Question 1

Evaluate the determinant. $\left| \begin{array} { c c } 8 & 10 \ - 8 & 4 \end{array} \right|$

Accepted Answer

A)  $\quad D = - 48$ 
B)  $\quad D = 2,560$ 
C)  $D = - 112$ 
D)  $\quad D = - 117$ 
E)  $\quad D = 112$ 
A)  $\quad D = - 48$ 
B)  $\quad D = 2,560$ 
C)  $D = - 112$ 
D)  $\quad D = - 117$ 
E)  $\quad D = 112$ E

Question 2

Find the inverse of the matrix. $$\left[ \begin{array} { c c } 
1 & 4 \
- 4 & - 1
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c } \frac { 1 } { 15 } & - \frac { 4 } { 15 } \ \frac { 4 } { 15 } & \frac { 1 } { 15 } \end{array} \right]$ 
B) 
$\left[ \begin{array} { c c } - \frac { 1 } { 15 } & - \frac { 4 } { 15 } \ - \frac { 4 } { 15 } & \frac { 1 } { 15 } \end{array} \right]$ 
C) 
$\left[\begin{array}{cc}
-\frac{1}{15} & \frac{4}{15} \
\frac{4}{15} & \frac{1}{15}
\end{array}\right]$ 
D)  $\left[ \begin{array} { c c } - \frac { 1 } { 15 } & - \frac { 4 } { 15 } \ \frac { 4 } { 15 } & \frac { 1 } { 15 } \end{array} \right]$ 
E)  $\left[ \begin{array} { c c } - \frac { 1 } { 15 } & - \frac { 4 } { 15 } \ \frac { 4 } { 15 } & - \frac { 1 } { 15 } \end{array} \right]$ 
A)  $\left[ \begin{array} { c c } \frac { 1 } { 15 } & - \frac { 4 } { 15 } \ \frac { 4 } { 15 } & \frac { 1 } { 15 } \end{array} \right]$ 
B) 
$\left[ \begin{array} { c c } - \frac { 1 } { 15 } & - \frac { 4 } { 15 } \ - \frac { 4 } { 15 } & \frac { 1 } { 15 } \end{array} \right]$ 
C) 
$\left[\begin{array}{cc}
-\frac{1}{15} & \frac{4}{15} \
\frac{4}{15} & \frac{1}{15}
\end{array}\right]$ 
D)  $\left[ \begin{array} { c c } - \frac { 1 } { 15 } & - \frac { 4 } { 15 } \ \frac { 4 } { 15 } & \frac { 1 } { 15 } \end{array} \right]$ 
E)  $\left[ \begin{array} { c c } - \frac { 1 } { 15 } & - \frac { 4 } { 15 } \ \frac { 4 } { 15 } & - \frac { 1 } { 15 } \end{array} \right]$ D

Question 3

Which fraction appears in the partial fraction decomposition of $\frac { 5 x ^ { 2 } + 49 x + 108 } { x ( x + 6 ) ^ { 2 } }$ ?

Accepted Answer

A)  $\quad \frac { 3 } { ( x + 6 ) ^ { 2 } }$ 
B)  $\frac { 1 } { x + 6 }$ 
C)  $\frac { 6 } { x }$ 
D)  $\frac { 9 } { x }$ 
E)  $\frac { 1 } { ( x + 6 ) ^ { 2 } }$ 
A)  $\quad \frac { 3 } { ( x + 6 ) ^ { 2 } }$ 
B)  $\frac { 1 } { x + 6 }$ 
C)  $\frac { 6 } { x }$ 
D)  $\frac { 9 } { x }$ 
E)  $\frac { 1 } { ( x + 6 ) ^ { 2 } }$ E

Question 4

Solve the system by Gauss-Jordan elimination, if possible. If (x, y) is the solution to the system, give the value of x. $$\left\{ \begin{array} { r } 
x - 2 y = 14 \
y = - 2
\end{array} \right.$$

Accepted Answer

A)  11 
B)  $- 10$ 
C)  $- 11$ 
D)  10 
E)  no solution 
A)  11 
B)  $- 10$ 
C)  $- 11$ 
D)  10 
E)  no solution

Question 5

Find the inverse of the matrix. $$\left[ \begin{array} { c c } 
1 & 2 \
- 2 & - 1
\end{array} \right]$$

Accepted Answer

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

Question 6

Solve the system using Gaussian elimination. If $( x , y )$ is the solution to the system, give the value of $2 x - y$.
$$\left\{ \begin{array} { c } 
x + y = 23 \
x - 2 y = - 13
\end{array} \right.$$

Accepted Answer

A)  $\quad 10$ 
B)  13 
C)  $\quad 7$ 
D)  $\quad 8$ 
E)  $\quad 9$ 
A)  $\quad 10$ 
B)  13 
C)  $\quad 7$ 
D)  $\quad 8$ 
E)  $\quad 9$

Question 7

Solve the system by the addition method, if possible. If a solution exists, give the value of x. $$\left\{ \begin{array} { c } 
2 ( x + y ) = y - 19 \
7 ( x + 10 ) = y + 17
\end{array} \right.$$

Accepted Answer

A)  $- 5$ 
B)  $- 11$ 
C)  $- 2$ 
D)  $- 8$ 
E)  no solution 
A)  $- 5$ 
B)  $- 11$ 
C)  $- 2$ 
D)  $- 8$ 
E)  no solution

Question 8

Use a graphing calculator to approximate the solutions of the system. $$\left\{ \begin{array} { c } 
4.2 x + 7.1 y = 39.35 \
- 5 x + 4 y = 6.7
\end{array} \right.$$

Accepted Answer

A)  $\quad ( 4.3,2.1 )$ 
B)  $\quad ( - 2.1 , - 4.3 )$ 
C)  $\quad ( - 2.2,7.4 )$ 
D)  $\quad ( 6.4 , - 1.2 )$ 
E)  $\quad ( 2.1,4.3 )$ 
A)  $\quad ( 4.3,2.1 )$ 
B)  $\quad ( - 2.1 , - 4.3 )$ 
C)  $\quad ( - 2.2,7.4 )$ 
D)  $\quad ( 6.4 , - 1.2 )$ 
E)  $\quad ( 2.1,4.3 )$

Question 9

Find the inverse of the matrix. $$\left[ \begin{array} { c c c } 
4 & 1 & - 1 \
4 & 4 & - 1 \
- 1 & - 1 & 1
\end{array} \right]$$

Accepted Answer

A) $\left[ \begin{array} { c c c } \frac { 1 } { 3 } & 1 & \frac { 1 } { 3 } \ - \frac { 1 } { 3 } & \frac { 1 } { 3 } & 0 \ - 5 & \frac { 1 } { 3 } & \frac { 4 } { 3 } \end{array} \right] \quad$ 
B)  $\left[ \begin{array} { c c c } - \frac { 1 } { 3 } & 0 & \frac { 1 } { 3 } \ \frac { 1 } { 3 } & \frac { 1 } { 3 } & 0 \ 0 & \frac { 1 } { 3 } & \frac { 4 } { 3 } \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } \frac { 1 } { 3 } & 0 & \frac { 1 } { 3 } \ - \frac { 1 } { 3 } & \frac { 1 } { 3 } & 0 \ 0 & \frac { 1 } { 3 } & \frac { 4 } { 3 } \end{array} \right]$ 
D)  $\quad \left[ \begin{array} { c c c } \frac { 1 } { 3 } & 0 & \frac { 1 } { 3 } \ \frac { 1 } { 3 } & - \frac { 1 } { 3 } & 0 \ 0 & \frac { 1 } { 3 } & \frac { 4 } { 3 } \end{array} \right]$ 
E)  $\left[ \begin{array} { c c c } - \frac { 1 } { 3 } & 0 & \frac { 1 } { 3 } \ - \frac { 1 } { 3 } & \frac { 1 } { 3 } & 0 \ 0 & \frac { 1 } { 3 } & \frac { 4 } { 3 } \end{array} \right]$ 
A) $\left[ \begin{array} { c c c } \frac { 1 } { 3 } & 1 & \frac { 1 } { 3 } \ - \frac { 1 } { 3 } & \frac { 1 } { 3 } & 0 \ - 5 & \frac { 1 } { 3 } & \frac { 4 } { 3 } \end{array} \right] \quad$ 
B)  $\left[ \begin{array} { c c c } - \frac { 1 } { 3 } & 0 & \frac { 1 } { 3 } \ \frac { 1 } { 3 } & \frac { 1 } { 3 } & 0 \ 0 & \frac { 1 } { 3 } & \frac { 4 } { 3 } \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } \frac { 1 } { 3 } & 0 & \frac { 1 } { 3 } \ - \frac { 1 } { 3 } & \frac { 1 } { 3 } & 0 \ 0 & \frac { 1 } { 3 } & \frac { 4 } { 3 } \end{array} \right]$ 
D)  $\quad \left[ \begin{array} { c c c } \frac { 1 } { 3 } & 0 & \frac { 1 } { 3 } \ \frac { 1 } { 3 } & - \frac { 1 } { 3 } & 0 \ 0 & \frac { 1 } { 3 } & \frac { 4 } { 3 } \end{array} \right]$ 
E)  $\left[ \begin{array} { c c c } - \frac { 1 } { 3 } & 0 & \frac { 1 } { 3 } \ - \frac { 1 } { 3 } & \frac { 1 } { 3 } & 0 \ 0 & \frac { 1 } { 3 } & \frac { 4 } { 3 } \end{array} \right]$

Question 10

Find the inverse of the matrix. $$\left[ \begin{array} { c c } 
2 & 1 \
- 1 & 8
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c } \frac { 8 } { 17 } & - \frac { 1 } { 17 } \ - \frac { 1 } { 17 } & \frac { 2 } { 17 } \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } \frac { 8 } { 17 } & \frac { 1 } { 17 } \ \frac { 1 } { 17 } & \frac { 2 } { 17 } \end{array} \right]$ 
C) 
$$\left[ \begin{array} { c c } 
- \frac { 8 } { 17 } & - \frac { 1 } { 17 } \
\frac { 1 } { 17 } & \frac { 2 } { 17 }
\end{array} \right]$$ 
D)  $\left[ \begin{array} { c c } \frac { 8 } { 17 } & - \frac { 1 } { 17 } \ \frac { 1 } { 17 } & \frac { 2 } { 17 } \end{array} \right]$ 
E)  $\left[ \begin{array} { c c } \frac { 8 } { 17 } & - \frac { 1 } { 17 } \ \frac { 1 } { 17 } & - \frac { 2 } { 17 } \end{array} \right]$ 
A)  $\left[ \begin{array} { c c } \frac { 8 } { 17 } & - \frac { 1 } { 17 } \ - \frac { 1 } { 17 } & \frac { 2 } { 17 } \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } \frac { 8 } { 17 } & \frac { 1 } { 17 } \ \frac { 1 } { 17 } & \frac { 2 } { 17 } \end{array} \right]$ 
C) 
$$\left[ \begin{array} { c c } 
- \frac { 8 } { 17 } & - \frac { 1 } { 17 } \
\frac { 1 } { 17 } & \frac { 2 } { 17 }
\end{array} \right]$$ 
D)  $\left[ \begin{array} { c c } \frac { 8 } { 17 } & - \frac { 1 } { 17 } \ \frac { 1 } { 17 } & \frac { 2 } { 17 } \end{array} \right]$ 
E)  $\left[ \begin{array} { c c } \frac { 8 } { 17 } & - \frac { 1 } { 17 } \ \frac { 1 } { 17 } & - \frac { 2 } { 17 } \end{array} \right]$

Question 11

Find the graph of the linear inequality. $$5 y \geq 2 x - 10$$

Accepted Answer

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

Question 12

What is element $a _ { 11 }$ of the inverse of the following matrix?
$$\left[ \begin{array} { c c } 
8 & 1 \
1 & 16
\end{array} \right]$$

Accepted Answer

A)  $- \frac { 8 } { 127 }$ 
B)  $\frac { 16 } { 127 }$ 
C)  $- \frac { 16 } { 127 }$ 
D)  $\quad \frac { 8 } { 127 }$ 
E)  $\frac { 16 } { 65 }$ 
A)  $- \frac { 8 } { 127 }$ 
B)  $\frac { 16 } { 127 }$ 
C)  $- \frac { 16 } { 127 }$ 
D)  $\quad \frac { 8 } { 127 }$ 
E)  $\frac { 16 } { 65 }$

Question 13

Decompose the fraction into partial fractions. $\frac { 7 x - 15 } { x ^ { 2 } + 6 x - 7 }$

Accepted Answer

A)  $\quad \frac { 8 } { x + 7 } + \frac { 1 } { x - 2 }$ 
B)  $\quad \frac { 8 } { x + 7 } - \frac { 1 } { x - 1 }$ 
C)  $\quad \frac { 6 } { x - 7 } - \frac { 1 } { x + 1 }$ 
D)  $\quad \frac { 6 } { x - 7 } + \frac { 1 } { x + 1 }$ 
E)  none of these 
A)  $\quad \frac { 8 } { x + 7 } + \frac { 1 } { x - 2 }$ 
B)  $\quad \frac { 8 } { x + 7 } - \frac { 1 } { x - 1 }$ 
C)  $\quad \frac { 6 } { x - 7 } - \frac { 1 } { x + 1 }$ 
D)  $\quad \frac { 6 } { x - 7 } + \frac { 1 } { x + 1 }$ 
E)  none of these

Question 14

Let $B = \left[ \begin{array} { l l } - & 3 \ 2 \end{array} \right] , C = \left[ \begin{array} { l l } 2 & 1 \end{array} \right]$.
Perform the operation: $( B C ) ^ { 2 }$.

Accepted Answer

A)  $\left[ \begin{array} { c } - 16 \ - 8 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } 24 & 12 \ - 16 & - 8 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l } 24 & 12 \end{array} \right]$ 
D)  $[ 24 ]$ 
E)  none of these 
A)  $\left[ \begin{array} { c } - 16 \ - 8 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } 24 & 12 \ - 16 & - 8 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l } 24 & 12 \end{array} \right]$ 
D)  $[ 24 ]$ 
E)  none of these

Question 15

Find the graph of the linear inequality. $$4 x - 2 y > 11$$

Accepted Answer

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

Question 16

Let $B = \left[ \begin{array} { l l } - & 3 \ 2 \end{array} \right] , C = \left[ \begin{array} { l l } 4 & 1 \end{array} \right]$.
Perform the operation: $( B C ) ^ { 2 }$.

Accepted Answer

A) 
$\left[ \begin{array} { l } - 80 \ - 20 \end{array} \right]$ 
B)  $[ 120 ]$ 
C)  $\left[ \begin{array} { r r } 120 & 30 \ - 80 & - 20 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l } 120 & 30 \end{array} \right]$ 
E)  none of these 
A) 
$\left[ \begin{array} { l } - 80 \ - 20 \end{array} \right]$ 
B)  $[ 120 ]$ 
C)  $\left[ \begin{array} { r r } 120 & 30 \ - 80 & - 20 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l } 120 & 30 \end{array} \right]$ 
E)  none of these

Question 17

Find $7 A$.
$$A = \left[ \begin{array} { l l } 
8 & 8 \
3 & 2
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c } 56 & 8 \ 3 & 2 \end{array} \right]$ 
B) 
$\left[ \begin{array} { c c } 56 & 8 \ 21 & 14 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c } 8 & 56 \ 21 & 14 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c } 8 & 56 \ 3 & 14 \end{array} \right]$ 
E)  $\left[ \begin{array} { l l } 56 & 56 \ 21 & 14 \end{array} \right]$ 
A)  $\left[ \begin{array} { c c } 56 & 8 \ 3 & 2 \end{array} \right]$ 
B) 
$\left[ \begin{array} { c c } 56 & 8 \ 21 & 14 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c } 8 & 56 \ 21 & 14 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c } 8 & 56 \ 3 & 14 \end{array} \right]$ 
E)  $\left[ \begin{array} { l l } 56 & 56 \ 21 & 14 \end{array} \right]$

Question 18

Which fraction appears in the partial fraction decomposition of $\frac { 5 x ^ { 2 } + 17 x + 12 } { x ( x + 2 ) ^ { 2 } }$ ?

Accepted Answer

A)  $\frac { 1 } { ( x + 2 ) ^ { 2 } }$ 
B)  $\frac { 2 } { x }$ 
C)  $\frac { 5 } { x }$ 
D)  $\frac { 3 } { ( x + 2 ) ^ { 2 } }$ 
E)  $\frac { 1 } { x + 2 }$ 
A)  $\frac { 1 } { ( x + 2 ) ^ { 2 } }$ 
B)  $\frac { 2 } { x }$ 
C)  $\frac { 5 } { x }$ 
D)  $\frac { 3 } { ( x + 2 ) ^ { 2 } }$ 
E)  $\frac { 1 } { x + 2 }$

Question 19

Illustration shows three circles traced out by a figure skater during her performance.If the centers of the circles are the given distances apart, find the radius of each circle.  
$$A = 10 , B = 14 , C = 20$$

Accepted Answer

A)  $\quad r _ { 1 } = 2 , r _ { 2 } = 12 , r _ { 3 } = 8$ 
B)  $\quad r _ { 1 } = 12 , r _ { 2 } = 2 , r _ { 3 } = 8$ 
C)  $\quad r _ { 1 } = 8 , r _ { 2 } = 12 , r _ { 3 } = 2$ 
D)  $\quad r _ { 1 } = 1 , r _ { 2 } = 8 , r _ { 3 } = 13$ 
E)  $\quad r _ { 1 } = 2 , r _ { 2 } = 8 , r _ { 3 } = 12$ 
A)  $\quad r _ { 1 } = 2 , r _ { 2 } = 12 , r _ { 3 } = 8$ 
B)  $\quad r _ { 1 } = 12 , r _ { 2 } = 2 , r _ { 3 } = 8$ 
C)  $\quad r _ { 1 } = 8 , r _ { 2 } = 12 , r _ { 3 } = 2$ 
D)  $\quad r _ { 1 } = 1 , r _ { 2 } = 8 , r _ { 3 } = 13$ 
E)  $\quad r _ { 1 } = 2 , r _ { 2 } = 8 , r _ { 3 } = 12$

Question 20

Find values of x and y, if any, that will make the matrices equal. $$\left[ \begin{array} { l l } 
x & y \
3 & 9
\end{array} \right] = \left[ \begin{array} { l l } 
2 & 8 \
3 & 9
\end{array} \right]$$

Accepted Answer

A)  $x = 2 , y = 8$ 
B)  $x = - 2 , y = 8$ 
C)  $x = 8 , y = 2$ 
D)  $x = - 2 , y = - 8$ 
E)  no solution 
A)  $x = 2 , y = 8$ 
B)  $x = - 2 , y = 8$ 
C)  $x = 8 , y = 2$ 
D)  $x = - 2 , y = - 8$ 
E)  no solution

Evaluate the determinant. $\left| \begin{array} { c c } 8 & 10 \\ - 8 & 4 \end{array} \right|$

Find the inverse of the matrix. $\left[ \begin{array} { c c } 1 & 4 \\- 4 & - 1\end{array} \right]$

Which fraction appears in the partial fraction decomposition of $\frac { 5 x ^ { 2 } + 49 x + 108 } { x ( x + 6 ) ^ { 2 } }$ ?

Solve the system by Gauss-Jordan elimination, if possible. If (x, y) is the solution to the system, give the value of x. $\left\{ \begin{array} { r } x - 2 y = 14 \\y = - 2\end{array} \right.$

Find the inverse of the matrix. $\left[ \begin{array} { c c } 1 & 2 \\- 2 & - 1\end{array} \right]$

Solve the system using Gaussian elimination. If $( x , y )$ is the solution to the system, give the value of $2 x - y$ . $\left\{ \begin{array} { c } x + y = 23 \\x - 2 y = - 13\end{array} \right.$

Solve the system by the addition method, if possible. If a solution exists, give the value of x. $\left\{ \begin{array} { c } 2 ( x + y ) = y - 19 \\7 ( x + 10 ) = y + 17\end{array} \right.$

Use a graphing calculator to approximate the solutions of the system. $\left\{ \begin{array} { c } 4.2 x + 7.1 y = 39.35 \\- 5 x + 4 y = 6.7\end{array} \right.$

Find the inverse of the matrix. $\left[ \begin{array} { c c c } 4 & 1 & - 1 \\4 & 4 & - 1 \\- 1 & - 1 & 1\end{array} \right]$

Find the inverse of the matrix. $\left[ \begin{array} { c c } 2 & 1 \\- 1 & 8\end{array} \right]$

Find the graph of the linear inequality. $5 y \geq 2 x - 10$

What is element $a _ { 11 }$ of the inverse of the following matrix? $\left[ \begin{array} { c c } 8 & 1 \\1 & 16\end{array} \right]$

Decompose the fraction into partial fractions. $\frac { 7 x - 15 } { x ^ { 2 } + 6 x - 7 }$

Let $B = \left[ \begin{array} { l l } - & 3 \\ 2 \end{array} \right] , C = \left[ \begin{array} { l l } 2 & 1 \end{array} \right]$ . Perform the operation: $( B C ) ^ { 2 }$ .

Find the graph of the linear inequality. $4 x - 2 y > 11$

Let $B = \left[ \begin{array} { l l } - & 3 \\ 2 \end{array} \right] , C = \left[ \begin{array} { l l } 4 & 1 \end{array} \right]$ . Perform the operation: $( B C ) ^ { 2 }$ .

Find $7 A$ . $A = \left[ \begin{array} { l l } 8 & 8 \\3 & 2\end{array} \right]$

Which fraction appears in the partial fraction decomposition of $\frac { 5 x ^ { 2 } + 17 x + 12 } { x ( x + 2 ) ^ { 2 } }$ ?

Illustration shows three circles traced out by a figure skater during her performance.If the centers of the circles are the given distances apart, find the radius of each circle. $A = 10 , B = 14 , C = 20$

Find values of x and y, if any, that will make the matrices equal. $\left[ \begin{array} { l l } x & y \\3 & 9\end{array} \right] = \left[ \begin{array} { l l } 2 & 8 \\3 & 9\end{array} \right]$

A Review of Basic Algebra

Equations and Inequalities

The Rectangular Coordinate System and Graphs of Equations

Functions Functions and Function Notation

Exponential and Logarithmic Functions

Solving Polynomial Equations

Conic Sections and Quadratic Systems

Natural Number Functions and Probability

Filters

Exam 7: Linear Systems

Evaluate the determinant. ∣810−84∣\left| \begin{array} { c c } 8 & 10 \\ - 8 & 4 \end{array} \right|​8−8​104​​

Find the inverse of the matrix. [14−4−1]\left[ \begin{array} { c c } 1 & 4 \\- 4 & - 1\end{array} \right][1−4​4−1​]

Which fraction appears in the partial fraction decomposition of 5x2+49x+108x(x+6)2\frac { 5 x ^ { 2 } + 49 x + 108 } { x ( x + 6 ) ^ { 2 } }x(x+6)25x2+49x+108​ ?

Solve the system by Gauss-Jordan elimination, if possible. If (x, y) is the solution to the system, give the value of x. {x−2y=14y=−2\left\{ \begin{array} { r } x - 2 y = 14 \\y = - 2\end{array} \right.{x−2y=14y=−2​

Find the inverse of the matrix. [12−2−1]\left[ \begin{array} { c c } 1 & 2 \\- 2 & - 1\end{array} \right][1−2​2−1​]

Solve the system using Gaussian elimination. If (x,y)( x , y )(x,y) is the solution to the system, give the value of 2x−y2 x - y2x−y . {x+y=23x−2y=−13\left\{ \begin{array} { c } x + y = 23 \\x - 2 y = - 13\end{array} \right.{x+y=23x−2y=−13​

Solve the system by the addition method, if possible. If a solution exists, give the value of x. {2(x+y)=y−197(x+10)=y+17\left\{ \begin{array} { c } 2 ( x + y ) = y - 19 \\7 ( x + 10 ) = y + 17\end{array} \right.{2(x+y)=y−197(x+10)=y+17​

Use a graphing calculator to approximate the solutions of the system. {4.2x+7.1y=39.35−5x+4y=6.7\left\{ \begin{array} { c } 4.2 x + 7.1 y = 39.35 \\- 5 x + 4 y = 6.7\end{array} \right.{4.2x+7.1y=39.35−5x+4y=6.7​

Find the inverse of the matrix. [41−144−1−1−11]\left[ \begin{array} { c c c } 4 & 1 & - 1 \\4 & 4 & - 1 \\- 1 & - 1 & 1\end{array} \right]​44−1​14−1​−1−11​​

Find the inverse of the matrix. [21−18]\left[ \begin{array} { c c } 2 & 1 \\- 1 & 8\end{array} \right][2−1​18​]

Find the graph of the linear inequality. 5y≥2x−105 y \geq 2 x - 105y≥2x−10

What is element a11a _ { 11 }a11​ of the inverse of the following matrix? [81116]\left[ \begin{array} { c c } 8 & 1 \\1 & 16\end{array} \right][81​116​]

Decompose the fraction into partial fractions. 7x−15x2+6x−7\frac { 7 x - 15 } { x ^ { 2 } + 6 x - 7 }x2+6x−77x−15​

Let B=[−32],C=[21]B = \left[ \begin{array} { l l } - & 3 \\ 2 \end{array} \right] , C = \left[ \begin{array} { l l } 2 & 1 \end{array} \right]B=[−2​3],C=[2​1​] . Perform the operation: (BC)2( B C ) ^ { 2 }(BC)2 .

Find the graph of the linear inequality. 4x−2y>114 x - 2 y > 114x−2y>11

Let B=[−32],C=[41]B = \left[ \begin{array} { l l } - & 3 \\ 2 \end{array} \right] , C = \left[ \begin{array} { l l } 4 & 1 \end{array} \right]B=[−2​3],C=[4​1​] . Perform the operation: (BC)2( B C ) ^ { 2 }(BC)2 .

Find 7A7 A7A . A=[8832]A = \left[ \begin{array} { l l } 8 & 8 \\3 & 2\end{array} \right]A=[83​82​]

Which fraction appears in the partial fraction decomposition of 5x2+17x+12x(x+2)2\frac { 5 x ^ { 2 } + 17 x + 12 } { x ( x + 2 ) ^ { 2 } }x(x+2)25x2+17x+12​ ?

Illustration shows three circles traced out by a figure skater during her performance.If the centers of the circles are the given distances apart, find the radius of each circle. A=10,B=14,C=20A = 10 , B = 14 , C = 20A=10,B=14,C=20

Find values of x and y, if any, that will make the matrices equal. [xy39]=[2839]\left[ \begin{array} { l l } x & y \\3 & 9\end{array} \right] = \left[ \begin{array} { l l } 2 & 8 \\3 & 9\end{array} \right][x3​y9​]=[23​89​]

A Review of Basic Algebra

Equations and Inequalities

The Rectangular Coordinate System and Graphs of Equations

Functions Functions and Function Notation

Exponential and Logarithmic Functions

Solving Polynomial Equations

Conic Sections and Quadratic Systems

Natural Number Functions and Probability

Filters

Evaluate the determinant. $\left| \begin{array} { c c } 8 & 10 \\ - 8 & 4 \end{array} \right|$

Find the inverse of the matrix. $\left[ \begin{array} { c c } 1 & 4 \\- 4 & - 1\end{array} \right]$

Which fraction appears in the partial fraction decomposition of $\frac { 5 x ^ { 2 } + 49 x + 108 } { x ( x + 6 ) ^ { 2 } }$ ?

Solve the system by Gauss-Jordan elimination, if possible. If (x, y) is the solution to the system, give the value of x. $\left\{ \begin{array} { r } x - 2 y = 14 \\y = - 2\end{array} \right.$

Find the inverse of the matrix. $\left[ \begin{array} { c c } 1 & 2 \\- 2 & - 1\end{array} \right]$

Solve the system using Gaussian elimination. If $( x , y )$ is the solution to the system, give the value of $2 x - y$ . $\left\{ \begin{array} { c } x + y = 23 \\x - 2 y = - 13\end{array} \right.$

Solve the system by the addition method, if possible. If a solution exists, give the value of x. $\left\{ \begin{array} { c } 2 ( x + y ) = y - 19 \\7 ( x + 10 ) = y + 17\end{array} \right.$

Use a graphing calculator to approximate the solutions of the system. $\left\{ \begin{array} { c } 4.2 x + 7.1 y = 39.35 \\- 5 x + 4 y = 6.7\end{array} \right.$

Find the inverse of the matrix. $\left[ \begin{array} { c c c } 4 & 1 & - 1 \\4 & 4 & - 1 \\- 1 & - 1 & 1\end{array} \right]$

Find the inverse of the matrix. $\left[ \begin{array} { c c } 2 & 1 \\- 1 & 8\end{array} \right]$

Find the graph of the linear inequality. $5 y \geq 2 x - 10$

What is element $a _ { 11 }$ of the inverse of the following matrix? $\left[ \begin{array} { c c } 8 & 1 \\1 & 16\end{array} \right]$

Decompose the fraction into partial fractions. $\frac { 7 x - 15 } { x ^ { 2 } + 6 x - 7 }$

Let $B = \left[ \begin{array} { l l } - & 3 \\ 2 \end{array} \right] , C = \left[ \begin{array} { l l } 2 & 1 \end{array} \right]$ . Perform the operation: $( B C ) ^ { 2 }$ .

Find the graph of the linear inequality. $4 x - 2 y > 11$

Let $B = \left[ \begin{array} { l l } - & 3 \\ 2 \end{array} \right] , C = \left[ \begin{array} { l l } 4 & 1 \end{array} \right]$ . Perform the operation: $( B C ) ^ { 2 }$ .

Find $7 A$ . $A = \left[ \begin{array} { l l } 8 & 8 \\3 & 2\end{array} \right]$

Which fraction appears in the partial fraction decomposition of $\frac { 5 x ^ { 2 } + 17 x + 12 } { x ( x + 2 ) ^ { 2 } }$ ?

Illustration shows three circles traced out by a figure skater during her performance.If the centers of the circles are the given distances apart, find the radius of each circle. $A = 10 , B = 14 , C = 20$

Find values of x and y, if any, that will make the matrices equal. $\left[ \begin{array} { l l } x & y \\3 & 9\end{array} \right] = \left[ \begin{array} { l l } 2 & 8 \\3 & 9\end{array} \right]$