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Name:____________________________________________ Period:___________ College Algebra: Ch.10.5-10.8 Test A For every problem, supporting work/reasoning must be shown in order to receive credit for your answer. 1. Solve for x. | a. b. c. d. e. 𝑥 3 1 | = −2 𝑥 2 or -1 1 or -1 3 or -3 0.5 or -0.5 None of the above. 1._______(+2) 2. Find the equation of the line perpendicular to 2x – 3y = -1 and contains the point (-4,2) 3 a. 𝑦 = − 𝑥 + 8 2._______(+2) 2 2 b. 𝑦 = − 𝑥 − 5 c. 𝑦= 2 3 1 3 𝑥+2 d. 𝑦 = 𝑥 − 1 2 e. None of the above. 3. Find the difference quotient, a. 4x + 3 – h b. 2x + 3 – h c. 4x – 3 + h d. 2x – 3 + h e. None of the above. 𝑓(𝑥+ℎ)−𝑓(𝑥) ℎ , ℎ ≠ 0, for 𝑓(𝑥) = 𝑥 2 − 3𝑥 − 2. 4. Find the average rate of change of 𝑓(𝑥) = 𝑥 3 − 2𝑥 + 1 from -3 to -2. a. 21 b. 14 c. 17 d. 12 e. None of the above. 5. Solve the system. a. b. c. d. e. 2𝑥 + 3𝑦 = 6 𝑥 − 𝑦 = 0.5 (2, 1) (1.5, 1) (.5, -1) (2,2) None of the above. 3._______(+2) 4._______(+2) 5._______(+2) Solve each system of nonlinear equations algebraically. 6. xy = 20 x + y = −9 6.__________________________(+5) 7. 𝑥 2 + 𝑦 2 = 61 𝑥−𝑦 =1 7.__________________________(+5) 8. 2𝑥 2 + 𝑦 2 = 17 3𝑥 2 − 2𝑦 2 = −6 8.__________________________(+5) 9. 2𝑥 2 − 3𝑥𝑦 + 8𝑦 + 2𝑥 + 6 = 0 2𝑥 − 3𝑦 + 6 = 0 9.__________________________(+5) Write the partial fraction decomposition for each rational expression.(+5 each) 10. 2𝑥 2 −𝑥−9 𝑥 3 −𝑥 10._________________________(+5) 2𝑥 2 −13𝑥+16 11. (𝑥+2)(𝑥+1)2 11._________________________(+5) 𝑥 2 −111 12. 𝑥 4 − 𝑥2 −72 12._________________________(+5) 13. Maximize 𝑧 = 2𝑥 + 3𝑦 subject to 𝑥 ≥ 0, 𝑦 ≥ 0, 𝑥 + 𝑦 ≥ 3, 𝑥 + 𝑦 ≤ 9, 𝑎𝑛𝑑 𝑥 + 3𝑦 ≥ 6. a. b. c. d. Graph the constraints. Shade the feasible region. Find the coordinates of the feasible region. Maximize 𝑧 = 2𝑥 + 3𝑦. 13._________________________(+10) 14. A doctor has told a patient to take vitamin pills. The patient needs at least 24 units of vitamin A, at least 8 units of vitamin C, and at least 54 units of vitamin D. The red vitamin pills cost $0.30 each and contain 6 units of A, 1 unit of C, and 6 units of D. The blue vitamin pills cost $0.40 each and contain 3 units of A, 1 unit of C, and 9 units of D. How many pills should the patient take each day to minimize costs? a. b. c. d. Graph the constraints. Shade the feasible region. Find the coordinates of the feasible region. Minimize the cost function. 14.________________________(+10)