Q18. A size 6 dress in Country C is size 52 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = 2(x + 20). Find a formula for the inverse of the function described.

a. f ^{-1}(x) = (x - 20)/2

b. f ^{-1}(x) = x - 20

c. f ^{-1}(x) = (x/2) - 20

d. f ^{-1}(x) = (x/2) + 20

Q19. If f(x) = 4^{x} and g(x) = 12, find the point of intersection of the graphs of f and g by solving f(x) = g(x). Give an exact answer.

a. (log _{4} 12, 12)

b. (log _{4} 12, 4)

c. (log _{4} 12, 0)

d. (12, 12)

Q20. Find functions f and g so that f รขยย g = H(x) = (5 - 2x^{3})^{2}.

a. f(x) = 5 - 2x^{3} ; g(x) = x^{2}

b. f(x) = (5 - 2x)^{3} ; g(x) = x^{2}

c. f(x) = x^{2} ; g(x) = 5 - 2x^{3}

d. f(x) = x^{3} ; g(x) = (5 - 2x)^{2}

Q29. Solve the system of equations using Cramer's Rule if it is applicable.

a. x = 9, y = 2, z = 5; (9, 2, 5)

b. x = 8, y = 4, z = 5; (8, 4, 5)

c. x = 4, y = 5, z = 4; (4, 5, 4)

d. x = 8, y = -4, z = -5; (8, -4, -5)

Q30. Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.

a. x = 2, y = 3, z = -7; (2, 3, -7)

b. x = 1, y = 3, z = -4; (1, 3, -4)

c. x = 5, y = 13/2, z = -3; (5, 13/2, -3)

d. x = 1, y = -3, z = -16; (1, -3, -16)

Q33. Write the partial fraction decomposition of the rational expression (4x^{3} + 4x^{2})/(x^{2} + 5)^{2}.

a. (4x - 4)/(x^{2} + 5) + (-20x + 20)/(x^{2} + 5)^{2}

b. (4x + 4)/(x^{2} + 5) + (-20x - 20)/(x^{2} + 5)^{2}

c. (4x + 4)/(x^{2} + 5) + (20x - 20)/(x^{2} + 5)^{2}

d. (4x + 4)/(x^{2} + 5) + (20x + 20)/(x^{2} + 5)^{2}

Q34. Solve the linear programming problem. Minimize z = 11x + 6y + 7 subject to: x = 0, y = 0, x + y = 1.

a. minimum: 7

b. minimum: 18

c. minimum: 24

d. minimum: 13

Q35. Solve the system of equations by elimination.

a. x = 10, y = 0; (10, 0)

b. x = 10, y = 10; (10, 10)

c. x = 0, y = 10; (0, 10)

d. x = 0, y = 0; (0, 0)

Q36. Perform the row operations on the given augmented matrix.

a.

b.

c.

d.

Q37. Solve the system of equations using Cramer's Rule if it is applicable.

a. x = -4, y = 3; (-4, 3)

b. x = -3, y = -4; (-3, -4)

c. x = 4, y = 3; (4, 3)

d. x = 3, y = 4; (3, 4)

Q38. Write the partial fraction decomposition of the rational expression x/(x^{2} - 9x + 20).

a. -4/(x - 4) + 5/(x - 5)

b. -5/(x - 4) + 4/(x - 5)

c. 4/(x - 4) + -5/(x - 5)

d. -4/(x - 4) + -5/(x - 5)

Q39. Solve the system of equations.

a. x = -4, y = 4, z = -3; (-4, 4, -3)

b. x = -3, y = 4, z = -4; (-3, 4, -4)

c. x = -4, y = -3, z = 4; (-4, -3, 4)

d. inconsistent

Q40. Find the value of the determinant.

a. 224

b. 24

c. -72

d. 72

3x + 8-64 -6x + 2y + 7z =-5 4x-4y = 16 456 874

Show transcribed image text 3x + 8-64 -6x + 2y + 7z =-5 4x-4y = 16 456 874