr2h, where r is the radius and h is the height of the cylinder. Find the volume of a cylinder that has a radius of 7.2 in. and a height of 3.5 in. Round answer to the nearest hundredth. 46. The volume of a cylinder is given by πr2h, where r is the radius and h is the height of the cylinder. Find the volume of a cylinder that has a radius of 2.4 in. and a height of 10.5 in. Round answer to the nearest hundredth. SECTION 1.3 Find the additive and multiplicative inverse of each expression. Assume that all denominators are nonzero. (See Objective 1.) 47. - 23 12 48. –17 49. –12 50. 25 51. 5 x + 3 52. x - 5 2 Identify the property that was used to write each equation. (See Objective 2.) 53. (4a - 19) + 45b = 4a + (-19 + 45b) 54. (5x - 8) + 12y = 5x + (-8 + 12y) 55. 3(v - u) · 12 = 3(v - u) · 12 56. 23(g + h) · 47 = 23(g + h) · 47 57. (a + b)(c + d ) = (a + b)c + (a + b)d 58. (a + b)(c + d ) = (c + d )(a + b) Simplify each expression. (See Objectives 2 and 3.) 59. 6m(m - 2) + 3(m2 - 7) 60. 14b(3b + 2) - 9(b2 + 3) 61. 2 3 x - 1 6 - 5 6 x + 7 4 62. 2 5 x - 7 3 - 3 10 x + 1 2 63. a3 - 15a2 + 2a + 8a2 - 5a + 11 64. 4b3 - 10b2 - 8b + 13 - 9b2 + 11b - 23 65. - 6a1 - 2x 3 b + 8a3x - 5 4 b 66. 4a2x - 7 2 b - 12a1 - x 3 b 67. 1 4 (12x - 5) + 3 5 10(x - 1) + 12 68. 3 5 (15x - 8) - 1 3 6(3 - 2x) - 6 69. 0.024m + 0.036(4300 - m) 70. 0.049x + 0.018(5600 - x) Translate each statement into an algebraic equation, using x to represent the unknown. (See Objective 4.) 71. Half the sum of a number and 6 equals the difference between the number and 20. 72. Double the difference of a number and 4 equals the sum of half the number and 19. Write an algebraic expression that represents each situation. (See Objective 5.) 73. Wesley has collected 120 quarters and dimes. If x represents the number of dimes he collected, write an expression for the number of quarters he collected. 74. Larry has collected 210 nickels and pennies. If x represents the number of nickels he collected, write an expression for the number of pennies he collected. 75. Ming is 10 years older than Fung. If x represents Fung’s age, write an expression for Ming’s age. 76. Owen is 5 years younger than CJ. If x represents CJ’s age, write an expression for Owen’s age. 77. The price of a movie ticket for all shows before 6 p.m. is $2.50 less than the price of a movie ticket after 6 p.m. If x represents the price of a movie ticket after 6 p.m., write an expression for the price of a movie ticket before 6 p.m. 78. The motion picture and television industry provides tremendous economic growth to cities and towns across America. One day of on-site shooting brings about $225,000 to the local economy. In 2010, the motion picture and television industry brought California $0.6 billion more in wages than twice the amount it brought New York. If x represents the amount in wages in billions of dollars brought to New York, write an expression for the amount in wages brought to California. (Source: http://www .mpaa.org/policy/state-by-state) 48 Chapter 1 Real Numbers and Algebraic Expressions
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