Question 1

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set.
-$$\begin{array} { l } 
8 x + 2 z = 52 \
7 x + 6 y + 8 z = 82 \
- 9 x - 8 y \quad = - 86
\end{array}$$

Accepted Answer

A)  $\{ ( 6 , - 4 , - 2 ) \}$ 
B)  $( \{ 7,2,2 ) \}$ 
C)  $\{ ( 4,2,4 ) \}$ 
D)  $\{ ( 6,4,2 ) \}$ 
A)  $\{ ( 6 , - 4 , - 2 ) \}$ 
B)  $( \{ 7,2,2 ) \}$ 
C)  $\{ ( 4,2,4 ) \}$ 
D)  $\{ ( 6,4,2 ) \}$

Question 2

Provide an appropriate response.
-When using the substitution or elimination method to solve a system of two equations,
you end up with an equation stating 0 = 0. What does this indicate to you about the
system of equations?

Accepted Answer

The answer of Provide an appropriate response.
-When using the substitution...

Question 3

Solve the problem.
-Two different gasohol mixtures are available. One contains 5% alcohol and the other 12% alcohol. How much of each should be mixed to obtain 1000 gal of gasohol containing 10% alcohol?

Accepted Answer

A)  714 gal 5%; 714 gal 12% 
B)  417 gal 5%; 583 gal 12% 
C)  50 gal 5%; 120 gal 12% 
D)  286 gal 5%; 714 gal 12% 
A)  714 gal 5%; 714 gal 12% 
B)  417 gal 5%; 583 gal 12% 
C)  50 gal 5%; 120 gal 12% 
D)  286 gal 5%; 714 gal 12%

Question 4

Evaluate the determinant.
-$$\left| \begin{array} { l l l l } 
0 & 7 & 9 & 7 \
0 & 2 & 9 & 5 \
5 & 4 & 7 & 2 \
4 & 1 & 2 & 2
\end{array} \right|$$

Accepted Answer

A)  4 
B)  $- 18$ 
C)  666 
D)  $- 31$ 
A)  4 
B)  $- 18$ 
C)  666 
D)  $- 31$

Question 5

Solve the problem.
-Bob fenced in a rectangular garden in his yard. The length of the rectangle is 7 ft longer than the width and the perimeter is 66 ft. What is the width of the rectangle?

Accepted Answer

A)  15 ft 
B)  26 ft 
C)  13 ft 
D)  12 ft 
A)  15 ft 
B)  26 ft 
C)  13 ft 
D)  12 ft

Question 6

Find the dimension of the matrix.
-$$\left[ \begin{array} { l l l } 
8 & 0 & 0 \
5 & 8 & 0 \
2 & 9 & 8
\end{array} \right]$$

Accepted Answer

A)  9 
B)  8 
C)  $3 \times 0$ 
D)  $3 \times 3$ 
A)  9 
B)  8 
C)  $3 \times 0$ 
D)  $3 \times 3$

Question 7

Solve the problem using matrices.
-Anne and Nancy use a metal alloy that is $19.69 \%$ copper to make jewelry. How many ounces of an alloy that is $15 \%$ copper must be mixed with an alloy that is $22 \%$ copper to form 100 ounces of the desired alloy?

Accepted Answer

A)  $72 \mathrm { oz }$ 
B)  $67 \mathrm { oz }$ 
C)  $35 \mathrm { oz }$ 
D)  $33 \mathrm { oz }$ 
A)  $72 \mathrm { oz }$ 
B)  $67 \mathrm { oz }$ 
C)  $35 \mathrm { oz }$ 
D)  $33 \mathrm { oz }$

Question 8

Provide an appropriate response.
-Describe the characteristics of an augmented matrix in diagonal or reduced-row echelon form.

Accepted Answer

A)  The matrix has ones on the main diagonal and zeros everywhere else. 
B)  The matrix has zeros on the main diagonal and ones below the main diagonal. 
C)  The matrix has ones on the main diagonal and zeros below the main diagonal. 
D)  The matrix has ones on the main diagonal and zeros above the main diagonal. 
A)  The matrix has ones on the main diagonal and zeros everywhere else. 
B)  The matrix has zeros on the main diagonal and ones below the main diagonal. 
C)  The matrix has ones on the main diagonal and zeros below the main diagonal. 
D)  The matrix has ones on the main diagonal and zeros above the main diagonal.

Question 9

Solve the system by using the inverse of the coefficient matrix.
-$$\begin{array} { l } 
5 x + 4 y = 8 \
6 x - 3 y = 33
\end{array}$$

Accepted Answer

A)  $\{ ( - 4,3 ) \}$ 
B)  $\{ ( 3 , - 4 ) \}$ 
C)  $\{ ( - 3,4 ) \}$ 
D)  $\{ ( 4 , - 3 ) \}$ 
A)  $\{ ( - 4,3 ) \}$ 
B)  $\{ ( 3 , - 4 ) \}$ 
C)  $\{ ( - 3,4 ) \}$ 
D)  $\{ ( 4 , - 3 ) \}$

Question 10

Find the partial fraction decomposition for the rational expression.
-$\frac { 21 x ^ { 2 } - 3 x ^ { 3 } } { x ^ { 2 } ( 7 - x ) }$

Accepted Answer

A)  7 
B)  $- 7$ 
C)  $- 3$ 
D)  3 
A)  7 
B)  $- 7$ 
C)  $- 3$ 
D)  3

Question 11

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the
solution with y arbitrary.
-$$\begin{array} { l } 
- 2 x - 8 y = - 6 \
- 8 x - 32 y = 6
\end{array}$$

Accepted Answer

A)  $\{ ( - 6,6 ) \}$ 
B)  $\varnothing$ 
C)  $\left\{ \frac { 3 } { 4 } y + 6 , y \right\}$ 
D)  $\{ ( 4,4 ) \}$ 
A)  $\{ ( - 6,6 ) \}$ 
B)  $\varnothing$ 
C)  $\left\{ \frac { 3 } { 4 } y + 6 , y \right\}$ 
D)  $\{ ( 4,4 ) \}$

Question 12

Graph the solution set of the system of inequalities.
-$$\begin{array} { l } 
x \leq 0 \
y \leq 0 \
x ^ { 2 } + y ^ { 2 } \geq 9 \
y + x \geq - 5
\end{array}$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 13

Which method should be used to solve the system? Explain your answer, including a description of the first step.
-$$\begin{aligned}
- 2 x ^ { 2 } + 5 y ^ { 2 } & = 4 \
- 2 x - 2 y & = - 1
\end{aligned}$$

Accepted Answer

Substitution should be used, b

Question 14

Find the inverse, if it exists, for the matrix.
-$\left[ \begin{array} { r r r r } 0 & 5 & 0 & - 2 \ 6 & 15 & - 3 & - 4 \ 12 & 10 & - 6 & - 2 \ 18 & 0 & - 6 & 0 \end{array} \right]$

Accepted Answer

A) 
$\left[ \begin{array} { r r r r } - \frac { 1 } { 3 } & - \frac { 3 } { 5 } & - 1 & - 2 \ \frac { 1 } { 3 } & \frac { 2 } { 5 } & 1 & \frac { 1 } { 2 } \ - \frac { 1 } { 3 } & - \frac { 1 } { 5 } & - 1 & - \frac { 1 } { 2 } \ \frac { 1 } { 6 } & 0 & \frac { 1 } { 3 } & 0 \end{array} \right]$ 
B) 
$$\left[ \begin{array} { c c c c } 
\frac { 1 } { 3 } & - \frac { 1 } { 3 } & \frac { 1 } { 3 } & - \frac { 1 } { 6 } \
\frac { 3 } { 5 } & - \frac { 2 } { 5 } & \frac { 1 } { 5 } & 0 \
1 & - 1 & 1 & \frac { 1 } { 3 } \
- \frac { 3 } { 2 } & - 1 & \frac { 1 } { 2 } & 0
\end{array} \right]$$ 
C)  The inverse does not exist. 
D) 
$$\left[ \begin{array} { c c c c } 
- \frac { 1 } { 3 } & \frac { 1 } { 3 } & - \frac { 1 } { 3 } & \frac { 1 } { 6 } \
- \frac { 3 } { 5 } & \frac { 2 } { 5 } & - \frac { 1 } { 5 } & 0 \
- 1 & 1 & - 1 & \frac { 1 } { 3 } \
- 2 & 1 & - \frac { 1 } { 2 } & 0
\end{array} \right]$$ 
A) 
$\left[ \begin{array} { r r r r } - \frac { 1 } { 3 } & - \frac { 3 } { 5 } & - 1 & - 2 \ \frac { 1 } { 3 } & \frac { 2 } { 5 } & 1 & \frac { 1 } { 2 } \ - \frac { 1 } { 3 } & - \frac { 1 } { 5 } & - 1 & - \frac { 1 } { 2 } \ \frac { 1 } { 6 } & 0 & \frac { 1 } { 3 } & 0 \end{array} \right]$ 
B) 
$$\left[ \begin{array} { c c c c } 
\frac { 1 } { 3 } & - \frac { 1 } { 3 } & \frac { 1 } { 3 } & - \frac { 1 } { 6 } \
\frac { 3 } { 5 } & - \frac { 2 } { 5 } & \frac { 1 } { 5 } & 0 \
1 & - 1 & 1 & \frac { 1 } { 3 } \
- \frac { 3 } { 2 } & - 1 & \frac { 1 } { 2 } & 0
\end{array} \right]$$ 
C)  The inverse does not exist. 
D) 
$$\left[ \begin{array} { c c c c } 
- \frac { 1 } { 3 } & \frac { 1 } { 3 } & - \frac { 1 } { 3 } & \frac { 1 } { 6 } \
- \frac { 3 } { 5 } & \frac { 2 } { 5 } & - \frac { 1 } { 5 } & 0 \
- 1 & 1 & - 1 & \frac { 1 } { 3 } \
- 2 & 1 & - \frac { 1 } { 2 } & 0
\end{array} \right]$$

Question 15

Evaluate the determinant.
-$\left| \begin{array} { l l l } 1 & 2 & 4 \ 2 & 4 & 3 \ 1 & 2 & 4 \end{array} \right|$

Accepted Answer

A)  -12 
B)  0 
C)  76 
D)  1 
A)  -12 
B)  0 
C)  76 
D)  1

Question 16

Graph the inequality.
-$y \geq|x+6|$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 17

Find the inverse, if it exists, for the matrix.
-$$\left[ \begin{array} { r r } 
2 & 3 \
0 & - 1
\end{array} \right]$$

Accepted Answer

A) 
$$\left[ \begin{array} { r r } 
\frac { 1 } { 2 } & - \frac { 3 } { 2 } \
0 & - 1
\end{array} \right]$$ 
B) 
$$\left[ \begin{array} { r r } 
0 & - 1 \
\frac { 1 } { 2 } & \frac { 3 } { 2 }
\end{array} \right]$$ 
C) 
$$\left[ \begin{array} { r r } 
\frac { 1 } { 2 } & \frac { 3 } { 2 } \
0 & - 1
\end{array} \right]$$
$$\left[ \begin{array} { r } 
- 1 \frac { 3 } { 2 } \
0 \frac { 1 } { 2 }
\end{array} \right]$$ 
D) 
$\left[\begin{array}{r}
-1 \frac{3}{2} \
0 \frac{1}{2}
\end{array}\right]$ 
A) 
$$\left[ \begin{array} { r r } 
\frac { 1 } { 2 } & - \frac { 3 } { 2 } \
0 & - 1
\end{array} \right]$$ 
B) 
$$\left[ \begin{array} { r r } 
0 & - 1 \
\frac { 1 } { 2 } & \frac { 3 } { 2 }
\end{array} \right]$$ 
C) 
$$\left[ \begin{array} { r r } 
\frac { 1 } { 2 } & \frac { 3 } { 2 } \
0 & - 1
\end{array} \right]$$
$$\left[ \begin{array} { r } 
- 1 \frac { 3 } { 2 } \
0 \frac { 1 } { 2 }
\end{array} \right]$$ 
D) 
$\left[\begin{array}{r}
-1 \frac{3}{2} \
0 \frac{1}{2}
\end{array}\right]$

Question 18

Graph the solution set of the system of inequalities.
-

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 19

Provide an appropriate response.
-Which of the following inequalities satisfies the following description: the region inside an ellipse centered at the origin, with $x$-intercepts at $- 2$ and 2 , and $y$-intercepts at 3 and $- 3$ ?

Accepted Answer

A) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } > 1$ B) $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 } < 1$ C) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } < 1$ D) $\frac { x ^ { 2 } } { 2 } + \frac { y ^ { 2 } } { 3 } < 1$ A) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } > 1$ B) $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 } < 1$ C) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } < 1$ D) $\frac { x ^ { 2 } } { 2 } + \frac { y ^ { 2 } } { 3 } < 1$

Question 20

The graph shows the region of feasible solutions. Find the maximum or minimum value, as specified, of the objective
function.
-objective function $= 4 x + 3 y ;$ maximum

Accepted Answer

A)  13 
B)  100 
C)  29 
D)  27 
A)  13 
B)  100 
C)  29 
D)  27

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set. - 8x+2z=52 7x+6y+8z=82 -9x-8y=-86

Provide an appropriate response. -When using the substitution or elimination method to solve a system of two equations, you end up with an equation stating 0 = 0. What does this indicate to you about the system of equations?

Solve the problem. -Two different gasohol mixtures are available. One contains 5% alcohol and the other 12% alcohol. How much of each should be mixed to obtain 1000 gal of gasohol containing 10% alcohol?

Evaluate the determinant. - $\left| \begin{array} { l l l l } 0 & 7 & 9 & 7 \\0 & 2 & 9 & 5 \\5 & 4 & 7 & 2 \\4 & 1 & 2 & 2\end{array} \right|$

Solve the problem. -Bob fenced in a rectangular garden in his yard. The length of the rectangle is 7 ft longer than the width and the perimeter is 66 ft. What is the width of the rectangle?

Find the dimension of the matrix. - $\left[ \begin{array} { l l l } 8 & 0 & 0 \\5 & 8 & 0 \\2 & 9 & 8\end{array} \right]$

Solve the problem using matrices. -Anne and Nancy use a metal alloy that is $19.69 \%$ copper to make jewelry. How many ounces of an alloy that is $15 \%$ copper must be mixed with an alloy that is $22 \%$ copper to form 100 ounces of the desired alloy?

Provide an appropriate response. -Describe the characteristics of an augmented matrix in diagonal or reduced-row echelon form.

Solve the system by using the inverse of the coefficient matrix. - 5x+4y=8 6x-3y=33

Find the partial fraction decomposition for the rational expression. - $\frac { 21 x ^ { 2 } - 3 x ^ { 3 } } { x ^ { 2 } ( 7 - x ) }$

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. - -2x-8y=-6 -8x-32y=6

Graph the solution set of the system of inequalities. - x\leq0 y\leq0 +\geq9 y+x\geq-5 $Graph the solution set of the system of inequalities. - \begin{array} { l } x \leq 0 \\ y \leq 0 \\ x ^ { 2 } + y ^ { 2 } \geq 9 \\ y + x \geq - 5 \end{array}$

Which method should be used to solve the system? Explain your answer, including a description of the first step. - -2+5 =4 -2x-2y =-1

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r r r } 0 & 5 & 0 & - 2 \\ 6 & 15 & - 3 & - 4 \\ 12 & 10 & - 6 & - 2 \\ 18 & 0 & - 6 & 0 \end{array} \right]$

Evaluate the determinant. - $\left| \begin{array} { l l l } 1 & 2 & 4 \\ 2 & 4 & 3 \\ 1 & 2 & 4 \end{array} \right|$

Graph the inequality. - $y \geq|x+6|$ $Graph the inequality. - y \geq|x+6|$

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r } 2 & 3 \\0 & - 1\end{array} \right]$

Graph the solution set of the system of inequalities. -

Provide an appropriate response. -Which of the following inequalities satisfies the following description: the region inside an ellipse centered at the origin, with $x$ -intercepts at $- 2$ and 2 , and $y$ -intercepts at 3 and $- 3$ ?

The graph shows the region of feasible solutions. Find the maximum or minimum value, as specified, of the objective function. -objective function $= 4 x + 3 y ;$ maximum

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 9: Systems and Matrices

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set. - 8x+2z=52 7x+6y+8z=82 -9x-8y=-86

Provide an appropriate response. -When using the substitution or elimination method to solve a system of two equations, you end up with an equation stating 0 = 0. What does this indicate to you about the system of equations?

Solve the problem. -Two different gasohol mixtures are available. One contains 5% alcohol and the other 12% alcohol. How much of each should be mixed to obtain 1000 gal of gasohol containing 10% alcohol?

Evaluate the determinant. - ∣0797029554724122∣\left| \begin{array} { l l l l } 0 & 7 & 9 & 7 \\0 & 2 & 9 & 5 \\5 & 4 & 7 & 2 \\4 & 1 & 2 & 2\end{array} \right|​0054​7241​9972​7522​​

Solve the problem. -Bob fenced in a rectangular garden in his yard. The length of the rectangle is 7 ft longer than the width and the perimeter is 66 ft. What is the width of the rectangle?

Find the dimension of the matrix. - [800580298]\left[ \begin{array} { l l l } 8 & 0 & 0 \\5 & 8 & 0 \\2 & 9 & 8\end{array} \right]​852​089​008​​

Solve the problem using matrices. -Anne and Nancy use a metal alloy that is 19.69%19.69 \%19.69% copper to make jewelry. How many ounces of an alloy that is 15%15 \%15% copper must be mixed with an alloy that is 22%22 \%22% copper to form 100 ounces of the desired alloy?

Provide an appropriate response. -Describe the characteristics of an augmented matrix in diagonal or reduced-row echelon form.

Solve the system by using the inverse of the coefficient matrix. - 5x+4y=8 6x-3y=33

Find the partial fraction decomposition for the rational expression. - 21x2−3x3x2(7−x)\frac { 21 x ^ { 2 } - 3 x ^ { 3 } } { x ^ { 2 } ( 7 - x ) }x2(7−x)21x2−3x3​

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. - -2x-8y=-6 -8x-32y=6

Graph the solution set of the system of inequalities. - x\leq0 y\leq0 +\geq9 y+x\geq-5

Which method should be used to solve the system? Explain your answer, including a description of the first step. - -2+5 =4 -2x-2y =-1

Find the inverse, if it exists, for the matrix. - [050−2615−3−41210−6−2180−60]\left[ \begin{array} { r r r r } 0 & 5 & 0 & - 2 \\ 6 & 15 & - 3 & - 4 \\ 12 & 10 & - 6 & - 2 \\ 18 & 0 & - 6 & 0 \end{array} \right]​061218​515100​0−3−6−6​−2−4−20​​

Evaluate the determinant. - ∣124243124∣\left| \begin{array} { l l l } 1 & 2 & 4 \\ 2 & 4 & 3 \\ 1 & 2 & 4 \end{array} \right|​121​242​434​​

Graph the inequality. - y≥∣x+6∣y \geq|x+6|y≥∣x+6∣

Find the inverse, if it exists, for the matrix. - [230−1]\left[ \begin{array} { r r } 2 & 3 \\0 & - 1\end{array} \right][20​3−1​]

Graph the solution set of the system of inequalities. -

Provide an appropriate response. -Which of the following inequalities satisfies the following description: the region inside an ellipse centered at the origin, with xxx -intercepts at −2- 2−2 and 2 , and yyy -intercepts at 3 and −3- 3−3 ?

The graph shows the region of feasible solutions. Find the maximum or minimum value, as specified, of the objective function. -objective function =4x+3y;= 4 x + 3 y ;=4x+3y; maximum

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Evaluate the determinant. - $\left| \begin{array} { l l l l } 0 & 7 & 9 & 7 \\0 & 2 & 9 & 5 \\5 & 4 & 7 & 2 \\4 & 1 & 2 & 2\end{array} \right|$

Find the dimension of the matrix. - $\left[ \begin{array} { l l l } 8 & 0 & 0 \\5 & 8 & 0 \\2 & 9 & 8\end{array} \right]$

Solve the problem using matrices. -Anne and Nancy use a metal alloy that is $19.69 \%$ copper to make jewelry. How many ounces of an alloy that is $15 \%$ copper must be mixed with an alloy that is $22 \%$ copper to form 100 ounces of the desired alloy?

Find the partial fraction decomposition for the rational expression. - $\frac { 21 x ^ { 2 } - 3 x ^ { 3 } } { x ^ { 2 } ( 7 - x ) }$

Graph the solution set of the system of inequalities. - x\leq0 y\leq0 +\geq9 y+x\geq-5 $Graph the solution set of the system of inequalities. - \begin{array} { l } x \leq 0 \\ y \leq 0 \\ x ^ { 2 } + y ^ { 2 } \geq 9 \\ y + x \geq - 5 \end{array}$

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r r r } 0 & 5 & 0 & - 2 \\ 6 & 15 & - 3 & - 4 \\ 12 & 10 & - 6 & - 2 \\ 18 & 0 & - 6 & 0 \end{array} \right]$

Evaluate the determinant. - $\left| \begin{array} { l l l } 1 & 2 & 4 \\ 2 & 4 & 3 \\ 1 & 2 & 4 \end{array} \right|$

Graph the inequality. - $y \geq|x+6|$ $Graph the inequality. - y \geq|x+6|$

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r } 2 & 3 \\0 & - 1\end{array} \right]$

Provide an appropriate response. -Which of the following inequalities satisfies the following description: the region inside an ellipse centered at the origin, with $x$ -intercepts at $- 2$ and 2 , and $y$ -intercepts at 3 and $- 3$ ?

The graph shows the region of feasible solutions. Find the maximum or minimum value, as specified, of the objective function. -objective function $= 4 x + 3 y ;$ maximum