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Part 1Question 1 of 205.0 PointsWrite an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x2?or g(x) = -3x2, but with the given maximum or minimum.?Maximum = 4 at x = -2?A. f(x) = 4(x + 6)2?- 4?B. f(x) = -5(x + 8)2?+ 1?C. f(x) = 3(x + 7)2?- 7?D. f(x) = -3(x + 2)2?+ 4Question 2 of 205.0 PointsUse the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers.?f(x) = x3?- x - 1; between 1 and 2?A. f(1) = -1; f(2) = 5?B. f(1) = -3; f(2) = 7?C. f(1) = -1; f(2) = 3?D. f(1) = 2; f(2) = 7Question 3 of 205.0 PointsIf f is a polynomial function of degree n, then the graph of f has at most __________ turning points.?A. n - 3?B. n - f?C. n - 1?D. n + fQuestion 4 of 205.0 PointsFind the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.f(x) = x2(x - 1)3(x + 2)?A. x = -1, x = 2, x = 3 ; f(x) crosses the x-axis at 2 and 3; f(x) touches the x-axis at -1?B. x = -6, x = 3, x = 2 ; f(x) crosses the x-axis at -6 and 3; f(x) touches the x-axis at 2.?C. x = 7, x = 2, x = 0 ; f(x) crosses the x-axis at 7 and 2; f(x) touches the x-axis at 0.?D. x = -2, x = 0, x = 1 ; f(x) crosses the x-axis at -2 and 1; f(x) touches the x-axis at 0.Question 5 of 205.0 PointsSolve the following polynomial inequality.3x2?+ 10x - 8 ≤ 0?A. [6, 1/3]?B. [-4, 2/3]?C. [-9, 4/5]?D. [8, 2/7]Question 6 of 205.0 PointsWrite an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x2?or g(x) = -3x2, but with the given maximum or minimum.Minimum = 0 at x = 11?A. f(x) = 6(x - 9)?B. f(x) = 3(x - 11)2?C. f(x) = 4(x + 10)?D. f(x) = 3(x2?- 15)2Question 7 of 205.0 PointsFind the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the following rational function.f(x) = x/x + 4?A. Vertical asymptote: x = -4; no holes?B. Vertical asymptote: x = -4; holes at 3x?C. Vertical asymptote: x = -4; holes at 2x?D. Vertical asymptote: x = -4; no holesQuestion 8 of 205.0 PointsBased on the synthetic division shown, the equation of the slant asymptote of f(x) = (3x2?- 7x + 5)/x – 4 is:?A. y = 3x + 5.?B. y = 6x + 7.?C. y = 2x - 5.?D. y = 3x2?+ 7.Question 9 of 205.0 PointsWrite an equation in standard form of the parabola that has the same shape as the graph of f(x) = 2x2, but with the given point as the vertex (5, 3).?A. f(x) = (2x - 4) + 4?B. f(x) = 2(2x + 8) + 3?C. f(x) = 2(x - 5)2?+ 3?D. f(x) = 2(x + 3)2?+ 3Question 10 of 205.0 Points"Y varies directly as the nth?power of x" can be modeled by the equation:?A. y = kxn.?B. y = kx/n.?C. y = kx*n.?D. y = knx.Question 11 of 205.0 PointsFind the coordinates of the vertex for the parabola defined by the given quadratic function.?f(x) = 2(x - 3)2?+ 1?A. (3, 1)?B. (7, 2)?C. (6, 5)?D. (2, 1)Question 12 of 205.0 PointsFind the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.f(x) = x4?- 9x2?A. x = 0, x = 3, x = -3; f(x) crosses the x-axis at -3 and 3; f(x) touches the x-axis at 0.?B. x = 1, x = 2, x = 3; f(x) crosses the x-axis at 2 and 3; f(x) crosses the x-axis at 0.?C. x = 0, x = -3, x = 5; f(x) touches the x-axis at -3 and 5; f(x) touches the x-axis at 0.?D. x = 1, x = 2, x = -4; f(x) crosses the x-axis at 2 and -4; f(x) touches the x-axis at 0.Question 13 of 205.0 PointsThe graph of f(x) = -x3?__________ to the left and __________ to the right.?A. rises; falls?B. falls; falls?C. falls; rises?D. falls; fallsQuestion 14 of 205.0 PointsFind the coordinates of the vertex for the parabola defined by the given quadratic function.?f(x) = -2(x + 1)2?+ 5?A. (-1, 5)?B. (2, 10)?C. (1, 10)?D. (-3, 7)Question 15 of 205.0 PointsFind the domain of the following rational function.f(x) = 5x/x - 4?A. {x │x ≠ 3}?B. {x │x = 5}?C. {x │x = 2}?D. {x │x ≠ 4}Question 16 of 205.0 PointsWrite an equation that expresses each relationship. Then solve the equation for y.?x varies jointly as y and z?A. x = kz; y = x/k?B. x = kyz; y = x/kz?C. x = kzy; y = x/z?D. x = ky/z; y = x/zkQuestion 17 of 205.0 PointsThe difference between two numbers is 8. If one number is represented by x, the other number can be expressed as:?A. x - 5.?B. x + 4.?C. x - 8.?D. x - x.Question 18 of 205.0 PointsFind the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.?f(x) = x3?+ 2x2?- x?- 2?A. x = 2, x = 2, x = -1; f(x) touches the x-axis at each.?B. x = -2, x = 2, x = -5; f(x) crosses the x-axis at each.?C. x = -3, x = -4, x = 1; f(x) touches the x-axis at each.?D. x = -2, x = 1, x = -1; f(x) crosses the x-axis at each.Question 19 of 205.0 PointsUse the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers.f(x) = 2x4?- 4x2?+ 1; between -1 and 0?A. f(-1) = -0; f(0) = 2?B. f(-1) = -1; f(0) = 1?C. f(-1) = -2; f(0) = 0?D. f(-1) = -5; f(0) = -3Question 20 of 205.0 PointsSolve the following polynomial inequality.9x2?- 6x + 1 < 0?A. (-∞, -3)?B. (-1, ∞)?C. [2, 4)?D. ?Part 2Question 1 of 402.5 PointsFind the domain of following logarithmic function.?f(x) = log5?(x + 4)?A. (-4, ∞)?B. (-5, -∞)?C. (7, -∞)?D. (-9, ∞)Question 2 of 402.5 PointsUse properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1.3 ln x – 1/3 ln y?A. ln (x / y1/2)?B. lnx?(x6?/ y1/3)?C. ln (x3?/ y1/3)?D. ln (x-3?/ y1/4)Question 3 of 402.5 PointsApproximate the following using a calculator; round your answer to three decimal places.3√5?A. .765?B. 14297?C. 11.494?D. 11.665Question 4 of 402.5 PointsFind the domain of following logarithmic function.f(x) = log (2 - x)?A. (∞, 4)?B. (∞, -12)?C. (-∞, 2)?D. (-∞, -3)Question 5 of 402.5 PointsUse properties of logarithms to expand the following logarithmic expression as much as possible.logb?(x2y)?A. 2 logy?x + logx?y?B. 2 logb?x + logb?y?C. logx?- logb?y?D. logb?x – logx?yQuestion 6 of 402.5 PointsEvaluate the following expression without using a calculator.8log8?19?A. 17?B. 38?C. 24?D. 19Question 7 of 402.5 PointsUse properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1.?log x + 3 log y?A. log (xy)?B. log (xy3)?C. log (xy2)?D. logy?(xy)3Question 8 of 402.5 PointsUse the exponential growth model, A = A0ekt, to show that the time it takes a population to double (to grow from A0?to 2A0?) is given by t = ln 2/k.?A. A0?= A0ekt; ln = ekt; ln 2 = ln ekt; ln 2 = kt; ln 2/k = t?B. 2A0?= A0e; 2= ekt; ln = ln ekt; ln 2 = kt; ln 2/k = t?C. 2A0?= A0ekt; 2= ekt; ln 2 = ln ekt; ln 2 = kt; ln 2/k = t?D. 2A0?= A0ekt; 2 = ekt; ln 1 = ln ekt; ln 2 = kt; ln 2/k = toeQuestion 9 of 402.5 PointsWrite the following equation in its equivalent exponential form.?5 = logb?32?A. b5?= 32?B. y5?= 32?C. Blog5?= 32?D. Logb?= 32Question 10 of 402.5 PointsThe graph of the exponential function f with base b approaches, but does not touch, the __________-axis. This axis, whose equation is __________, is a __________ asymptote.?A. x; y = 0; horizontal?B. x; y = 1; vertical?C. -x; y = 0; horizontal?D. x; y = -1; verticalQuestion 11 of 402.5 PointsUse properties of logarithms to expand the following logarithmic expression as much as possible.?logb?(x2?y) / z2?A. 2 logb?x + logb?y - 2 logb?z?B. 4 logb?x - logb?y - 2 logb?z?C. 2 logb?x + 2 logb?y + 2 logb?z?D. logb?x - logb?y + 2 logb?zQuestion 12 of 402.5 PointsApproximate the following using a calculator; round your answer to three decimal places.?e-0.95?A. .483?B. 1.287?C. .597?D. .387Question 13 of 402.5 PointsSolve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, to two decimal places, for the solution.2 log x = log 25?A. {12}?B. {5}?C. {-3}?D. {25}Question 14 of 402.5 PointsSolve 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.32x?+ 3x?- 2 = 0?A. {1}?B. {-2}?C. {5}?D. {0}Question 15 of 402.5 PointsSolve the following exponential equation by expressing each side as a power of the same base and then equating exponents.ex+1?= 1/e?A. {-3}?B. {-2}?C. {4}?D. {12}Question 16 of 402.5 PointsThe exponential function f with base b is defined by f(x) = __________, b > 0 and b ≠ 1. Using interval notation, the domain of this function is __________ and the range is __________.?A. bx; (∞, -∞); (1, ∞)?B. bx; (-∞, -∞); (2, ∞)?C. bx; (-∞, ∞); (0, ∞)?D. bx; (-∞, -∞); (-1, ∞)Question 17 of 402.5 PointsUse properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1.log2?96 – log2?3?A. 5?B. 7?C. 12?D. 4Question 18 of 402.5 PointsYou have $10,000 to invest. One bank pays 5% interest compounded quarterly and a second bank pays 4.5% interest compounded monthly. Use the formula for compound interest to write a function for the balance in each bank at any time t.?A. A = 20,000(1 + (0.06/4))4t; A = 10,000(1 + (0.044/14))12t?B. A = 15,000(1 + (0.07/4))4t; A = 10,000(1 + (0.025/12))12t?C. A = 10,000(1 + (0.05/4))4t; A = 10,000(1 + (0.045/12))12t?D. A = 25,000(1 + (0.05/4))4t; A = 10,000(1 + (0.032/14))12tQuestion 19 of 402.5 PointsEvaluate the following expression without using a calculator.Log7?√7?A. 1/4?B. 3/5?C. 1/2?D. 2/7Question 20 of 402.5 PointsFind the domain of following logarithmic function.f(x) = ln (x - 2)2?A. (∞, 2) ∪ (-2, -∞)?B. (-∞, 2) ∪ (2, ∞)?C. (-∞, 1) ∪ (3, ∞)?D. (2, -∞) ∪ (2, ∞)Question 21 of 402.5 PointsSolve each equation by the addition method.x2?+ y2?= 25?(x - 8)2?+ y2?= 41?A. {(3, 5), (3, -2)}?B. {(3, 4), (3, -4)}?C. {(2, 4), (1, -4)}?D. {(3, 6), (3, -7)}Question 22 of 402.5 PointsSolve each equation by the substitution method.y2?= x2?- 9?2y = x – 3?A. {(-6, -4), (2, 0)}?B. {(-4, -4), (1, 0)}?C. {(-3, -4), (2, 0)}?D. {(-5, -4), (3, 0)}Question 23 of 402.5 PointsFind the quadratic function y = ax2?+ bx + c whose graph passes through the given points.(-1, -4), (1, -2), (2, 5)?A. y = 2x2?+ x - 6?B. y = 2x2?+ 2x - 4?C. y = 2x2?+ 2x + 3?D. y = 2x2?+ x - 5Question 24 of 402.5 PointsSolve the following system.x + y + z = 6?3x + 4y - 7z?= 1?2x - y + 3z = 5?A. {(1, 3, 2)}?B. {(1, 4, 5)}?C. {(1, 2, 1)}?D. {(1, 5, 7)}Question 25 of 402.5 PointsWrite the partial fraction decomposition for the following rational expression.?ax +b/(x – c)2?(c ≠ 0)?A. a/a – c +ac + b/(x – c)2?B. a/b – c +ac + b/(x – c)?C. a/a – b +ac + c/(x – c)2?D. a/a – b +ac + b/(x – c)Question 26 of 402.5 PointsSolve the following system.2x + 4y + 3z = 2?x + 2y - z = 0?4x + y - z = 6?A. {(-3, 2, 6)}?B. {(4, 8, -3)}?C. {(3, 1, 5)}?D. {(1, 4, -1)}Question 27 of 402.5 PointsSolve each equation by the substitution method.x2?- 4y2?= -7?3x2?+ y2?= 31?A. {(2, 2), (3, -2), (-1, 2), (-4, -2)}?B. {(7, 2), (3, -2), (-4, 2), (-3, -1)}?C. {(4, 2), (3, -2), (-5, 2), (-2, -2)}?D. {(3, 2), (3, -2), (-3, 2), (-3, -2)}Question 28 of 402.5 PointsSolve the following system by the addition method.{2x + 3y = 6?{2x – 3y = 6?A. {(4, 1)}?B. {(5, 0)}?C. {(2, 1)}?D. {(3, 0)}Reset SelectionQuestion 29 of 402.5 PointsSolve the following system by the substitution method.{x + 3y = 8?{y = 2x - 9?A. {(5, 1)}?B. {(4, 3)}?C. {(7, 2)}?D. {(4, 3)}Question 30 of 402.5 PointsWrite the form of the partial fraction decomposition of the rational expression.?7x - 4/x2?- x - 12?A. 24/7(x - 2) + 26/7(x + 5)?B. 14/7(x - 3) + 20/7(x2?+ 3)?C. 24/7(x - 4) + 25/7(x + 3)?D. 22/8(x - 2) + 25/6(x + 4)Question 31 of 402.5 PointsSolve each equation by either substitution or addition method.x2?+ 4y2?= 20?x + 2y = 6?A. {(5, 2), (-4, 1)}?B. {(4, 2), (3, 1)}?C. {(2, 2), (4, 1)}?D. {(6, 2), (7, 1)}Question 32 of 402.5 PointsSolve the following system by the substitution method.{x + y = 4?{y = 3x?A. {(1, 4)}?B. {(3, 3)}?C. {(1, 3)}?D. {(6, 1)}Question 33 of 402.5 PointsSolve the following system.2x + y = 2x + y - z = 4?3x + 2y + z = 0?A. {(2, 1, 4)}?B. {(1, 0, -3)}?C. {(0, 0, -2)}?D. {(3, 2, -1)}Reset SelectionQuestion 34 of 402.5 PointsFind the quadratic function y = ax2?+ bx + c whose graph passes through the given points.(-1, 6), (1, 4), (2, 9)?A. y = 2x2?- x + 3?B. y = 2x2?+ x2?+ 9?C. y = 3x2?- x - 4?D. y = 2x2?+ 2x + 4Question 35 of 402.5 PointsSolve each equation by the substitution method.x + y = 1?x2?+ xy – y2?= -5?A. {(4, -3), (-1, 2)}?B. {(2, -3), (-1, 6)}?C. {(-4, -3), (-1, 3)}?D. {(2, -3), (-1, -2)}Question 36 of 402.5 PointsWrite the partial fraction decomposition for the following rational expression.1/x2?– c2?(c ≠ 0)?A. 1/4c/x - c - 1/2c/x + c?B. 1/2c/x - c - 1/2c/x + c?C. 1/3c/x - c - 1/2c/x + c?D. 1/2c/x - c - 1/3c/x + cQuestion 37 of 402.5 PointsMany elevators have a capacity of 2000 pounds.?If a child averages 50 pounds and an adult 150 pounds, write an inequality that describes when x children and y adults will cause the elevator to be overloaded.?A. 50x + 150y > 2000?B. 100x + 150y > 1000?C. 70x + 250y > 2000?D. 55x + 150y > 3000Question 38 of 402.5 PointsA television manufacturer makes rear-projection and plasma televisions. The pro?t per unit is $125 for the rear-projection televisions and $200 for the plasma televisions.?Let x = the number of rear-projection televisions manufactured in a month and let y = the number of plasma televisions manufactured in a month. Write the objective function that models the total monthly profit.?A. z = 200x + 125y?B. z = 125x + 200y?C. z = 130x + 225y?D. z = -125x + 200yQuestion 39 of 402.5 PointsSolve the following system.3(2x+y) + 5z = -1?2(x - 3y + 4z) = -9?4(1 + x) = -3(z - 3y)?A. {(1, 1/3, 0)}?B. {(1/4, 1/3, -2)}?C. {(1/3, 1/5, -1)}?D. {(1/2, 1/3, -1)}Question 40 of 402.5 PointsOn your next vacation, you will divide lodging between large resorts and small inns. Let x represent the number of nights spent in large resorts. Let y represent the number of nights spent in small inns.?Write a system of inequalities that models the following conditions:?You want to stay at least 5 nights. At least one night should be spent at a large resort. Large resorts average $200 per night and small inns average $100 per night. Your budget permits no more than $700 for lodging.?A.y ≥ 1?x + y ≥ 5x ≥ 1?300x + 200y ≤ 700?B.y ≥ 0x + y ≥ 3?x ≥ 0?200x + 200y ≤ 700?C.y ≥ 1x + y ≥ 4x ≥ 2?500x + 100y ≤ 700?D.y ≥ 0x + y ≥ 5x ≥ 1?200x + 100y ≤ 700Part 3Question 1 of 402.5 PointsGive the order of the following matrix; if A = [aij], identify a32?and a23.?1?0?-2-5?7? 1/2∏?-6? 11e?-∏? -1/5?A. 3 * 4; a32?= 1/45; a23?= 6?B. 3 * 4; a32?= 1/2; a23?= -6?C. 3 * 2; a32?= 1/3; a23?= -5?D. 2 * 3; a32?= 1/4; a23?= 4Question 2 of 402.5 PointsSolve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.?x + y - z = -2?2x - y + z = 5?-x + 2y + 2z = 1?A. {(0, -1, -2)}?B. {(2, 0, 2)}?C. {(1, -1, 2)}?D. {(4, -1, 3)}Question 3 of 402.5 PointsFind values for x, y, and z so that the following matrices are equal.2x?z? y + 7?4?=?-106? 134?A. x = -7; y = 6; z = 2?B. x = 5; y = -6; z = 2?C. x = -3; y = 4; z = 6?D. x = -5; y = 6; z = 6Question 4 of 402.5 PointsUse Cramer’s Rule to solve the following system.2x = 3y + 2?5x = 51 - 4y?A. {(8, 2)}?B. {(3, -4)}?C. {(2, 5)}?D. {(7, 4)}Question 5 of 402.5 PointsSolve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.?x + 3y = 0?x + y + z = 1?3x - y - z = 11?A. {(3, -1, -1)}?B. {(2, -3, -1)}?C. {(2, -2, -4)}?D. {(2, 0, -1)}Question 6 of 402.5 PointsUse Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.?w - 2x - y - 3z = -9?w + x - y = 0?3w + 4x + z = 6?2x - 2y + z = 3?A. {(-1, 2, 1, 1)}?B. {(-2, 2, 0, 1)}?C. {(0, 1, 1, 3)}?D. {(-1, 2, 1, 1)}Question 7 of 402.5 PointsUse Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.?2w + x - y = 3?w - 3x + 2y = -4?3w + x - 3y + z = 1?w + 2x - 4y - z = -2?A. {(1, 3, 2, 1)}?B. {(1, 4, 3, -1)}?C. {(1, 5, 1, 1)}?D. {(-1, 2, -2, 1)}Question 8 of 402.5 PointsUse Gaussian elimination to find the complete solution to each system.x - 3y + z = 1?-2x + y + 3z = -7?x - 4y + 2z = 0?A. {(2t + 4, t + 1, t)}?B. {(2t + 5, t + 2, t)}?C. {(1t + 3, t + 2, t)}?D. {(3t + 3, t + 1, t)}Question 9 of 402.5 PointsSolve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.?x + y + z = 4?x - y - z = 0?x - y + z = 2?A. {(3, 1, 0)}?B. {(2, 1, 1)}?C. {(4, 2, 1)}?D. {(2, 1, 0)}Question 10 of 402.5 PointsUse Cramer’s Rule to solve the following system.?x + y = 7?x - y = 3?A. {(7, 2)}?B. {(8, -2)}?C. {(5, 2)}?D. {(9, 3)}Question 11 of 402.5 PointsUse Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.?5x + 8y - 6z = 14?3x + 4y - 2z = 8?x + 2y - 2z = 3?A. {(-4t + 2, 2t + 1/2, t)}?B. {(-3t + 1, 5t + 1/3, t)}?C. {(2t + -2, t + 1/2, t)}?D. {(-2t + 2, 2t + 1/2, t)}Question 12 of 402.5 PointsUse Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.?8x + 5y + 11z = 30?-x - 4y + 2z = 3?2x - y + 5z = 12?A. {(3 - 3t, 2 + t, t)}?B. {(6 - 3t, 2 + t, t)}?C. {(5 - 2t, -2 + t, t)}?D. {(2 - 1t, -4 + t, t)}Question 13 of 402.5 PointsUse Cramer’s Rule to solve the following system.?12x + 3y = 15?2x - 3y = 13?A. {(2, -3)}?B. {(1, 3)}?C. {(3, -5)}?D. {(1, -7)}Question 14 of 402.5 PointsSolve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.x - 2y + z = 0?y - 3z = -1?2y + 5z = -2?A. {(-1, -2, 0)}?B. {(-2, -1, 0)}?C. {(-5, -3, 0)}?D. {(-3, 0, 0)}Question 15 of 402.5 PointsSolve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.?x + 2y = z - 1?x = 4 + y - z?x + y - 3z = -2?A. {(3, -1, 0)}?B. {(2, -1, 0)}?C. {(3, -2, 1)}?D. {(2, -1, 1)}Question 16 of 402.5 PointsUse Gaussian elimination to find the complete solution to each system.x1?+ 4x2?+ 3x3?- 6x4?= 5?x1?+ 3x2?+ x3?- 4x4?= 3?2x1?+ 8x2?+ 7x3?- 5x4?= 11?2x1?+ 5x2?- 6x4?= 4?A. {(-47t + 4, 12t, 7t + 1, t)}?B. {(-37t + 2, 16t, -7t + 1, t)}?C. {(-35t + 3, 16t, -6t + 1, t)}?D. {(-27t + 2, 17t, -7t + 1, t)}Question 17 of 402.5 PointsFind the products AB and BA to determine whether B is the multiplicative inverse of A.?A =00110? 001? 0B?=01000? 110? 0?A. AB = I; BA = I3; B = A?B. AB = I3; BA = I3; B = A-1?C. AB = I; AB = I3; B = A-1?D. AB = I3; BA = I3; A = B-1Question 18 of 402.5 PointsSolve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.?3x1?+ 5x2?- 8x3?+ 5x4?= -8?x1?+ 2x2?- 3x3?+ x4?= -7?2x1?+ 3x2?- 7x3?+ 3x4?= -11?4x1?+ 8x2?- 10x3+ 7x4?= -10?A. {(1, -5, 3, 4)}?B. {(2, -1, 3, 5)}?C. {(1, 2, 3, 3)}?D. {(2, -2, 3, 4)}Question 19 of 402.5 PointsUse Cramer’s Rule to solve the following system.x + 2y + 2z = 5?2x + 4y + 7z = 19?-2x - 5y - 2z = 8?A. {(33, -11, 4)}?B. {(13, 12, -3)}?C. {(23, -12, 3)}?D. {(13, -14, 3)}Question 20 of 402.5 PointsSolve the system using the inverse that is given for the coefficient matrix.2x + 6y + 6z = 82x + 7y + 6z =102x + 7y + 7z = 9The inverse of:222? 677? 667is7/2-10? 01-1? -301?A. {(1, 2, -1)}?B. {(2, 1, -1)}?C. {(1, 2, 0)}?D. {(1, 3, -1)}Question 21 of 402.5 PointsFind the vertices and locate the foci of each hyperbola with the given equation.x2/4 - y2/1 =1?A.Vertices at (2, 0) and (-2, 0); foci at (√5, 0) and (-√5, 0)?B.Vertices at (3, 0) and (-3 0); foci at (12, 0) and (-12, 0)?C. Vertices at (4, 0) and (-4, 0); foci at (16, 0) and (-16, 0)?D. Vertices at (5, 0) and (-5, 0); foci at (11, 0) and (-11, 0)Question 22 of 402.5 PointsFind the vertex, focus, and directrix of each parabola with the given equation.(y + 1)2?= -8x?A. Vertex: (0, -1); focus: (-2, -1); directrix: x = 2?B. Vertex: (0, -1); focus: (-3, -1); directrix: x = 3?C. Vertex: (0, -1); focus: (2, -1); directrix: x = 1?D. Vertex: (0, -3); focus: (-2, -1); directrix: x = 5Question 23 of 402.5 PointsConvert each equation to standard form by completing the square on x and y.9x2?+ 16y2?- 18x + 64y - 71 = 0?A. (x - 1)2/9 + (y + 2)2/18 = 1?B. (x - 1)2/18 + (y + 2)2/71 = 1?C. (x - 1)2/16 + (y + 2)2/9 = 1?D. (x - 1)2/64 + (y + 2)2/9 = 1Question 24 of 402.5 PointsLocate the foci and find the equations of the asymptotes.?4y2?– x2?= 1?A. (0, ±√4/2); asymptotes: y = ±1/3x?B. (0, ±√5/2); asymptotes: y = ±1/2x?C. (0, ±√5/4); asymptotes: y = ±1/3x?D. (0, ±√5/3); asymptotes: y = ±1/2xQuestion 25 of 402.5 PointsFind the focus and directrix of each parabola with the given equation.x2?= -4y?A. Focus: (0, -1), directrix: y = 1?B. Focus: (0, -2), directrix: y = 1?C. Focus: (0, -4), directrix: y = 1?D. Focus: (0, -1), directrix: y = 2Question 26 of 402.5 PointsFind the standard form of the equation of each hyperbola satisfying the given conditions.Center: (4, -2)Focus: (7, -2)Vertex: (6, -2)?A. (x - 4)2/4 - (y + 2)2/5 = 1?B. (x - 4)2/7 - (y + 2)2/6 = 1?C. (x - 4)2/2 - (y + 2)2/6 = 1?D. (x - 4)2/3 - (y + 2)2/4 = 1Question 27 of 402.5 PointsFind the standard form of the equation of the following ellipse satisfying the given conditions.?Foci: (0, -4), (0, 4)Vertices: (0, -7), (0, 7)?A. x2/43 + y2/28 = 1?B. x2/33 + y2/49 = 1?C. x2/53 + y2/21 = 1?D. x2/13 + y2/39 = 1Question 28 of 402.5 PointsLocate the foci of the ellipse of the following equation.?7x2?= 35 - 5y2?A. Foci at (0, -√2) and (0, √2)?B. Foci at (0, -√1) and (0, √1)?C. Foci at (0, -√7) and (0, √7)?D. Foci at (0, -√5) and (0, √5)Question 29 of 402.5 PointsConvert each equation to standard form by completing the square on x or y. Then ?nd the vertex, focus, and directrix of the parabola.x2?- 2x - 4y + 9 = 0?A. (x - 4)2?= 4(y - 2); vertex: (1, 4); focus: (1, 3) ; directrix: y = 1?B. (x - 2)2?= 4(y - 3); vertex: (1, 2); focus: (1, 3) ; directrix: y = 3?C. (x - 1)2?= 4(y - 2); vertex: (1, 2); focus: (1, 3) ; directrix: y = 1?D. (x - 1)2?= 2(y - 2); vertex: (1, 3); focus: (1, 2) ; directrix: y = 5Question 30 of 402.5 PointsFind the standard form of the equation of the ellipse satisfying the given conditions.Major axis vertical with length =?10Length of minor axis = 4Center: (-2, 3)?A. (x + 2)2/4 + (y - 3)2/25 = 1?B. (x + 4)2/4 + (y - 2)2/25 = 1?C. (x + 3)2/4 + (y - 2)2/25 = 1?D. (x + 5)2/4 + (y - 2)2/25 = 1Question 31 of 402.5 PointsFind the focus and directrix of the parabola with the given equation.8x2?+ 4y = 0?A. Focus: (0, -1/4); directrix: y = 1/4?B. Focus: (0, -1/6); directrix: y = 1/6?C. Focus: (0, -1/8); directrix: y = 1/8?D. Focus: (0, -1/2); directrix: y = 1/2Question 32 of 402.5 PointsFind the standard form of the equation of each hyperbola satisfying the given conditions.Foci: (-4, 0), (4, 0)Vertices: (-3, 0), (3, 0)?A. x2/4 - y2/6 = 1?B. x2/6 - y2/7 = 1?C. x2/6 - y2/7 = 1?D. x2/9 - y2/7 = 1Question 33 of 402.5 PointsConvert each equation to standard form by completing the square on x or y. Then ?nd the vertex, focus, and directrix of the parabola.y2?- 2y + 12x - 35 = 0?A. (y - 2)2?= -10(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 9?B. (y - 1)2?= -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 6?C. (y - 5)2?= -14(x - 3); vertex: (2, 1); focus: (0, 1); directrix: x = 6?D. (y - 2)2?= -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 8Question 34 of 402.5 PointsFind the solution set for each system by finding points of intersection.x2?+ y2?= 1?x2?+ 9y = 9?A. {(0, -2), (0, 4)}?B. {(0, -2), (0, 1)}?C. {(0, -3), (0, 1)}?D. {(0, -1), (0, 1)}Question 35 of 402.5 PointsFind the vertex, focus, and directrix of each parabola with the given equation.(x + 1)2?= -8(y + 1)?A. Vertex:?(-1, -2); focus: (-1, -2); directrix: y = 1?B. Vertex: (-1, -1); focus: (-1, -3); directrix: y = 1?C. Vertex: (-3, -1); focus: (-2, -3); directrix: y = 1?D. Vertex: (-4, -1); focus: (-2, -3); directrix: y = 1Question 36 of 402.5 PointsLocate the foci of the ellipse of the following equation.x2/16 + y2/4 = 1?A. Foci at (-2√3, 0) and (2√3, 0)?B. Foci at (5√3, 0) and (2√3, 0)?C. Foci at (-2√3, 0) and (5√3, 0)?D. Foci at (-7√2, 0) and (5√2, 0)Question 37 of 402.5 PointsFind the standard form of the equation of the following ellipse satisfying the given conditions.?Foci: (-5, 0), (5, 0)Vertices: (-8, 0), (8, 0)?A. x2/49 + y2/ 25 = 1?B. x2/64 + y2/39 = 1?C. x2/56 + y2/29 = 1?D. x2/36 + y2/27 = 1Question 38 of 402.5 PointsFind the standard form of the equation of the ellipse satisfying the given conditions.Endpoints of major axis: (7, 9) and (7, 3)?Endpoints of minor axis: (5, 6) and (9, 6)?A. (x - 7)2/6 + (y - 6)2/7 = 1?B. (x - 7)2/5 + (y - 6)2/6 = 1?C. (x - 7)2/4 + (y - 6)2/9 = 1?D. (x - 5)2/4 + (y - 4)2/9 = 1Question 39 of 402.5 PointsLocate the foci and find the equations of the asymptotes.?x2/9 - y2/25 = 1?A. Foci: ({±√36, 0) ;asymptotes: y = ±5/3x?B. Foci: ({±√38, 0) ;asymptotes: y = ±5/3x?C. Foci: ({±√34, 0) ;asymptotes: y = ±5/3x?D. Foci: ({±√54, 0) ;asymptotes: y = ±6/3xQuestion 40 of 402.5 PointsFind the vertices and locate the foci of each hyperbola with the given equation.y2/4 - x2/1 = 1?A. Vertices at (0, 5) and (0, -5); foci at (0, 14) and (0, -14)?B. Vertices at (0, 6) and (0, -6); foci at (0, 13) and (0, -13)?C.Vertices at (0, 2) and (0, -2); foci at (0, √5) and (0, -√5)?D. Vertices at (0, 1) and (0, -1); foci at (0, 12) and (0, -12)Part 4Question 1 of 205.0 PointsWrite the first six terms of the following arithmetic sequence.an?= an-1?- 0.4, a1?= 1.6?A. 1.6, 1.2, 0.8, 0.4, 0, -0.4?B. 1.6, 1.4, 0.9, 0.3, 0, -0.3?C. 1.6, 2.2, 1.8, 1.4, 0, -1.4?D. 1.3, 1.5, 0.8, 0.6, 0, -0.6Question 2 of 205.0 PointsIf three people are selected at random, find the probability that they all have different birthdays.?A. 365/365 * 365/364 * 363/365 ≈ 0.98?B. 365/364 * 364/365 * 363/364 ≈ 0.99?C. 365/365 * 365/363 * 363/365 ≈ 0.99?D. 365/365 * 364/365 * 363/365 ≈ 0.99Question 3 of 205.0 PointsWrite the first four terms of the following sequence whose general term is given.an?= 3n?A. 3, 9, 27, 81?B. 4, 10, 23, 91?C. 5, 9, 17, 31?D. 4, 10, 22, 41Question 4 of 205.0 PointsThe following are defined using recursion formulas. Write the first four terms of each sequence.a1?= 3 and an?= 4an-1?for n ≥ 2?A. 3, 12, 48, 192?B. 4, 11, 58, 92?C. 3, 14, 79, 123?D. 5, 14, 47, 177Question 5 of 205.0 PointsAn election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done??A. 20 ways?B. 30 ways?C. 10 ways?D. 15 waysQuestion 6 of 205.0 PointsUse the Binomial Theorem to find a polynomial expansion for the following function.f1(x) = (x - 2)4?A. f1(x) = x4?- 5x3?+ 14x2?- 42x + 26?B. f1(x) = x4?- 16x3?+ 18x2?- 22x + 18?C. f1(x) = x4?- 18x3?+ 24x2?- 28x + 16?D. f1(x) = x4?- 8x3?+ 24x2?- 32x + 16Question 7 of 205.0 PointsWrite the first four terms of the following sequence whose general term is given.an?= 3n + 2?A. 4, 6, 10, 14?B. 6, 9, 12, 15?C. 5, 8, 11, 14?D. 7, 8, 12, 15Question 8 of 205.0 PointsUse the formula for the sum of the first n terms of a geometric sequence to solve the following.Find the sum of the first 12 terms of the geometric sequence: 2, 6, 18, 54 . . .?A. 531,440?B. 535,450?C. 535,445?D. 431,440Question 9 of 205.0 PointsIf two people are selected at random, the probability that they do not have the same birthday (day and month) is 365/365 * 364/365. (Ignore leap years and assume 365 days in a year.)?A. The first person can have any birthday in the year. The second person can have all but one birthday.?B. The second person can have any birthday in the year. The first person can have all but one birthday.?C. The first person cannot a birthday in the year. The second person can have all but one birthday.?D. The first person can have any birthday in the year. The second cannot have all but one birthday.Question 10 of 205.0 PointsThe following are defined using recursion formulas. Write the first four terms of each sequence.?a1?= 4 and an?= 2an-1?+ 3 for n ≥ 2?A. 4, 15, 35, 453?B. 4, 11, 15, 13?C. 4, 11, 25, 53?D. 3, 19, 22, 53Question 11 of 205.0 PointsUse the Binomial Theorem to expand the following binomial and express the result in simpli?ed form.(x2?+ 2y)4?A. x8?+ 8x6?y + 24x4?y2?+ 32x2?y3?+ 16y4?B. x8?+ 8x6?y + 20x4?y2?+ 30x2?y3?+ 15y4?C. x8?+ 18x6?y + 34x4?y2?+ 42x2?y3?+ 16y4?D. x8?+ 8x6?y + 14x4?y2?+ 22x2?y3?+ 26y4Question 12 of 205.0 PointsWrite the first six terms of the following arithmetic sequence.an?= an-1?- 10, a1?= 30?A. 40, 30, 20, 0, -20, -10?B. 60, 40, 30, 0, -15, -10?C. 20, 10, 0, 0, -15, -20?D. 30, 20, 10, 0, -10, -20Question 13 of 205.0 PointsTo win at LOTTO in the state of Florida, one must correctly select 6 numbers from a collection of 53 numbers (1 through 53). The order in which the selection is made does not matter. How many different selections are possible??A. 32,957,326 selections?B. 22,957,480 selections?C. 28,957,680 selections?D. 225,857,480 selectionsQuestion 14 of 205.0 PointsA club with ten members is to choose three officers—president, vice president, and secretary-treasurer. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled??A. 650 ways?B. 720 ways?C. 830 ways?D. 675 waysQuestion 15 of 205.0 PointsUse the formula for the sum of the first n terms of a geometric sequence to solve the following.Find the sum of the first 11 terms of the geometric sequence: 3, -6, 12, -24 . . .?A. 1045?B. 2108?C. 10478?D. 2049Question 16 of 205.0 PointsHow large a group is needed to give a 0.5 chance of at least two people having the same birthday??A. 13 people?B. 23 people?C. 47 people?D. 28 peopleQuestion 17 of 205.0 PointsIf three people are selected at random, ?nd the probability that at least two of them have the same birthday.?A. ≈ 0.07?B. ≈ 0.02?C. ≈ 0.01?D. ≈ 0.001Question 18 of 205.0 PointsFind the indicated term of the arithmetic sequence with first term, a1, and common difference, d.?Find a6?when a1?= 13, d = 4?A. 36?B. 63?C. 43?D. 33Question 19 of 205.0 PointsThe following are defined using recursion formulas. Write the first four terms of each sequence.?a1?= 7 and an?= an-1?+ 5 for n ≥ 2?A. 8, 13, 21, 22?B. 7, 12, 17, 22?C. 6, 14, 18, 21?D. 4, 11, 17, 20Question 20 of 205.0 PointsConsider the statement "2 is a factor of n2?+ 3n."If n = 1, the statement is "2 is a factor of __________."If n = 2, the statement is "2 is a factor of __________."If n = 3, the statement is "2 is a factor of __________."If n = k + 1, the statement before the algebra is simpli?ed is "2 is a factor of __________."If n = k + 1, the statement after the algebra is simpli?ed is "2 is a factor of __________."?A.4; 15; 28; (k + 1)2?+ 3(k + 1); k2?+ 5k + 8?B.4; 20; 28; (k + 1)2?+ 3(k + 1); k2?+ 5k + 7?C.4; 10; 18; (k + 1)2?+ 3(k + 1); k2?+ 5k + 4?D.4; 15; 18; (k + 1)2?+ 3(k + 1); k2?+ 5k + 6 ................
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