989 CHAPTER 9 Test Use Cramer’s rule to solve each system of equations. 12. 2x - 3y = -33 4x + 5y = 11 13. x + y - z = -4 2x - 3y - z = 5 x + 2y + 2z = 3 Find the partial fraction decomposition for each rational expression. 14. 9x + 19 x2 + 2x - 3 15. x + 2 x3 + 2x2 + x Evaluate each determinant. 10. 2 6 2 8 -72 11. 3 2 -1 12 0 7 5 8 9 -33 Solve each nonlinear system of equations. 16. 2x2 + y2 = 6 x2 - 4y2 = -15 17. x2 + y2 = 25 x + y = 7 Work each problem. 18. Unknown Numbers Find two numbers such that their sum is -1 and the sum of their squares is 61. 19. Graph the solution set. x - 3y Ú 6 y2 … 16 - x2 20. Maximize the objective function 2x + 3y for the following constraints. x Ú 0 y Ú 0 x + 2y … 24 3x + 4y … 60 21. Jewelry Profits The Schwab Company designs and sells two types of rings: the VIP and the SST. The company can produce up to 24 rings each day using up to 60 total hours of labor. It takes 3 hr to make one VIP ring and 2 hr to make one SST ring. How many of each type of ring should be made daily in order to maximize the company’s profit, if the profit on one VIP ring is $30 and the profit on one SST ring is $40? What is the maximum profit? 22. Find the value of each variable for which the statement is true. c 5 0 x + 6 4 d = c y - 2 0 4 - x w + 7d Perform each operation, if possible. 23. 3£ 2 1 5 3 -4 9§ - £ -2 3 0 6 -1 8§ 25. c 2 4 1 0 -3 5d £ 1 2 3 3 4 -2§ 24. c 1 2d + c 4 -6d + c 2 -7 8 5d 26. c 2 3 -4 5d £ 4 2 7§
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