186 Chapter 2 Linear Equations and Inequalities in One Variable Use the perimeter, area, or circumference formula to find the indicated quantity. (See Objective 2.) 65. Find the height of a triangle whose area is 84 m2 and whose base is 12 m. 66. Find the perimeter of the rectangle whose area is 432 in.2 and whose length is 27 in. 67. Find the area of a rectangle if the perimeter is 74 m and whose width is 20 m. 68. Find the radius and area of a circle with circumference 150.72 cm. Use 3.14 for the value of π to approximate answers to two decimal places. Solve each formula for the specified variable. (See Objective 3.) 69. R = xp for p 70. C = 3l + 4w for l 71. 7x + 3y = 21 for y 72. y = 1 4 x - 1 for x 73. 0.05x + 0.02y = 35 for x 74. 0.36x - 0.2y = 216 for y Find the measure of each unknown angle. (See Objective 4.) 75. Find the measure of an angle whose complement is 25º less than the measure of the angle. 76. Find the measure of an angle whose supplement is 54º more than the measure of the angle. 77. Find the measure of an angle whose supplement is 20º less than three times the measure of the angle. 78. The supplement of an angle is 30º more than three times its complement. Find the measure of the angle. Find the measure of each angle labeled in the figure. (See Objectives 5 and 6.) 79. (6a + 5)° (4a – 35)° 80. (9x – 12)° (2x + 44)° 81. (5a + 8)° (2a – 4)° a° 82. In triangle ABC, the measure of angle B is 18° less than the measure of angle A. The measure of angle C is 27° more than the measure of angle A. Find the measure of each angle in the triangle. 41. The quotient of a number and 3 is -12. Find the number. 42. 60% of a number is 9. Find the number. 43. The sum of a number and 15 is the same as three more than twice a number. Find the number. 44. How many nickels will it take to make $8.50? 45. The sum of two consecutive integers is -97. Find the integers. 46. The cost to rent a midsize car for one day is $55 plus $0.32 per mile. The daily cost is represented by the expression 55 + 0.32x, where x is the number of miles driven. How many miles has the car been driven if the cost of the rental car is $167? SECTION 2.4 Solve each equation. If the equation is a contradiction, write the solution as ∅. If the equation is an identity, write the solution as . (See Objectives 1– 4.) 47. 2x - 5 = 5 48. 4(y + 1) - (y - 5) = 3( y + 1) 49. 2 5 x - 4 = 3 10 x 50. 1.2x + 0.8x = 900 51. x - 8 14 + 1 = x + 5 7 52. 0.032x + 0.013(540 - x) = 13.67 53. 5 6 (x - 2) = 1 6 (5x - 8) - 1 3 54. 3 4 a - 5 8 = 1 2 a + 1 4 55. 0.3(a - 1) + 0.5a = 0.4(2a + 9) 56. 0.64x + 1.6(-4.5) = 0.4(x - 17.1) SECTION 2.5 The formula A = P(1 + r)t is used to calculate the amount of money in an account at the end of t years if P dollars are invested at an annual interest rate, r. (See Objective 1.) 57. Find the value of A if $1200 is invested for 2 yr at 1.5% annual interest. 58. Find the value of P if $2521.50 is expected to be accumulated at the end of 2 yr at 2.5% annual interest. The distance d, rate r, and time t of an object in motion can be related by the formula d = rt. (See Objective 1.) 59. Find d if r = 62 mph and t = 2.5 hr. 60. Find t if d = 306 mi and r = 68 mph. The revenue R, unit price p, and sale level x of a product are related by the formula R = xp. (See Objective 1.) 61. Find R if p = $125 and x = 56. 62. Find p if R = $1392 and x = 96. The formula to find the volume of a cylinder with radius r and height h is V = πr2h. Use π = 3.14. (See Objective 1.) 63. Find V if r = 6 in. and h = 15 in. 64. Find h if V = 157 m3 and r = 2.5 m.
hendricks_beginning_algebra_1e_ch1_3
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