1. Solve the following equation. Determine whether the equation is an identity, conditional equation, or an inconsistent equation: 3-5(2x+1)-2(x-4)=0 a. 1/4, identity b. 1/6, inconsistent c. 1/9, conditional d. 1/2, conditional 2. Find the slope of the line passing through each pair of points or state that the slope is undefined: (0, a) and (b, 0) a. M=-a/b b. Undefined c. M=a/b d. M=-a/ab 3. Find the slope of the line passing through each pair of points or state that the slope is undefined: (a, b) and (a, b + c) a. =-b/abc b. =b/ab c. Undefined Slope d. =a/abc 4. Find all the zeros of each polynomial function and write the polynomial as a product of linear factors. a. -2, 1/2, +- i ; f(x) = (x - i)(x + i)(x + 2)(2x - 1) b. 2, 1/2, +- i ; f(x) = (x - i)(x - i)(x + 2)(2x - 1) c. -2, 1/2, +- i ; f(x) = (x + i)(x + i)(x + 2)(2x - 1) d. -1, 1/2, +- i ; f(x) = (x - i)(x + i)(x + 2)(2x + 1) 5. Solve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms to a decimal approximation, of two decimal places, for the solution: a. { ln 10, 478 + 3/5}; 2.45 b. { ln 10, 376 + 3/5}; 1.78 c. { ln 12, 402 + 2/5}; 2.16 d. { ln 10, 277 + 3/8}; 1.57 6. a. b. c. d. Solve the following system: {(2, -3), ( -1, 4)} {(4, -8), ( -2, 4)} {(1, -2), ( -2, 9)} {(4, -3), ( -3, 4)} 7. Solve the following system of equations using matrices: x + 2y - z = -3 2x - 4y + z = -7 -2x + 2y - 3z = 4 a. {(-4, 1/2, 0)} b. {(-3, 1/2, 1)} c. {(-2, 1/2, -1)} d. {(3, 1/2, 2)} 8. Locate the foci and find the equations of the asymptotes. a. foci: (1, -1+-2v4); asymptotes: (y + 2) = 1/2 (x - 2) b. foci: (1, -2+-2v3); asymptotes: (y + 2) = 1/2 (x - 2) c. foci: (1, -2+-2v5); asymptotes: (y + 2) = 1/2 (x - 1) d. foci: (1, -2+-2v7); asymptotes: (y + 2) = 1/2 (x - 2) 9. Locate the foci and find the equations of the asymptotes: (x - 1)2- (y - 2)2 = 3 a. foci: (1 {16, 2); asymptotes: (y - 2) = {(x - 1) b. foci: (1 {12, 2); asymptotes: (y - 3) = {(x - 3) c. foci: (1 {12, 2); asymptotes: (y - 1) = {(x - 1) d. foci: (1 {14, 2); asymptotes: (y - 2) = {(x - 1) 10. In a class of 50 students, 29 are Democrats, 11 are business majors, and 5 of the business majors are Democrats. If one student is randomly selected from the class, find the probability of choosing: (a) Democrat who is not a business major. (b) A student who is neither a Democrat nor a business major. a. a. 11/25 b. 4/10 b. a. 12/25 b. 3/10 c. a. 9/25 b. 6/10 d. a. 7/25 b. 5/10