CHAPTER 6 Review Exercises 407 55. MODELING—Taxi Business Cost Tony’s weekly cost, C, in dollars, of operating a taxi business can be approximated by the equation = + C m 0.20 80, where m is the number of miles driven in a week. a) Draw a graph of weekly cost versus the number of miles driven for up to and including 500 miles driven per week. * b) If, during one week, Tony drove the taxi 150 miles, what would be the cost? $110 c) How many miles would Tony have to drive for the weekly cost to be $104? 120 miles 6.7 In Exercises 56 and 57, solve the system of equations graphically. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent. 56. x y3 5 + = x y 3 3 3 − = * 57. x y2 5 + = x y 2 4 4 + = * In Exercises 58–61, solve the system of equations by the substitution method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent. 58. x y 2 − + = − x y2 5 + = (3, 1) 59. x y2 9 − = y x2 3 = − − − ( 1, 5) 60. x y 2 4 − = x y 3 2 − = − − ( 2, 8) 61. x y 3 1 + = y x 3 9 4 = − − No solution; inconsistent In Exercises 62– 65, solve the system of equations by the addition method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent. 62. x y 2 + = x y3 2 + = − − (4, 2) 63. x y 4 8 16 − = x y2 4 − = An infinite number of solutions; dependent 64. x y 3 4 10 − = x y 5 3 7 + = − (2, 1) 65. x y 3 4 6 + = x y 2 3 4 − = (2, 0) 66. MODELING—Borrowing Money A company borrows $400,000 for 1 year to expand its product line. Some of the money was borrowed at a 3% simple interest rate, and the rest of the money was borrowed at a 6% simple interest rate. How much money was borrowed at each rate if the total annual interest was $16,500? $250,000 at 3%,$150,000 at 6% 67. MODELING—Chemistry In chemistry class, Tom has an 80% acid solution and a 50% acid solution. How much of each solution should he mix to get 100 liters of a 75% acid solution? Mix 83 1 3 of 80% acid solution with 16 2 3 of 50% acid solution. 68. MODELING—Air Conditioner Emily needs to purchase a new air conditioner for the office. Model 1600A costs $950 to purchase and $32 per month to operate. Model 6070B, a more efficient unit, costs $1275 to purchase and $22 per month to operate. a) After how many months will the total cost of both units be equal? 32.5 months b) Which model will be the more cost effective if the life of both units is guaranteed for 10 years? Model 6070B $ $ $ 33. Property Tax The property tax, t, on a house is directly proportional to the assessed value, v, of the house. If the property tax on a house with an assessed value of $155,000 is $2325, what is the property tax on a house with an assessed value of $210,000? $3150 34. Electric Bill An electric company charges $0.162 per kilowatt-hour (kWh). What is the electric bill if 740 kWh are used in a month? $119.88 6.5 In Exercises 35–38, graph the solution set for the set of real numbers on the real number line. 35. x x 8 9 6 4 + ≤ − * 36. x x 3( 9) 4 11 + ≤ + * 37. x5 13 22 + ≥ − * 38. x 8 2 7 − ≤ + ≤ * 6.6 In Exercises 39– 42, graph the ordered pair in the Cartesian coordinate system. 39. ( 2, 1) − * 40. − (2, 2) * 41. ( 4, 3) − * 42. (5, 3) * In Exercises 43 and 44, graph the equation by plotting points. 43. x y 2 − = * 44. x y 2 3 12 + = * In Exercises 45 and 46, graph the equation, using the x- and y-intercepts. 45. x y2 6 − = * 46. x y 4 3 12 − = * In Exercises 47–50, determine the slope of the line through the given points. 47. (1, 3), (4, 7) 4 3 48. (3, 1), (5, 4) − − − 3 2 49. − − ( 1, 4), (2, 3) 7 3 50. − (6, 2), (6, 2) Undefined In Exercises 51 and 52, graph the equation by plotting the y-intercept and then plotting a second point by making use of the slope. 51. y x2 5 = − * 52. y x 2 4 3 − = * In Exercises 53 and 54, determine the equation of the graph. 53. 2 4 2 22 y x = + y x2 4 54. 2 4 2 4 22 22 y x = − + y x 1 $ $ *See Instructor Answer Appendix
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