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Algebra Supplement Part 2 Solve the equation. 1) 153 = 10x + 13 Finite Math Name: _______________________________ 17) The area of a circle with radius r is given by the formula A = πr2 . Find the area of a circle with radius 9 centimeters. Use 3.14 for π. 2) 80 = 15x + 5x 18) When a ball is thrown upward at a speed of 18 m/s, its height s above the ground (in meters) after t seconds is given by the formula s = 18t - 4.9t2 . Find the height of the ball after 3) 13x - 7x = -12 4) -9b + 4 + 7b = -3b + 9 3 seconds. 5) 6y - 4 = -1 - 7y Solve the formula for the indicated letter. 1 19) A = bh, for h 2 6) -5b + 9 = -7 + 8b 7) 2x x - = 3 5 3 8) p 3p - = 5 8 3 9 20) F = C + 32 for C 5 21) a + b = s + r for s 22) 1 1 + = c for b a b 23) 1 1 1 + = for c a b c 9) -3.4q = -20 - 1.4q 10) 8x - (2x - 1) = 2 11) (y - 4) - (y + 4) = 6y 12) 24) S = 4πr2 , for r2 (surface area of a sphere with radius r) 1 3 1 2 10x - - = 6 4 4 3 Solve. 25) What is 10% of 500 Solve. Label any contradictions or identities. 13) 3(x + 6) = 3x + 18 26) What number is 120% of 310 14) 12m + 96 = 3(4m + 32) 27) 79 is 50% of what number? 15) 18(x + 3) = 2(9x + 1) + 52 28) 199 is 32% of what number? Solve the problem. 16) The perimeter of a rectangle with length L and width W is given by the formula P = 2L + 2W. Find the perimeter of a rectangle with length 7 meters and width 9 meters. 29) 912 is what percent of 787? 30) What percent of 118 is 59? 1 31) During one year, the Greenʹs real estate bill included $269 for city services. The fire department received 30% of that amount. How much money went to the fire department? 43) In order for a chemical reaction to remain stable, its Celsius temperature must be no more than 51.33°C. Find the Fahrenheit temperatures at which the reaction will remain 9 stable. (F = C + 32) 5 32) During one year, the Schmidtʹs real estate bill included $262 for miscellaneous services. Of this amount, 66% went to the library fund. How much money did the library receive? 44) If the formula R = -0.037t + 50.1 can be used to predict the world record in the 400-meter dash t years after 1925, for what years will the world records be 47.3 seconds or less? Solve the problem. 33) On Monday, an investor bought 100 shares of stock. On Tuesday, the value of the shares went up 8%. How much did the investor pay for the 100 shares if he sold them Wednesday morning for $1458? Round to the nearest dollar if necessary. 45) Company A rents copiers for a monthly charge of $180 plus 12 cents per copy. Company B rents copiers for a monthly charge of $360 plus 6 cents per copy. What is the number of copies above which Company Aʹs charges are the higher of the two? 34) Midtown Antiques collects 2% sales tax on all sales. If total sales including tax are $1219.27, find the portion that is the tax. Round to the nearest cent if necessary. 46) A bag of marbles has twice as many blue marbles as green marbles, and the bag has at least 33 marbles in it. At least how many green marbles does it have? Solve using the addition and multiplication principles. 35) 4z - 1 ≥ 3z + 7 Provide an appropriate response. 47) True or false: The solution of the equation 7y 6 = 7y + 3 is zero. 36) -10y + 3 ≥ -9y + 4 48) What value of K makes this equation equivalent to x = 3? 2x - 9 = K 37) -8 < 8t + 2 - 7t 38) 10x - 8 > 2(4x - 11) 49) What value of K makes this equation equivalent to x = 5? 5x + 15x - 7 = K + 2 39) -18r - 27 ≤ -3(5r + 16) 40) 2 (2x - 1) < -2 3 50) Two angles are complementary. One of the angles is r. How do you express the other angle? Use an inequality to solve the problem. 41) One side of a triangle is 6 cm shorter than the base, x. The other side is 4 cm longer than the base. What lengths of the base will allow the perimeter of the triangle to be at least 25 cm? 51) One positive number is twice another. If the larger number is m, how do you express the other number in terms of m? 52) True or False? If x > 9 then 2x > 18. 42) The area of a triangle must be at most 44 square inches, the base is 8 inches, and the height is x inches. Find the possible values for x. 2