Question 1

Find the equation of the parabola $y = a x ^ { 2 } + b x + c$ that passes through the points.
$$( - 3,9 ) , ( - 2,7 ) , ( - 1,7 )$$

Accepted Answer

A)  $y = x ^ { 2 } - 3 x - 9$ 
B)  $y = x ^ { 2 } + 3 x - 9$ 
C)  $y = 2 x ^ { 2 } + 3 x + 0$ 
D)  $y = 2 x ^ { 2 } + 3 x + 5$ 
E)  $y = x ^ { 2 } + 3 x + 9$ 
A)  $y = x ^ { 2 } - 3 x - 9$ 
B)  $y = x ^ { 2 } + 3 x - 9$ 
C)  $y = 2 x ^ { 2 } + 3 x + 0$ 
D)  $y = 2 x ^ { 2 } + 3 x + 5$ 
E)  $y = x ^ { 2 } + 3 x + 9$

Question 2

Write the system of linear equations as a matrix equation $A X = B$, and use Gauss-Jordan elimination on the augmented matrix $[ A \vdots B ]$ to solve for the matrix $X$.
$$\left\{ \begin{aligned}
x _ { 1 } - 3 x _ { 2 } - 9 x _ { 3 } & = 43 \
x _ { 1 } + 4 x _ { 2 } + 7 x _ { 3 } & = - 51 \
7 x _ { 1 } - 7 x _ { 2 } + 3 x _ { 3 } & = - 57
\end{aligned} \right.$$

Accepted Answer

A) 
$X = \left[ \begin{array} { c } - 16 \ 10 \ - 40 \end{array} \right]$ 
B) 
$X = \left[ \begin{array} { c } 10 \ 8 \ - 2 \end{array} \right]$ 
C) 
$X = \left[ \begin{array} { l } - 8 \ - 2 \ - 5 \end{array} \right]$ 
D) 
$X = \left[ \begin{array} { c } - 10 \ 16 \ 40 \end{array} \right]$ 
E) 
$X = \left[ \begin{array} { c } 8 \ 5 \ - 2 \end{array} \right]$ 
A) 
$X = \left[ \begin{array} { c } - 16 \ 10 \ - 40 \end{array} \right]$ 
B) 
$X = \left[ \begin{array} { c } 10 \ 8 \ - 2 \end{array} \right]$ 
C) 
$X = \left[ \begin{array} { l } - 8 \ - 2 \ - 5 \end{array} \right]$ 
D) 
$X = \left[ \begin{array} { c } - 10 \ 16 \ 40 \end{array} \right]$ 
E) 
$X = \left[ \begin{array} { c } 8 \ 5 \ - 2 \end{array} \right]$

Question 3

Solve for $X$ in the equation given.
$$16 A + 12 B = - 4 X , A = \left[ \begin{array} { c c c } 
5 & 6 & 3 \
- 2 & 5 & - 4
\end{array} \right] \text { and } B = \left[ \begin{array} { c c c } 
- 5 & 8 & - 1 \
- 3 & - 9 & - 5
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c c } 20 & 192 & 36 \ - 68 & - 28 & - 124 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } 0 & 14 & 2 \ - 5 & - 4 & - 9 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } - 5 & - 48 & - 9 \ 17 & 7 & 31 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } - 35 & 0 & - 15 \ - 1 & - 47 & 1 \end{array} \right]$ 
E)  not possible 
A)  $\left[ \begin{array} { c c c } 20 & 192 & 36 \ - 68 & - 28 & - 124 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } 0 & 14 & 2 \ - 5 & - 4 & - 9 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } - 5 & - 48 & - 9 \ 17 & 7 & 31 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } - 35 & 0 & - 15 \ - 1 & - 47 & 1 \end{array} \right]$ 
E)  not possible

Question 4

Match the system of linear equations with its graph.
$$\left\{ \begin{array} { r } 
3 x + 6 y - 12 = 0 \
15 x - 5 y - 10 = 0
\end{array} \right.$$

Accepted Answer

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

Question 5

An object moving vertically is at the given heights at the specified times. Find the position equation $s = \frac { 1 } { 2 } a t ^ { 2 } + v _ { o } t + s _ { o }$ for the object.
At $t = 1$ second, $s = 273$ feet
At $t = 2$ seconds, $s = 241$ feet
At $t = 3$ seconds, $s = 177$ feet

Accepted Answer

A)  $s = - 32 t ^ { 2 } + 16 t + 273$ 
B)  $s = - 16 t ^ { 2 } + 16 t - 273$ 
C)  $s = - 16 t ^ { 2 } + 16 t + 273$ 
D)  $s = - 8 t ^ { 2 } + t - 273$ 
E)  $s = - 16 t ^ { 2 } - 16 t + 273$ 
A)  $s = - 32 t ^ { 2 } + 16 t + 273$ 
B)  $s = - 16 t ^ { 2 } + 16 t - 273$ 
C)  $s = - 16 t ^ { 2 } + 16 t + 273$ 
D)  $s = - 8 t ^ { 2 } + t - 273$ 
E)  $s = - 16 t ^ { 2 } - 16 t + 273$

Question 6

Write the system of linear equations represented by the augmented matrix. Then use back-substitution to solve. (Use variables x, y, and z.) $$\left[ \begin{array} { c c c : c } 
1 & 4 & - 3 & - 23 \
0 & 1 & 4 & 19 \
0 & 0 & 1 & 5
\end{array} \right]$$

Accepted Answer

A)  $x = - 44 , y = 3 , z = - 3$ 
B)  $x = - 1 , y = - 4 , z = 5$ 
C)  $x = - 4 , y = 1 , z = - 5$ 
D)  $x = - 4 , y = - 1 , z = 5$ 
E)  $x = 1 , y = 5 , z = 4$ 
A)  $x = - 44 , y = 3 , z = - 3$ 
B)  $x = - 1 , y = - 4 , z = 5$ 
C)  $x = - 4 , y = 1 , z = - 5$ 
D)  $x = - 4 , y = - 1 , z = 5$ 
E)  $x = 1 , y = 5 , z = 4$

Question 7

Determine whether the system of linear equations is consistent or inconsistent.
$$\left\{ \begin{aligned}
- x + 9 y & = 5 \
- 4 x + 36 y & = 21
\end{aligned} \right.$$

Accepted Answer

A)  inconsistent 
B)  consistent 
A)  inconsistent 
B)  consistent

Question 8

Evaluate the expression.
$$\frac { 2 } { 9 } \left[ \begin{array} { l l l } 
5 & - 2 & 1
\end{array} \right] + \left[ \begin{array} { l l l } 
4 & 8 & - 1
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { l l l } 9 & 6 & 0 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l l } - \frac { 26 } { 9 } & - \frac { 76 } { 9 } & \frac { 11 } { 9 } \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } \frac { 14 } { 9 } & \frac { 4 } { 9 } & \frac { 1 } { 9 } \end{array} \right]$ 
D)  $\left[ \begin{array} { l l l } \frac { 46 } { 9 } & \frac { 68 } { 9 } & - \frac { 7 } { 9 } \end{array} \right]$ 
E)  not possible 
A)  $\left[ \begin{array} { l l l } 9 & 6 & 0 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l l } - \frac { 26 } { 9 } & - \frac { 76 } { 9 } & \frac { 11 } { 9 } \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } \frac { 14 } { 9 } & \frac { 4 } { 9 } & \frac { 1 } { 9 } \end{array} \right]$ 
D)  $\left[ \begin{array} { l l l } \frac { 46 } { 9 } & \frac { 68 } { 9 } & - \frac { 7 } { 9 } \end{array} \right]$ 
E)  not possible

Question 9

Determine whether the system of linear equations is consistent or inconsistent.
$$\left\{ \begin{aligned}
- 9 x + 6 y & = - 1 \
- 81 x + 54 y & = - 10
\end{aligned} \right.$$

Accepted Answer

A)  inconsistent 
B)  consistent 
A)  inconsistent 
B)  consistent

Question 10

Write the system of linear equations as a matrix equation $A X = B$, and use Gauss-Jordan elimination on the augmented matrix $[ A \vdots B ]$ to solve for the matrix $X$.
$$\left\{ \begin{aligned}
x _ { 1 } + 6 x _ { 2 } + 9 x _ { 3 } & = - 44 \
- 7 x _ { 1 } + 2 x _ { 2 } - x _ { 3 } & = - 54 \
8 x _ { 1 } + 3 x _ { 2 } + 6 x _ { 3 } & = 26
\end{aligned} \right.$$

Accepted Answer

A) 
$X = \left[ \begin{array} { l } 28 \ 12 \ 21 \end{array} \right]$ 
B)  $X = \left[ \begin{array} { c } 12 \ - 7 \ - 4 \end{array} \right]$ 
C) $X = \left[ \begin{array} { c } 7 \ - 4 \ - 3 \end{array} \right]$ 
D) $X = \left[ \begin{array} { r } - 12 \ - 28 \ - 21 \end{array} \right]$ 
E)  $X = \left[ \begin{array} { c } - 7 \ 3 \ - 4 \end{array} \right]$ 
A) 
$X = \left[ \begin{array} { l } 28 \ 12 \ 21 \end{array} \right]$ 
B)  $X = \left[ \begin{array} { c } 12 \ - 7 \ - 4 \end{array} \right]$ 
C) $X = \left[ \begin{array} { c } 7 \ - 4 \ - 3 \end{array} \right]$ 
D) $X = \left[ \begin{array} { r } - 12 \ - 28 \ - 21 \end{array} \right]$ 
E)  $X = \left[ \begin{array} { c } - 7 \ 3 \ - 4 \end{array} \right]$

Question 11

Solve the system of equations.
$$\left\{ \begin{array} { c } 
- \frac { 1 } { x } - \frac { 4 } { y } - \frac { 1 } { z } = - 3 \
- \frac { 5 } { x } - \frac { 2 } { y } - \frac { 2 } { z } = - 5 \
- \frac { 1 } { x } - \frac { 5 } { y } + \frac { 2 } { z } = - 3
\end{array} \right.$$

Accepted Answer

A)  $\left( \frac { 41 } { 57 } , \frac { 10 } { 19 } , \frac { 10 } { 57 } \right)$ 
B)  $\left( \frac { 1 } { 2 } , \frac { 1 } { 5 } , - \frac { 1 } { 19 } \right)$ 
C)  $\left( \frac { 827 } { 285 } , \frac { 13 } { 10 } , \frac { 10 } { 57 } \right)$ 
D)  $\left( \frac { 85 } { 41 } , \frac { 17 } { 6 } , \frac { 17 } { 2 } \right)$ 
E)  $\left( \frac { 57 } { 41 } , \frac { 19 } { 10 } , \frac { 57 } { 10 } \right)$ 
A)  $\left( \frac { 41 } { 57 } , \frac { 10 } { 19 } , \frac { 10 } { 57 } \right)$ 
B)  $\left( \frac { 1 } { 2 } , \frac { 1 } { 5 } , - \frac { 1 } { 19 } \right)$ 
C)  $\left( \frac { 827 } { 285 } , \frac { 13 } { 10 } , \frac { 10 } { 57 } \right)$ 
D)  $\left( \frac { 85 } { 41 } , \frac { 17 } { 6 } , \frac { 17 } { 2 } \right)$ 
E)  $\left( \frac { 57 } { 41 } , \frac { 19 } { 10 } , \frac { 57 } { 10 } \right)$

Question 12

Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.
$\frac { x + 9 } { x \left( x ^ { 2 } + 3 \right) ^ { 2 } }$

Accepted Answer

A)  $\frac { A x + B } { x ^ { 2 } + 3 } + \frac { C x + D } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
B)  $\frac { A } { x } + \frac { B } { x ^ { 2 } + 3 } + \frac { C } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
C)  $\frac { A } { x } + \frac { B x + C } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
D)  $\frac { A x + B } { x } + \frac { C x + D } { x ^ { 2 } + 3 } + \frac { E x + F } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
E)  $\frac { A } { x } + \frac { B x + C } { x ^ { 2 } + 3 } + \frac { D x + E } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
A)  $\frac { A x + B } { x ^ { 2 } + 3 } + \frac { C x + D } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
B)  $\frac { A } { x } + \frac { B } { x ^ { 2 } + 3 } + \frac { C } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
C)  $\frac { A } { x } + \frac { B x + C } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
D)  $\frac { A x + B } { x } + \frac { C x + D } { x ^ { 2 } + 3 } + \frac { E x + F } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
E)  $\frac { A } { x } + \frac { B x + C } { x ^ { 2 } + 3 } + \frac { D x + E } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$

Question 13

Solve the system by the method of substitution.
$$\left\{ \begin{aligned}
x ^ { 2 } + y ^ { 2 } & = 625 \
7 x - 24 y & = 0
\end{aligned} \right.$$

Accepted Answer

A)  $( 24,7 ) , ( - 24 , - 7 )$ 
B)  $( 24,7 )$ 
C)  $( 24,7 ) , ( - 24,7 ) , ( - 24 , - 7 ) , ( 24 , - 7 )$ 
D)  $( 7,24 ) , ( 7 , - 24 )$ 
E)  no real solution 
A)  $( 24,7 ) , ( - 24 , - 7 )$ 
B)  $( 24,7 )$ 
C)  $( 24,7 ) , ( - 24,7 ) , ( - 24 , - 7 ) , ( 24 , - 7 )$ 
D)  $( 7,24 ) , ( 7 , - 24 )$ 
E)  no real solution

Question 14

Write the partial fraction decomposition of the rational expression. $$\frac { x ^ { 2 } } { x ^ { 4 } - 21 x ^ { 2 } - 100 }$$

Accepted Answer

A)  $\frac { 1 } { 29 } \left( \frac { 4 } { x ^ { 2 } + 4 } + \frac { 5 } { 2 ( x - 5 ) } - \frac { 5 } { 2 ( x + 5 ) } \right)$ 
B)  $\frac { 1 } { x ^ { 2 } } - \frac { 1 } { 2 } - \frac { x ^ { 2 } } { 20 }$ 
C)  $\frac { 1 } { 29 } \left( \frac { 4 } { x ^ { 2 } + 4 } + \frac { 5 ( x + 4 ) } { 2 ( x - 5 ) } + \frac { 5 } { 2 ( x - 5 ) } \right)$ 
D)  $\frac { 1 } { 29 } \left( \frac { 4 } { x ^ { 2 } + 4 } - \frac { 5 } { 2 ( x - 5 ) } + \frac { 5 } { 2 ( x + 5 ) } \right)$ 
E)  $\frac { 1 } { 29 } \left( \frac { 1 } { x ^ { 2 } + 4 } + \frac { 1 } { 2 ( x - 5 ) } - \frac { 1 } { 2 ( x + 5 ) } \right)$ 
A)  $\frac { 1 } { 29 } \left( \frac { 4 } { x ^ { 2 } + 4 } + \frac { 5 } { 2 ( x - 5 ) } - \frac { 5 } { 2 ( x + 5 ) } \right)$ 
B)  $\frac { 1 } { x ^ { 2 } } - \frac { 1 } { 2 } - \frac { x ^ { 2 } } { 20 }$ 
C)  $\frac { 1 } { 29 } \left( \frac { 4 } { x ^ { 2 } + 4 } + \frac { 5 ( x + 4 ) } { 2 ( x - 5 ) } + \frac { 5 } { 2 ( x - 5 ) } \right)$ 
D)  $\frac { 1 } { 29 } \left( \frac { 4 } { x ^ { 2 } + 4 } - \frac { 5 } { 2 ( x - 5 ) } + \frac { 5 } { 2 ( x + 5 ) } \right)$ 
E)  $\frac { 1 } { 29 } \left( \frac { 1 } { x ^ { 2 } + 4 } + \frac { 1 } { 2 ( x - 5 ) } - \frac { 1 } { 2 ( x + 5 ) } \right)$

Question 15

If possible, find $3 A + 4 B$.
$$A = \left[ \begin{array} { c c c } 
- 4 & 3 & 9 \
3 & - 2 & 5
\end{array} \right] , B = \left[ \begin{array} { c c c } 
- 8 & 9 & 5 \
0 & 2 & 1
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c c } 20 & - 27 & 7 \ 9 & - 14 & 11 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } - 12 & 12 & 14 \ 3 & 0 & 6 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } - 44 & 45 & 47 \ 9 & 2 & 19 \end{array} \right]$ 
E)  not possible 
A)  $\left[ \begin{array} { c c c } 20 & - 27 & 7 \ 9 & - 14 & 11 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } - 12 & 12 & 14 \ 3 & 0 & 6 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } - 44 & 45 & 47 \ 9 & 2 & 19 \end{array} \right]$ 
E)  not possible

Question 16

An object moving vertically is at the given heights at the specified times. Find the position equation $s = \frac { 1 } { 2 } a t ^ { 2 } + v _ { o } t + s _ { o }$ for the object.
At $t = 1$ second, $s = 234$ feet
At $t = 2$ seconds, $s = 202$ feet
At $t = 3$ seconds, $s = 138$ feet

Accepted Answer

A)  $s = - 32 t ^ { 2 } + 16 t + 234$ 
B)  $s = - 16 t ^ { 2 } + 16 t - 234$ 
C)  $s = - 16 t ^ { 2 } + 16 t + 234$ 
D)  $s = - 8 t ^ { 2 } + t - 234$ 
E)  $s = - 16 t ^ { 2 } - 16 t + 234$ 
A)  $s = - 32 t ^ { 2 } + 16 t + 234$ 
B)  $s = - 16 t ^ { 2 } + 16 t - 234$ 
C)  $s = - 16 t ^ { 2 } + 16 t + 234$ 
D)  $s = - 8 t ^ { 2 } + t - 234$ 
E)  $s = - 16 t ^ { 2 } - 16 t + 234$

Question 17

Determine whether the two systems of linear equations yield the same solutions. If so, find the solutions using matrices.
$\left\{ \begin{aligned} x + y - 9 z & = - 67 \ y + 5 z & = 31 \ z & = 7 \end{aligned} \right.$
$\left\{ \begin{aligned} x - 9 y + 6 z & = 76 \ y - 9 z & = - 67 \ z & = 7 \end{aligned} \right.$

Accepted Answer

A)  $x = 0 , y = - 4 , z = 7$ 
B)  $x = 0 , y = 4 , z = 7$ 
C)  $x = 4 , y = 7 , z = 0$ 
D)  $x = - 4 , y = 7 , z = 0$ 
E)  The systems yield different solutions. 
A)  $x = 0 , y = - 4 , z = 7$ 
B)  $x = 0 , y = 4 , z = 7$ 
C)  $x = 4 , y = 7 , z = 0$ 
D)  $x = - 4 , y = 7 , z = 0$ 
E)  The systems yield different solutions.

Question 18

Solve the system by the method of elimination.
$$\left\{ \begin{array} { l } 
7 x - 6 y = - 73 \
- 8 x - y = 52
\end{array} \right.$$

Accepted Answer

A)  $( 2 , - 68 )$ 
B)  $( - 7,4 )$ 
C)  $\left( \frac { 239 } { 15 } , \frac { 2812 } { 15 } \right)$ 
D)  $\left( - 8 , - \frac { 121 } { 7 } \right)$ 
E)  inconsistent 
A)  $( 2 , - 68 )$ 
B)  $( - 7,4 )$ 
C)  $\left( \frac { 239 } { 15 } , \frac { 2812 } { 15 } \right)$ 
D)  $\left( - 8 , - \frac { 121 } { 7 } \right)$ 
E)  inconsistent

Question 19

Write the augmented matrix for the system of linear equations.
$$\left\{ \begin{array} { r } 
x - 8 y + 8 z = 9 \
8 y - 9 z = 1 \
x + z = 7
\end{array} \right.$$

Accepted Answer

A)  $\left[ \begin{array} { c c c : c } 1 & - 8 & 8 & 9 \ 1 & 8 & - 9 & 1 \ 1 & 1 & 1 & 7 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c : c } 1 & - 8 & 8 & 9 \ 0 & 8 & - 9 & 1 \ 1 & 0 & 1 & 7 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c : c } 1 & - 8 & 8 & 9 \ & 8 & - 9 & 1 \ 1 & & 1 & 7 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r : r } 1 & - 8 & 8 & 9 \ 8 & - 9 & 0 & 1 \ 1 & 1 & 0 & 7 \end{array} \right]$ 
E)  $\left[ \begin{array} { c c c : c } 1 & - 8 & 8 & 9 \ 0 & 8 & - 9 & 1 \ 1 & 1 & 0 & 7 \end{array} \right]$ 
A)  $\left[ \begin{array} { c c c : c } 1 & - 8 & 8 & 9 \ 1 & 8 & - 9 & 1 \ 1 & 1 & 1 & 7 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c : c } 1 & - 8 & 8 & 9 \ 0 & 8 & - 9 & 1 \ 1 & 0 & 1 & 7 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c : c } 1 & - 8 & 8 & 9 \ & 8 & - 9 & 1 \ 1 & & 1 & 7 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r : r } 1 & - 8 & 8 & 9 \ 8 & - 9 & 0 & 1 \ 1 & 1 & 0 & 7 \end{array} \right]$ 
E)  $\left[ \begin{array} { c c c : c } 1 & - 8 & 8 & 9 \ 0 & 8 & - 9 & 1 \ 1 & 1 & 0 & 7 \end{array} \right]$

Question 20

Solve system of equations by the method of substitution.
$$\left\{ \begin{aligned}
4 x ^ { 3 } - 25 y & = 0 \
4 x - y & = 0
\end{aligned} \right.$$

Accepted Answer

A)  (0,0) , (-5, -20) , (5, 20) 
B)  (0,0) , (-5, 20) , (5, 20) 
C)  (0,0) , (5, -20) , (5, 20) 
D)  (0,0) , (-5, 21) , (5, 21) 
E)  (0,0) , (-5, -19) , (5,19) 
A)  (0,0) , (-5, -20) , (5, 20) 
B)  (0,0) , (-5, 20) , (5, 20) 
C)  (0,0) , (5, -20) , (5, 20) 
D)  (0,0) , (-5, 21) , (5, 21) 
E)  (0,0) , (-5, -19) , (5,19)

Find the equation of the parabola $y = a x ^ { 2 } + b x + c$ that passes through the points. $( - 3,9 ) , ( - 2,7 ) , ( - 1,7 )$

Solve for $X$ in the equation given. $16 A + 12 B = - 4 X , A = \left[ \begin{array} { c c c } 5 & 6 & 3 \\- 2 & 5 & - 4\end{array} \right] \text { and } B = \left[ \begin{array} { c c c } - 5 & 8 & - 1 \\- 3 & - 9 & - 5\end{array} \right]$

Match the system of linear equations with its graph. $\left\{ \begin{array} { r } 3 x + 6 y - 12 = 0 \\15 x - 5 y - 10 = 0\end{array} \right.$

An object moving vertically is at the given heights at the specified times. Find the position equation $s = \frac { 1 } { 2 } a t ^ { 2 } + v _ { o } t + s _ { o }$ for the object. At $t = 1$ second, $s = 273$ feet At $t = 2$ seconds, $s = 241$ feet At $t = 3$ seconds, $s = 177$ feet

Write the system of linear equations represented by the augmented matrix. Then use back-substitution to solve. (Use variables x, y, and z.) $\left[ \begin{array} { c c c : c } 1 & 4 & - 3 & - 23 \\0 & 1 & 4 & 19 \\0 & 0 & 1 & 5\end{array} \right]$

Determine whether the system of linear equations is consistent or inconsistent. $\left\{ \begin{aligned}- x + 9 y & = 5 \\- 4 x + 36 y & = 21\end{aligned} \right.$

Evaluate the expression. $\frac { 2 } { 9 } \left[ \begin{array} { l l l } 5 & - 2 & 1\end{array} \right] + \left[ \begin{array} { l l l } 4 & 8 & - 1\end{array} \right]$

Determine whether the system of linear equations is consistent or inconsistent. $\left\{ \begin{aligned}- 9 x + 6 y & = - 1 \\- 81 x + 54 y & = - 10\end{aligned} \right.$

Solve the system of equations. $\left\{ \begin{array} { c } - \frac { 1 } { x } - \frac { 4 } { y } - \frac { 1 } { z } = - 3 \\- \frac { 5 } { x } - \frac { 2 } { y } - \frac { 2 } { z } = - 5 \\- \frac { 1 } { x } - \frac { 5 } { y } + \frac { 2 } { z } = - 3\end{array} \right.$

Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. $\frac { x + 9 } { x \left( x ^ { 2 } + 3 \right) ^ { 2 } }$

Solve the system by the method of substitution. $\left\{ \begin{aligned}x ^ { 2 } + y ^ { 2 } & = 625 \\7 x - 24 y & = 0\end{aligned} \right.$

Write the partial fraction decomposition of the rational expression. $\frac { x ^ { 2 } } { x ^ { 4 } - 21 x ^ { 2 } - 100 }$

If possible, find $3 A + 4 B$ . $A = \left[ \begin{array} { c c c } - 4 & 3 & 9 \\3 & - 2 & 5\end{array} \right] , B = \left[ \begin{array} { c c c } - 8 & 9 & 5 \\0 & 2 & 1\end{array} \right]$

An object moving vertically is at the given heights at the specified times. Find the position equation $s = \frac { 1 } { 2 } a t ^ { 2 } + v _ { o } t + s _ { o }$ for the object. At $t = 1$ second, $s = 234$ feet At $t = 2$ seconds, $s = 202$ feet At $t = 3$ seconds, $s = 138$ feet

Solve the system by the method of elimination. $\left\{ \begin{array} { l } 7 x - 6 y = - 73 \\- 8 x - y = 52\end{array} \right.$

Write the augmented matrix for the system of linear equations. $\left\{ \begin{array} { r } x - 8 y + 8 z = 9 \\8 y - 9 z = 1 \\x + z = 7\end{array} \right.$

Solve system of equations by the method of substitution. $\left\{ \begin{aligned}4 x ^ { 3 } - 25 y & = 0 \\4 x - y & = 0\end{aligned} \right.$

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Exam 7: Linear Systems and Matrices

Find the equation of the parabola y=ax2+bx+cy = a x ^ { 2 } + b x + cy=ax2+bx+c that passes through the points. (−3,9),(−2,7),(−1,7)( - 3,9 ) , ( - 2,7 ) , ( - 1,7 )(−3,9),(−2,7),(−1,7)

Match the system of linear equations with its graph. {3x+6y−12=015x−5y−10=0\left\{ \begin{array} { r } 3 x + 6 y - 12 = 0 \\15 x - 5 y - 10 = 0\end{array} \right.{3x+6y−12=015x−5y−10=0​

Determine whether the system of linear equations is consistent or inconsistent. {−x+9y=5−4x+36y=21\left\{ \begin{aligned}- x + 9 y & = 5 \\- 4 x + 36 y & = 21\end{aligned} \right.{−x+9y−4x+36y​=5=21​

Evaluate the expression. 29[5−21]+[48−1]\frac { 2 } { 9 } \left[ \begin{array} { l l l } 5 & - 2 & 1\end{array} \right] + \left[ \begin{array} { l l l } 4 & 8 & - 1\end{array} \right]92​[5​−2​1​]+[4​8​−1​]

Determine whether the system of linear equations is consistent or inconsistent. {−9x+6y=−1−81x+54y=−10\left\{ \begin{aligned}- 9 x + 6 y & = - 1 \\- 81 x + 54 y & = - 10\end{aligned} \right.{−9x+6y−81x+54y​=−1=−10​

Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. x+9x(x2+3)2\frac { x + 9 } { x \left( x ^ { 2 } + 3 \right) ^ { 2 } }x(x2+3)2x+9​

Solve the system by the method of substitution. {x2+y2=6257x−24y=0\left\{ \begin{aligned}x ^ { 2 } + y ^ { 2 } & = 625 \\7 x - 24 y & = 0\end{aligned} \right.{x2+y27x−24y​=625=0​

Write the partial fraction decomposition of the rational expression. x2x4−21x2−100\frac { x ^ { 2 } } { x ^ { 4 } - 21 x ^ { 2 } - 100 }x4−21x2−100x2​

If possible, find 3A+4B3 A + 4 B3A+4B . A=[−4393−25],B=[−895021]A = \left[ \begin{array} { c c c } - 4 & 3 & 9 \\3 & - 2 & 5\end{array} \right] , B = \left[ \begin{array} { c c c } - 8 & 9 & 5 \\0 & 2 & 1\end{array} \right]A=[−43​3−2​95​],B=[−80​92​51​]

Solve the system by the method of elimination. {7x−6y=−73−8x−y=52\left\{ \begin{array} { l } 7 x - 6 y = - 73 \\- 8 x - y = 52\end{array} \right.{7x−6y=−73−8x−y=52​

Write the augmented matrix for the system of linear equations. {x−8y+8z=98y−9z=1x+z=7\left\{ \begin{array} { r } x - 8 y + 8 z = 9 \\8 y - 9 z = 1 \\x + z = 7\end{array} \right.⎩⎨⎧​x−8y+8z=98y−9z=1x+z=7​

Solve system of equations by the method of substitution. {4x3−25y=04x−y=0\left\{ \begin{aligned}4 x ^ { 3 } - 25 y & = 0 \\4 x - y & = 0\end{aligned} \right.{4x3−25y4x−y​=0=0​