f01.justanswer.com · Web view2014/09/30 · Write an equation in standard form of the parabola...

Part 1

Question 1 of 20 5.0 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 + 4

Question 2 of 20 5.0 Points

Use 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) = 7

Question 3 of 20 5.0 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 + f


Find 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.


Solve the following polynomial inequality.

3x2 + 10x - 8 ≤ 0

A. [6, 1/3]

B. [-4, 2/3]

C. [-9, 4/5]

D. [8, 2/7]


Write 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)2

Question 7 of 20 5.0 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 holes


Based 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.


Write 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 + 3


"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.


Find 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 20 5.0 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; falls


Find 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 20 5.0 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}


Write 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/zk

Question 17 of 20 5.0 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.


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.


Use 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) = -3


Solve the following polynomial inequality.

9x2 - 6x + 1 < 0

A. (-∞, -3)

B. (-1, ∞)

C. [2, 4)

D. Ø

Part 2

Question 1 of 40 2.5 PointsFind the domain of following logarithmic function.

f(x) = log5 (x + 4)

A. (-4, ∞)

B. (-5, -∞)

C. (7, -∞)

D. (-9, ∞)


Use 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)


Approximate the following using a calculator; round your answer to three decimal places.

3√5

A. .765

B. 14297

C. 11.494

D. 11.665

Question 4 of 40 2.5 PointsFind the domain of following logarithmic function.

f(x) = log (2 - x)

A. (∞, 4)

B. (∞, -12)

C. (-∞, 2)

D. (-∞, -3)


Use 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 y


Evaluate the following expression without using a calculator.

8log8 19

A. 17

B. 38

C. 24

D. 19

Question 7 of 40 2.5 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)3

Question 8 of 40 2.5 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 = toe

Question 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 = 32


The 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; vertical


Use 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 z

Question 12 of 40 2.5 PointsApproximate the following using a calculator; round your answer to three decimal places.

e-0.95

A. .483

B. 1.287

C. .597

D. .387


Solve 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}


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.

32x + 3x - 2 = 0

A. {1}

B. {-2}

C. {5}

D. {0}


Solve 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}


The 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, ∞)


Use 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. 4

Question 18 of 40 2.5 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))12t


PointsEvaluate the following expression without using a calculator.

Log7 √7

A. 1/4

B. 3/5

C. 1/2

D. 2/7


Find the domain of following logarithmic function.

f(x) = ln (x - 2)2

A. (∞, 2) ∪ (-2, -∞)

B. (-∞, 2) ∪ (2, ∞)

C. (-∞, 1) ∪ (3, ∞)

D. (2, -∞) ∪ (2, ∞)


Solve 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)}


Solve 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 40 2.5 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 - 5

Question 24 of 40 2.5 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)}


Write 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)


Solve 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)}


Solve 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)}


Solve 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 Selection


Solve 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)}


Write 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 40 2.5 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)}


Solve the following system by the substitution method.

{x + y = 4 {y = 3x

A. {(1, 4)}

B. {(3, 3)}

C. {(1, 3)}

D. {(6, 1)}


Solve 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 Selection

Question 34 of 40 2.5 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 + 4

Question 35 of 40 2.5 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)}


Write 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 + c

Question 37 of 40 2.5 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 > 3000


PointsA television manufacturer makes rear-projection and plasma televisions. The profit 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 + 200y

Question 39 of 40 2.5 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 40 2.5 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 ≤ 700

Part 3

Question 1 of 40 2.5 PointsGive the order of the following matrix; if A = [aij], identify a32 and a23.

1 0

-2

-5 7

1/2

∏

-6

11

e

-∏

-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 = 4


Solve 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)}


Find values for x, y, and z so that the following matrices are equal.

2x

z

y + 7

4 =

-10

6

13

4

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 = 6

Question 4 of 40 2.5 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 40 2.5 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 40 2.5 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 40 2.5 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)}


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)}


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)}


Use 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)}


Use 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)}


Use 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)}


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)}


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)}


Use 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)}


Find the products AB and BA to determine whether B is the multiplicative inverse of A.

A =

0

0

1

1

0

0

0

1

0

B =

0

1

0

0

0

1

1

0

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-1


Solve 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)}


Use 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 40 2.5 PointsSolve the system using the inverse that is given for the coefficient matrix.

2x + 6y + 6z = 82x + 7y + 6z =102x + 7y + 7z = 9

The inverse of:

2

2

2

6

7

7

6

6

7

is

7/2

-1

0

0

1

-1

-3

0

1

A. {(1, 2, -1)}

B. {(2, 1, -1)}

C. {(1, 2, 0)}

D. {(1, 3, -1)}


Find 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)


Find 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 = 5


Convert 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 = 1


Locate 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 = ±1/2x


Find 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 = 2


Find 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 = 1


Find 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 = 1

Question 28 of 40 2.5 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)


Convert each equation to standard form by completing the square on x or y. Then find 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 = 5

Question 30 of 40 2.5 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 = 1


Find 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 = 1/2


Find 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 = 1


Convert each equation to standard form by completing the square on x or y. Then find 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 = 8

Question 34 of 40 2.5 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)}


Find 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 = 1


Locate 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)


Find 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 = 1


Find 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 = 1

Question 39 of 40 2.5 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 = ±6/3x


Find 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 4


Write 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, -0.6


If 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 ≈ 0.99


Write 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, 41

Question 4 of 20 5.0 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, 177


An 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 ways


Use 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 + 16

Question 7 of 20 5.0 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, 15


Use 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. 431,440


If 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 20 5.0 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, 53


PointsUse the Binomial Theorem to expand the following binomial and express the result in simplified 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 + 26y4


Write 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, -20


To 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 selections


A 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 ways

Question 15 of 20 5.0 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. 2049


How 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 people


If three people are selected at random, find the probability that at least two of them have the same birthday.

A. ≈ 0.07

B. ≈ 0.02

C. ≈ 0.01

D. ≈ 0.001


Find 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. 33


The 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, 20


Consider 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 simplified is "2 is a factor of __________."If n = k + 1, the statement after the algebra is simplified 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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