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. π₯ 3 1 | = −2 π₯ 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. π¦ = π₯ + 8 2 2._______(+2) 2 b. π¦ = − π₯ − 5 c. π¦= 2 3 1 3 π₯+2 d. π¦ = π₯ − 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. π(π₯+β)−π(π₯) β , β ≠ 0, for π(π₯) = π₯ 2 − 3π₯ − 2. 4. Find the average rate of change of π(π₯) = π₯ 3 − 2π₯ + 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. 2π₯ + 3π¦ = 6 π₯ − π¦ = 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. π₯ 2 + π¦ 2 = 61 π₯−π¦ =1 7.__________________________(+5) 8. 2π₯ 2 + π¦ 2 = 17 3π₯ 2 − 2π¦ 2 = −6 8.__________________________(+5) 9. π₯ 2 − π₯π¦ − 2π¦ 2 = 0 π₯π¦ + π₯ + 6 = 0 9.__________________________(+5) Write the partial fraction decomposition for each rational expression.(+5 each) 10. 2π₯ 2 −π₯−9 π₯ 3 −π₯ 10._________________________(+5) 2π₯ 2 −13π₯+16 11. (π₯+2)(π₯+1)2 11._________________________(+5) 12. π₯ 2 −111 π₯ 4 − π₯ 2 −72 12._________________________(+5) 13. Maximize π§ = 2π₯ + 3π¦ subject to π₯ ≥ 0, π¦ ≥ 0, π₯ + π¦ ≥ 3, π₯ + π¦ ≤ 9, πππ π₯ + 3π¦ ≥ 6. 13._________________________(+5) 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 81 units of vitamin D. The red vitamin pills cost $0.20 each and contain 7 units of A, 1 unit of C, and 7 units of D. The blue vitamin pills cost $0.40 each and contain 3 units of A, 1 unit of C, and 12 units of D. How many pills should the patient take each day to minimize costs? 14.________________________(+10)