# Project #35622 - 80 Multiple choice questions College Algebra

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Question 1

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The graph of a function is given. Decide whether it is even, odd, or neither.

 even odd neither

Question 2

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The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval.

(-5, -4)

 constant decreasing increasing

Question 3

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Determine whether the relation represents a function. If it is a function, state the domain and range.

 function domain: {Ms. Lee, Mr. Bar} range: {Bob, Ann, Dave} function domain: {Bob, Ann, Dave} range: {Ms. Lee, Mr. Bar} not a function

Question 4

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Determine algebraically whether the function is even, odd, or neither.

f(x) = -5x2 + 4

 even odd neither

Question 5

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For the given functions f and g, find the requested function and state its domain.

f(x) = 3x + 5; g(x) = 7x + 8
Find f ∙ g.

 (f ∙ g)(x) = 10x2 + 59x + 13; all real numbers (f ∙ g)(x) = 21x2 + 43x + 40; {x|x ≠ 40} (f ∙ g)(x) = 21x2 + 40; {x|x ≠ 40} (f ∙ g)(x) = 21x2 + 59x + 40; all real numbers

Question 6

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Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin.

 function domain: {x|-1 ≤ x ≤ 1} range: {y|-π ≤ y ≤ π} intercepts: (-π, 0), (- , 0), (0, 0), (, 0), (π, 0)  symmetry: none function domain: {x|-π ≤ x ≤ π} range: {y|-1 ≤ y ≤ 1} intercepts: (-π, 0), (- , 0), (0, 0), (, 0), (π, 0)  symmetry: origin function domain: all real numbers range: {y|-1 ≤ y ≤ 1} intercepts: (-π, 0), (- , 0), (0, 0), (, 0), (π, 0)  symmetry: origin not a function

Question 7

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Given: E=I/R and P=IE with the values: P=10 and E=100 What are the values for I and R?

 R=.001, I=0.1 R=100, I=100 R=0.1, I=1000 Cannot be solved without the value of another variable.

Question 8

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Determine algebraically whether the function is even, odd, or neither.

f(x) =

 even odd neither

Question 9

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Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin.

 function domain: {x|x = 5 or x = -6} range: all real numbers intercept: (-6, 0) symmetry: x-axis function domain: all real numbers range: all real numbers intercept: (0, -6) symmetry: none function domain: all real numbers range: {y|y = 5 or y = -6} intercept: (0, -6) symmetry: none not a function

Question 10

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Determine whether the equation is a function.

y = |x|

 function not a function

Question 11

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Solve the problem.

The monthly payment p on a mortgage varies directly with the amount borrowed B. If the monthly payment on a 30-year mortgage is  for every \$1000 borrowed, find a linear function that relates the monthly payment p to the amount borrowed B for a mortgage with the same terms. Then find the monthly payment p when the amount borrowed is

 p = ; \$0.02 p = ; \$885.84 p = ; \$6466.67 p = 0.0073B; \$1416.20

Question 12

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Find the average rate of change for the function between the given values.

f(x) = ; from 1 to 4

 -2 - -28

Question 13

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The graph of a function f is given. Use the graph to answer the question.

Find the numbers, if any, at which f has a local minimum. What are the local maxima?

 f has a local minimum at x = -2.5 and 5; the local minimum at -2.5 is -3.3; the local minimum at 5 is -2.5 f has a local maximum at x = -3.3 and -2.5; the local maximum at -3.3 is -2.5; the local maximum at -2.5 is 5 f has a local minimum at x = -3.3 and -2.5; the local minimum at -3.3 is -2.5; the local minimum at -2.5 is 5 f has a local maximum at x = -2.5 and 5; the local maximum at -2.5 is -3.3; the local maximum at 5 is -2.5

Question 14

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List the intercepts of the graph.Tell whether the graph is symmetric with respect to the x-axis, y-axis, origin, or none of these.

 (-1, 0), (0, 0), (1, 0); symmetric to origin, x-axis, and y-axis (-1, 0), (0, 0), (1, 0); symmetric to origin (-1, 0), (0, 0), (1, 0); symmetric to y-axis (-1, 0), (0, 0), (1, 0); symmetric to x-axis

Question 15

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For the given functions f and g, find the requested function and state its domain.

f(x) = 2x + 1; g(x) = 5x - 2
Find .

 ()(x) = ; {x|x ≠ } ()(x) = ; {x|x ≠ - } ()(x) = ; {x|x ≠ - } ()(x) = ; {x|x ≠ }

Question 16

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Solve the problem.

Identify the scatter diagram of the relation that appears linear.

Question 17

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Find the average rate of change for the function between the given values.

f(x) = ; from 2 to 8

 2 - 7

Question 18

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Find the domain of the function.

f(x) =

 {x|x ≤ 11} {x|x ≠ } {x|x ≠ 11} {x|x ≤ }

Question 19

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Match the graph to the function listed whose graph most resembles the one given.

 square function cube function square root function cube root function

Question 20

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Find the domain of the function.

f(x) = -6x - 9

 {x|x > 0} all real numbers {x|x ≥ 9} {x|x ≠ 0}

Part 2:

Question 1

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Give the equation of the horizontal asymptote, if any, of the function.

f(x) =

 y = 2 y = 6 y = 1 no horizontal asymptotes

Question 2

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For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept.

f(x) = 5(x - 5)(x + 4)3

 -5, multiplicity 1, touches x-axis; 4, multiplicity 3 5, multiplicity 1, touches x-axis; -4, multiplicity 3 5, multiplicity 1, crosses x-axis; -4, multiplicity 3, crosses x-axis -5, multiplicity 1, crosses x-axis; 4, multiplicity 3, crosses x-axis

Question 3

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Solve the problem.

A ball is thrown vertically upward with an initial velocity of 160 feet per second. The distance in feet of the ball from the ground after t seconds is  For what interval of time is the ball more than 256 above the ground?

 {x  2 sec < x < 8 sec} {x  7 sec < x < 13 sec} {x  1.5 sec < x < 8.5 sec} {x  4.5 sec < x < 5.5 sec}

Question 4

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Use the Factor Theorem to determine whether x - c is a factor of f(x).

8x3 + 36x2 - 19x - 5; x + 5

 Yes No

Question 5

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Find the indicated intercept(s) of the graph of the function.

x-intercepts of f(x) =

 (5, 0) (2, 0) (-2, 0), (2, 0) (- 8, 0)

Question 6

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Solve the inequality.

x2 + 6x ≥ 0

 (-∞, -6] or [0, ∞) (-∞, 0] or [6, ∞) [0, 6] [-6, 0]

Question 7

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Solve.

The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P. A measuring device is calibrated to give  when  and  What is the volume on this device when the temperature is  and the pressure is

 V = 168 in3 V = 188 in3 V = 148 in3 V = 12 in3

Question 8

5 points

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Solve the inequality.

(x - 5)(x2 + x + 1) >

 (-∞, -1) or (1, ∞) (-1, 1) (-∞, 5) (5, ∞)

Question 9

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Solve the problem.

When the temperature stays the same, the volume of a gas is inversely proportional to the pressure of the gas. If a balloon is filled with 20 cubic inches of a gas at a pressure of 14 pounds per square inch, find the new pressure of the gas if the volume is decreased to 10 cubic inches.

 14 pounds per square inch pounds per square inch 26 pounds per square inch 28 pounds per square inch

Question 10

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Determine whether the rational function has symmetry with respect to the origin, symmetry with respect to the y-axis, or neither.

f(x) =

 symmetry with respect to the y-axis symmetry with respect to the origin neither

Question 11

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Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.

f(x) = -3x2 - 2x - 4

 maximum; maximum; - minimum; - minimum;

Question 12

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Use the graph to find the vertical asymptotes, if any, of the function.

 x = -3, x = 3, x = 0 x = -3, x = 3, y = 0 none x = -3, x = 3

Question 13

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Solve.

The power that a resistor must dissipate is jointly proportional to the square of the current flowing through the resistor and the resistance of the resistor. If a resistor needs to dissipate  of power when  of current is flowing through the resistor whose resistance is  find the power that a resistor needs to dissipate when  of current are flowing through a resistor whose resistance is

 63 watts 147 watts 84 watts 21 watts

Question 14

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Solve the inequality.

x4 - 32x2 - 144 > 0

 (-∞, -6) or (6, ∞) (-∞, -6) or (-2, 2) or (6, ∞) (-6, 6) (-6, -2) or (2, 6)

Question 15

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Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval.

f(x) = 3x3 + 5x + 5; [-1, 0]

 f(-1) = 3 and f(0) = -5; yes f(-1) = -3 and f(0) = 5; yes f(-1) = 3 and f(0) = 5; no f(-1) = -3 and f(0) = -5; no

Question 16

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Solve the inequality.

x(x - 5) ≥ -6

 [3, ∞) [2, 3] (-∞, 2] or [3, ∞) (-∞, 2]

Question 17

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Find the domain of the rational function.

f(x) =

Question 18

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Use the Theorem for bounds on zeros to find a bound on the real zeros of the polynomial function.

f(x) = x4 + 2x2 - 3

 -4 and 4 -3 and 3 -6 and 6 -5 and 5

Question 19

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Find all zeros of the function and write the polynomial as a product of linear factors.

f(x) = 3x4 + 4x3 + 13x2 + 16x + 4

 f(x) = (3x - 1)(x - 1)(x + 2)(x - 2) f(x) = (3x + 1)(x + 1)(x + 2i)(x - 2i) f(x) = (3x - 1)(x - 1)(x + 2i)(x - 2i) f(x) = (3x + 1)(x + 1)(x + 2)(x - 2)

Question 20

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Solve the problem.

The price p (in dollars) and the quantity x sold of a certain product obey the demand equation
p = -20x + 480, 0 ≤ x ≤ 24.
What price should the company charge to maximize revenue?

 \$6 \$14.4 \$18 \$12

Part 3:

Question 1

5 points

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Decide whether or not the functions are inverses of each other.

f(x) = 5 - 9x; g(x) = (x - 5)

 Yes No

Question 2

5 points

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Find the present value. Round to the nearest cent.

To get \$25,000 after 6 years at 13% compounded semiannually

 \$12,505.31 \$13,257.93 \$12,007.96 \$11,742.07

Question 3

5 points

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Find the exact value of the logarithmic expression.

log

 3 -3 -

Question 4

5 points

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Solve the equation.

5x =

 {-3} {3}

Question 5

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Solve the exponential equation. Express the solution set in terms of natural logarithms.

5 3x = 3.5

 > > > >

Question 6

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Solve the problem.

During 1991, 200,000 people visited Rave Amusement Park. During 1997, the number had grown to 834,000. If the number of visitors to the park obeys the law of uninhibited growth, find the exponential growth function that models this data.

 f(t) = 200,000e0.238t f(t) = 634,000e0.238t f(t) = 200,000e0.248t f(t) = 634,000e0.248t

Question 7

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The graph of an exponential function is given. Match the graph to one of the following functions.

>

 f(x) = - 5x f(x) = 5x f(x) = 5 -x f(x) = - 5 -x

Question 8

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Solve the equation.

log6 (x2 - 5x) = 1

 {6} {1} {6, -1} {-6, 1}

Question 9

5 points

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Solve the problem.

The half-life of plutonium-234 is 9 hours. If 70 milligrams is present now, how much will be present in 6 days? (Round your answer to three decimal places.)

 0.689 44.096 0.001 23.091

Question 10

5 points

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The graph of a logarithmic function is shown. Select the function which matches the graph.

 f(x) = -log4x f(x) = log4x f(x) = log4(-x) f(x) = 1 - log4x

Question 11

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Find the effective rate of interest.

50.11% compounded daily

 50.233% 51.015% 50.315% 64.997%

Question 12

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Solve the problem.

The function f(x) = 300(0.5) x/60 models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. Find the amount of radioactive material in the vault after > Round to the nearest whole number.

 425 pounds 42 pounds 235 pounds 53 pounds

Question 13

5 points

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Solve the problem.

pH = -log10[H+] Find the [H+] if the pH = 8.4.

 3.98 x 10-8 2.51 x 10-8 3.98 x 10-9 2.51 x 10-9

Question 14

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Solve the problem.

Conservationists tagged 90 black-nosed rabbits in a national forest in 1990. In 1993, they tagged 180 black-nosed rabbits in the same range. If the rabbit population follows the exponential law, how many rabbits will be in the range 4 years from 1990?

 151 303 227 454

Question 15

5 points

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Solve the equation. Express irrational answers in exact form and as a decimal rounded to 3 decimal places.

ln x + ln (x + 7) = -5

 ≈ -7.001 -7 + ≈ 0.002 ≈ 0.001 ≈ 3.500

Question 16

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Solve the problem.

The amount of a certain drug in the bloodstream is modeled by the function , where y0 is the amount of the drug injected (in milligrams) and t is the elapsed time (in hours). Suppose that 10 milligrams are injected at 10:00 A.M. If a second injection is to be administered when there is 1 milligram of the drug present in the bloodstream, approximately when should the next dose be given? Express your answer to the nearest quarter hour.

 12:30 P.M 3:45 P.M 5:45 P.M 5: 30 P.M

Question 17

5 points

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Solve the equation.

8 + 4 ln x = 5

 {e-3/4}

Question 18

5 points

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The graph of an exponential function is given. Match the graph to one of the following functions.

 f(x) = 3x f(x) = 3x + 2 f(x) = 3x - 2 f(x) = 3x - 2

Question 19

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Solve the equation.

(ex)x∙ e48 = e14x

 {8} {6} {8, 6} {-8, -6}

Question 20

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Solve the problem.

A thermometer reading  is brought into a room with a constant temperature of  If the thermometer reads  after 5 minutes, what will it read after being in the room for 8 minutes? Assume the cooling follows Newton's Law of Cooling:
U = T + (Uo - T)ekt.

 104.4°F 30.85°F 66.42°F 45.6°F

Part 4:

Question 1

5 points

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Use the properties of determinants to find the value of the second determinant, given the value of the first.

= 11  = ?

 -11 -33 33 11

Question 2

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Perform the indicated matrix operations.

Let A =  and B = . Find 3A + 4B.

Question 3

5 points

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Write the partial fraction decomposition of the rational expression.

 +  + +  + +  + +  +

Question 4

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Solve the problem.

Given that  = 3, find the value of the determinant .

 0 -9 6 9

Question 5

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Solve the problem.

Jenny receives \$1270 per year from three different investments totaling \$20,000. One of the investments pays 6% , the second one pays 8%, and the third one pays 5%. If the money invested at 8% is \$1500 less than the amount invested at 5%, how much money has Jenny invested in the investment that pays 6%?

 \$8500 \$4500 \$10,000 \$1500

Question 6

5 points

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Write a system of equations associated with the augmented matrix. Do not solve.

Question 7

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Solve the system of equations.

 x = -4, y = 3, z = -2 x = -2, y = 3, z = -4 x = -2, y = -4, z = 3 inconsistent (no solution)

Question 8

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Write a system of equations associated with the augmented matrix. Do not solve.

Question 9

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Find the value of the determinant.

 33 22 -22 58

Question 10

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Perform the matrix multiplication.

Given A =  and B = , find AB.

Question 11

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Write the partial fraction decomposition of the rational expression.

 - + + +

Question 12

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Graph the inequality.

x + y < -2

Question 13

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Find the value of the determinant.

 -54 -30 0 30

Question 14

5 points

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Write the partial fraction decomposition of the rational expression.

 +  + +  + +  + +  +

Question 15

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Solve the problem.

A company has sales (measured in millions of dollars) of 50, 60, and 75 during the first three consecutive years. Find a quadratic function that fits these data, and use the result to predict the sales during the fourth year. Assume that the quadratic function is of the form y = ax2 + bx + c

 y = x2 - x + ; sales during the fourth year = \$151.25 million y = -5x2 + 40x + 15; sales during the fourth year = \$95 million y = x2 + x + 45; sales during the fourth year = \$95 million y = 5x2 + 5x + 40; sales during the fourth year = \$180 million

Question 16

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Find the maximum or minimum value of the objective function, subject to the constraints graphed in this feasible region.

z = x + 6y + 9 Find minimum.

 Minimum 25 Minimum 31 No Minimum Minimum 41

Question 17

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Verify that the values of the variables listed are solutions of the system of equations.

x = -4, y = 5, z = -2

 solution not a solution

Question 18

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Solve the system using the inverse method.

 x = 5, y = -2, z = 2 x = -5, y = -2, z = -2 x = 5, y = 2, z = -2 x = 2, y = 5, z = 2

Question 19

5 points

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Use Cramer's rule to solve the linear system.

 x = 2, y = 4 x = 4, y = 2 x = -2, y = 4 x = -4, y = -2

Question 20

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Find the inverse of the matrix.

 Subject Mathematics Due By (Pacific Time) 07/17/2014 06:04 pm
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