# logarithmic equation

Multiple Choic e. Circle the c orrec t letter. (4 points each). 1. Solve the following logarithmic equation. Simplify the answer. A)8 2. C) 42 Solve the following linear equation. is/z – 4) – A) 1 3. B) 18 B) 0 None of these -5 D) None of these Solve the following exponential equation. Express your answer correct to two decimal places. A) 1.18 580 C)3.58 B) 2.38 D) None of these Solve the following quadratic equation by the square root method. If needed, write your answer as a fraction reduced to lowest terms. y A) 5 + 7i 5. = C} No solution 62x + 1 4. ii D) 2 lOy + 25 = -49 C} A and B B) 5 – 7i D) A or B Solve the following quadratic equation by completing the square. If needed, write your answer as a fraction reduced to lowest terms. 3x 2 A) 4 or – 3 B) -4 or 3 3x – 36 = 0 C) -4 or – 3 D) 4 or 3 • 6. Add or subtract the following rational expressions, as indicated, and simplify your answer. y+S_y-6 y + 4 – y2 y- 1 A) B) C) D) 7. 16y y-1 -16y+9 (y-l)(y+4) 16y-9 (y-l)(y-4) 16y+9 (y-l)(y+4) Solve the following rational equation and simplify your answer. -x 1 x+2 – x-3 A) x 8. =4 = -4 B) x = -1 C) x = -8 =0 X D) none of these 4 C) x = 2 D) none of these Find the equation of the line in slope-intercept form that passes through the following point with the given slope. Simplify your answer. Point(9,-10);Slope= -;3 A) y = -3x + 7 10. B) x Solve the following radical equation. ✓,-16—X A) x = 4 9. 5 + 3y- 4 B) y = -3x – 7 7 3 C)y=–x-2 2 3 7 D)y=–x+2 2 Find the equation of the line in standard form that passes through the following points. Eliminate any fractions and simplify your answer. (6,-12) and(10, 11) A) y = 23x – 186 B) y 23 93 += –x 4 4 C) 23x – 4y = 186 23 93 D)y=–x-4 4 11. Find the standard form of the equation for the circle with the following properties. Center (-7, -2) and radius 5 A) B) C) D) 12. (x + 7) 2 + (x + 2) 2 = 5 (x – 7) 2 + (x – 2) 2 = 25 (x – 2) 2 + (x – 7) 2 = 5 2 none of these Determine the implied domain of the following function. Express your answer in interval notation. -Jx + 7 + 5 f( x ) A) [7,oo) B) (-oo,-7] 13-14. Consider the following function. q( x) 13. Find the vertex. A. (-4,4) B) (4,-4) D) [-7,oo) C) (7, oo) ( X – 4 )2 4 – C) (-4, -4) D) (4,4) 14. Find the x-intercepts, if any. Express the intercept{s) as ordered pair{s). D) A and B C) A or B B) (2, 0) A. (6, 0) 15. A card is drawn from a standard 52-card deck. Find the probability of drawing a red card or a 4. Write your answer as a fraction in simplest form. A. .2.. 52 16. B )� 13 Consider the following function. w(x) D)2. 13 ci2. 52 = – -Jx + l Describe the transformation of w(x) based on f(x) A) Reflection with the x – axis; B) Shifted 1 unit to the left; C) Shifted 3 units up; D) All of the above + 3 = Jx. 17. Determine the implied domain of the following function. Express your answer in interval notation. 12 f (x) – x+l A) (-1,oo) 18. B) (-oo,-1) U (-1,oo) C) (- oo, oo) D) (-oo,1) n (-1,oo) Find a formula for the inverse of the following function on the given domain, if possible. q (x) = (x + 4) 4 + 4, where x 2::: -4 A) q-1 (x) = VX – 4 B)q-1(x) = Vx + 4- 4 C)q-1(x) = Vx-4 + 4 D)q-1(x) = 1/x-4- 4 19. Find all solutions of the following polynomial equation. x 3 + 3x 2 A){-1,-1,-3} 20. C){-1,-1,3} D) {l, -1, -3} O B) -14 B) -860 = -7 C)-7 Evaluate the determinant of the matrix. A = [-16 14 A) -86 22. 3-x = 0 Find (f g)(l) for the following functions. -14andg(1) f(-7) A) 14 21. B){l,1,3} – D) 7 42 ] 17 C) 86 D) 960 Solve the following polynomial inequality. x(x + 2) (x – 3) < 0 A) (-2,-3) B) (0, 3) C) (-oo,2) U (0,-3) 0) (-oo, -2) u (0, 3) Solve the rational inequality. Express your answer in interval notation. 23. x x+4 >_ _ x-4 x-3 A) 8) C) D) (1s2,-3) u (-4, oo ) (-1s2,3) U (4, oo ) (1s2,3) u (4, oo) (1s2,3) u ( -4, oo ) Indicate which of the following four graphs is the correct graph of this function. 0 p(x) = (1)-x 4 24. B) A) I � l. t 1 . .l. – .I� X t .x I -t- 4- I + X +1 : T- j � }t t f I ii I D) C) 25. I Statistics show that the fractional part of a pair of flashlight batteries, P, that is still good after t hours of use is given by P = 4-o.o2t_ What fractional part of the batteries is still operating after 100 hours of use? Express your answer as a fraction or as a decimal rounded to six decimal places. A)� 16 B)�6 C) 2. 16 D) none of these 26. Determine values of the variables that will make the following equation true, if possible. If not, state “Not Possible”. 2 [-w -2y -2x ] -2z _ 3 [w 4x ] Sy 2z A) w = 10, x = 7, y = -3, z = -4 C) w = -10, x = -7, y = 3, z = 4 27. 112 ] -40 B) w = -10, x = 7, y = – 3, z = 4 D) w =10,x=-7,y=3,z=-4 B) 8 years C) 7.3 years D) none of these B) -3 C) A and B D) none of these Solve for x. A) 5 29. 60 – 57 How long does it take for \$1925 to double if it is invested at 9.5% compounded continuously? Round your answer to two decimal places, if necessary. A) 7 years 28. = [w + Which statement is not true? A) P(n): 1 + 5 + 9 + ··· + (4n – 3) = 2n 2 B) P(n): 7 is a factor of 11n – 4n C) P(n): 2 – n (3n+l) + 5 + 8 + ··· + (3n – 1) = 2 D) All of the above 30. In how many different ways can first-place, second-place, and third-place be decided in a 22-person race? A) 66 B) 132 C) 9240 D) 22 PROBLEM SOLVING. Use the space provided to show your complete work. (6 points each) 31. What is the probability that an 8-digit driver’s license number chosen at random will not have 4 as a digit (express the answer as a fraction in simplest form)? 32. Use a system of equations to solve the following problem. The sum of three integers is 155. The sum of the first and second integers exceeds the third by 81. The third integer is 56 less than the first. Find the three integers. 33. Dwight is saving up money for a down payment on a condominium. He currently has \$3225, but knows he can get a loan at a lower interest rate if he can put down \$4064. If he invests the \$3225 in an account that earns 5.1 % annually, compounded monthly, how long will it take Dwight to accumulate the \$4064? Round your answer to two decimal places, if necessary. 34. The developer of a housing development finds that the sale of the first house gives him a \$250 profit. His profit on the second sale is \$375, and he finds that each additional house sold increases his profit per house by \$125. How many houses did he sell if his profit on the last house sold was \$6000 and his total profit was \$146,875? 35. The total cost of producing a type of truck is given by C(x) = 24000 – 10x + 0.04x 2 , where x is the number of trucks produced. How many trucks should be produced to incur minimum cost?
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