# alegegra test

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Question description

Solve the following system.

 2x + y = 2 x + y - z = 4 3x + 2y + z = 0
 A. {(2, 1, 4)} B. {(1, 0, -3)} C. {(0, 0, -2)} D. {(3, 2, -1)}

Write the partial fraction decomposition for the following rational expression.

x2– 6x + 3/(x – 2)3

A. 1/x – 4 – 2/(x – 2)2 – 6/(x – 2)

B. 1/x – 2 – 4/(x – 2)2 – 5/(x – 1)3

C. 1/x – 3 – 2/(x – 3)2 – 5/(x – 2)

D. 1/x – 2 – 2/(x – 2)2 – 5/(x – 2)3

Evaluate 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) = log5(x + 4)

A. (-4, ∞)

B. (-5, -∞)

C. (7, -∞)

D. (-9, ∞)

The half-life of the radioactive element krypton-91 is 10 seconds. If 16 grams of krypton-91 are initially present, how many grams are present after 10 seconds? 20 seconds?

 A. 10 grams after 10 seconds; 6 grams after 20 seconds B. 12 grams after 10 seconds; 7 grams after 20 seconds C. 4 grams after 10 seconds; 1 gram after 20 seconds D. 8 grams after 10 seconds; 4 grams after 20 seconds

Write the partial fraction decomposition for the following rational expression.

x2– 6x + 3/(x – 2)3

A. 1/x – 4 – 2/(x – 2)2 – 6/(x – 2)

B. 1/x – 2 – 4/(x – 2)2 – 5/(x – 1)3

C. 1/x – 3 – 2/(x – 3)2 – 5/(x – 2)

D. 1/x – 2 – 2/(x – 2)2 – 5/(x – 2)

Solve the following system.

 2x + y = 2 x + y - z = 4 3x + 2y + z = 0
 A. {(2, 1, 4)} B. {(1, 0, -3)} C. {(0, 0, -2)} D. {(3, 2, -1)}

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)}

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 + 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)}

Perform the long division and write the partial fraction decomposition of the remainder term.

x4– x2+ 2/x3- x2

A. x + 3 - 2/x - 1/x2 + 4x - 1

B. 2x + 1 - 2/x - 2/x + 2/x + 1

C. 2x + 1 - 2/x2 - 2/x + 5/x - 1

D. x + 1 - 2/x - 2/x2 + 2/x – 1

Solve the following system.

 x = y + 4 3x + 7y = -18
 A. {(2, -1)} B. {(1, 4)} C. {(2, -5)} D. {(1, -3)}

Write the partial fraction decomposition for the following rational expression.

4/2x2- 5x – 3

 A. 4/6(x - 2) - 8/7(4x + 1) B. 4/7(x - 3) - 8/7(2x + 1) C. 4/7(x - 2) - 8/7(3x + 1) D. 4/6(x - 2) - 8/7(3x + 1)

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