Question 1 of 20 / 5.0 Points
Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x2or 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 Points
If 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
Question 4 of 20 / 5.0 Points
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.
Question 5 of 20 / 5.0 Points
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]
Question 6 of 20 / 5.0 Points
Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x2or 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 Points
Find 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
Question 8 of 20 / 5.0 Points
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.
Question 9 of 20 / 5.0 Points
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
Question 10 of 20 / 5.0 Points
"Y varies directly as the nthpower 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 20 / 5.0 Points
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 Points
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) = 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 20 / 5.0 Points
The graph of f(x) = -x3______to the left and ______to the right.
A. rises; falls
B. falls; falls
C. falls; rises
D. falls; falls
Question 14 of 20 / 5.0 Points
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 Points
Find 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 20 / 5.0 Points
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 Points
The 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 20 / 5.0 Points
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) = 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 20 / 5.0 Points
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
Question 20 of 20 / 5.0 Points
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, ∞)
Question 2 of 40 / 2.5 Points
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)
Question 3 of 40 / 2.5 Points
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 Points
Find the domain of following logarithmic function.
f(x) = log (2 - x)
A. (∞, 4)
B. (∞, -12)
C. (-∞, 2)
D. (-∞, -3)
Question 5 of 40 / 2.5 Points
Use properties of logarithms to expand the following logarithmic expression as much as possible.
logb(x2y)
A. 2 logyx + logxy
B. 2 logbx + logby
C. logx- logby
D. logbx – logxy
Question 6 of 40 / 2.5 Points
Evaluate the following expression without using a calculator.
8log819
A. 17
B. 38
C. 24
D. 19
Question 7 of 40 / 2.5 Points
Use 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 Points
Use the exponential growth model, A = A0ekt, to show that the time it takes a population to double (to grow from A0to 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 40 / 2.5 Points
Write the following equation in its equivalent exponential form.
5 = logb32
A. b5= 32
B. y5= 32
C. Blog5= 32
D. Logb= 32
Question 10 of 40 / 2.5 Points
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
Question 11 of 40 / 2.5 Points
Use properties of logarithms to expand the following logarithmic expression as much as possible.
logb(x2y) / z2
A. 2 logbx + logby - 2 logbz
B. 4 logbx - logby - 2 logbz
C. 2 logbx + 2 logby + 2 logbz
D. logbx - logby + 2 logbz
Question 12 of 40 / 2.5 Points
Approximate the following using a calculator; round your answer to three decimal places.
e-0.95
A. .483
B. 1.287
C. .597
D. .387
Question 13 of 40 / 2.5 Points
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}
Question 14 of 40 / 2.5 Points
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}
Question 15 of 40 / 2.5 Points
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}
Question 16 of 40 / 2.5 Points
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, ∞)
Question 17 of 40 / 2.5 Points
Use properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1.
log296 – log23
A. 5
B. 7
C. 12
D. 4
Question 18 of 40 / 2.5 Points
You 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
Question 19 of 40 / 2.5 Points
Evaluate the following expression without using a calculator.
Log7√7
A. 1/4
B. 3/5
C. 1/2
D. 2/7
Question 20 of 40 / 2.5 Points
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, ∞)
Question 21 of 40 / 2.5 Points
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)}
Question 22 of 40 / 2.5 Points
Solve each equation by the substitution method.
/ y2= x2- 92y = 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 Points
Find 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 Points
Solve 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 40 / 2.5 Points
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)
Question 26 of 40 / 2.5 Points
Solve the following system.
/ 2x + 4y + 3z = 2x + 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 40 / 2.5 Points
Solve each equation by the substitution method.
/ x2- 4y2= -73x2+ 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 40 / 2.5 Points
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
Question 29 of 40 / 2.5 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 40 / 2.5 Points
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 Points
Solve 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 40 / 2.5 Points
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)}
Question 33 of 40 / 2.5 Points
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 Points
Solve 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 40 / 2.5 Points
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 Points
Many 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
Question 38 of 40 / 2.5 Points
A 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 Points
Solve 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 Points
On 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 ≥ 5
x ≥ 1
300x + 200y ≤ 700
B.
/ y ≥ 0
x + y ≥ 3
x ≥ 0
200x + 200y ≤ 700
C.
/ y ≥ 1
x + y ≥ 4
x ≥ 2
500x + 100y ≤ 700
D.
/ y ≥ 0
x + y ≥ 5
x ≥ 1
200x + 100y ≤ 700
Part 3
Question 1 of 40 / 2.5 PointsGive the order of the following matrix; if A = [aij], identify a32and 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
Question 2 of 40 / 2.5 Points
Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.
/ x + y - z = -22x - 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 40 / 2.5 Points
Find values for x, y, and z so that the following matrices are equal.
/ 2xz / 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 Points
Use 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 Points
Solve 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 Points
Use 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 40 / 2.5 Points
Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.
/ 2w + x - y = 3w - 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 Points
Use 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 40 / 2.5 Points
Solve 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 40 / 2.5 Points
Use Cramer’s Rule to solve the following system.
x - y = 3
A. {(7, 2)}
B. {(8, -2)}
C. {(5, 2)}
D. {(9, 3)}
Question 11 of 40 / 2.5 Points
Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.
/ 5x + 8y - 6z = 143x + 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 40 / 2.5 Points
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)}
Question 13 of 40 / 2.5 Points
Use Cramer’s Rule to solve the following system.
2x - 3y = 13
A. {(2, -3)}
B. {(1, 3)}
C. {(3, -5)}
D. {(1, -7)}
Question 14 of 40 / 2.5 Points
Solve 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 40 / 2.5 Points
Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.
/ x + 2y = z - 1x = 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 40 / 2.5 Points
Use Gaussian elimination to find the complete solution to each system.
/ x1+ 4x2+ 3x3- 6x4= 5x1+ 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 40 / 2.5 Points
Find the products AB and BA to determine whether B is the multiplicative inverse of A.
A = / / 00
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
Question 18 of 40 / 2.5 Points
Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.
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 40 / 2.5 Points
Use Cramer’s Rule to solve the following system.
/ x + 2y + 2z = 52x + 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 Points
Solve the system using the inverse that is given for the coefficient matrix.
/ 2x + 6y + 6z = 8
2x + 7y + 6z =10
2x + 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)}
Question 21 of 40 / 2.5 Points
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)
Question 22 of 40 / 2.5 Points
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
Question 23 of 40 / 2.5 Points
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
Question 24 of 40 / 2.5 Points
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
Question 25 of 40 / 2.5 Points
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
Question 26 of 40 / 2.5 Points
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
Question 27 of 40 / 2.5 Points
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 Points
Locate 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 40 / 2.5 Points
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 Points
Find the standard form of the equation of the ellipse satisfying the given conditions.
Major axis vertical with length =10
Length of minor axis = 4
Center: (-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
Question 31 of 40 / 2.5 Points
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
Question 32 of 40 / 2.5 Points
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
Question 33 of 40 / 2.5 Points
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 Points
Find 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 40 / 2.5 Points
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
Question 36 of 40 / 2.5 Points
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)
Question 37 of 40 / 2.5 Points
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
Question 38 of 40 / 2.5 Points
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 Points
Locate 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
Question 40 of 40 / 2.5 Points
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
Question 1 of 20 / 5.0 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, -0.6
Question 2 of 20 / 5.0 Points
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
Question 3 of 20 / 5.0 Points
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 Points
The following are defined using recursion formulas. Write the first four terms of each sequence.
a1= 3 and an= 4an-1for n ≥ 2
A. 3, 12, 48, 192
B. 4, 11, 58, 92
C. 3, 14, 79, 123
D. 5, 14, 47, 177
Question 5 of 20 / 5.0 Points
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
Question 6 of 20 / 5.0 Points
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 Points
Write 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
Question 8 of 20 / 5.0 Points
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
Question 9 of 20 / 5.0 Points
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 Points
The 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
Question 11 of 20 / 5.0 Points
Use the Binomial Theorem to expand the following binomial and express the result in simplified form.
(x2+ 2y)4
A. x8+ 8x6y + 24x4y2+ 32x2y3+ 16y4
B. x8+ 8x6y + 20x4y2+ 30x2y3+ 15y4
C. x8+ 18x6y + 34x4y2+ 42x2y3+ 16y4
D. x8+ 8x6y + 14x4y2+ 22x2y3+ 26y4
Question 12 of 20 / 5.0 Points
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
Question 13 of 20 / 5.0 Points
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
Question 14 of 20 / 5.0 Points
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 Points
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 11 terms of the geometric sequence: 3, -6, 12, -24 . . .
A. 1045
B. 2108
C. 10478
D. 2049
Question 16 of 20 / 5.0 Points
How large a group is needed to give a 0.5 chance of at least two people having the same birthday?