Question 1

Use the elimination method to solve the system.
-$$\left\{ \begin{array} { r } 
3 x + 48 y = 48 \
3 x - 6 y = - 6
\end{array} \right.$$

Accepted Answer

A)  x = 0, y = 1 
B)  x = 1, y = 1 
C)  x = 0, y = 0 
D)  x = 1, y = 0 
A)  x = 0, y = 1 
B)  x = 1, y = 1 
C)  x = 0, y = 0 
D)  x = 1, y = 0

Question 2

Use the properties of determinants to find the value of the second determinant, given the value of the first.
-$$\left| \begin{array} { r r r } 
\mathrm { x } & \mathrm { y } & \mathrm { z } \
\mathrm { u } & \mathrm { v } & \mathrm { w } \
1 & - 2 & - 4
\end{array} \right| = 119 \left| \begin{array} { r r r } 
1 & - 2 & - 4 \
\mathrm { u } & \mathrm { V } & \mathrm { w } \
\mathrm { x } & \mathrm { y } & \mathrm { z }
\end{array} \right| = ?$$

Accepted Answer

A)  119 
B)  -119 
C)  0 
D)  Cannot determine 
A)  119 
B)  -119 
C)  0 
D)  Cannot determine

Question 3

Perform the indicated matrix operations.
-Let $A = \left[ \begin{array} { l l } - 4 & 2 \end{array} \right]$ and $B = \left[ \begin{array} { l l } 1 & 0 \end{array} \right]$. Find $3 A + 4 B$.

Accepted Answer

A)  $\left[ \begin{array} { l l } - 1 & 2 \end{array} \right]$ 
B)  $[ - 74 ]$ 
C)  $\left[ \begin{array} { l l } - 8 & 6 \end{array} \right]$ 
D)  $[ - 124 ]$ 
A)  $\left[ \begin{array} { l l } - 1 & 2 \end{array} \right]$ 
B)  $[ - 74 ]$ 
C)  $\left[ \begin{array} { l l } - 8 & 6 \end{array} \right]$ 
D)  $[ - 124 ]$

Question 4

Solve the system of equations using elimination.
-$$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 61 \
x ^ { 2 } - y ^ { 2 } = 11
\end{array} \right.$$

Accepted Answer

A)  x = -6, y = -5; x = -5, y = -6 
B)  x = 6, y = 5; x = -6, y = 5; x = 6, y = -5; x = -6, y = -5 
C)  x = 6, y = -5; x = 6, y = 5 
D)  x = 6, y = 5; x = 5, y = 6; x = -6, y = -5; x = -5, y = -6 
A)  x = -6, y = -5; x = -5, y = -6 
B)  x = 6, y = 5; x = -6, y = 5; x = 6, y = -5; x = -6, y = -5 
C)  x = 6, y = -5; x = 6, y = 5 
D)  x = 6, y = 5; x = 5, y = 6; x = -6, y = -5; x = -5, y = -6

Question 5

Solve the problem.
-An airline with two types of airplanes, $\mathrm { P } _ { 1 }$ and $\mathrm { P } _ { 2 }$, has contracted with a tour group to provide transportation for a minimum of 400 first class, 750 tourist class, and 1500 economy class passengers. For a certain trip, airplane $\mathrm { P } _ { 1 }$ costs $\$ 10,000$ to operate and can accommodate 20 first class, 50 tourist class, and 110 economy class passengers. Airplane $\mathrm { P } _ { 2 }$ costs $\$ 8500$ to operate and can accommodate 18 first class, 30 tourist class, and 44 economy class passengers. How many of each type of airplane should be used in order to minimize the operating cost?

Accepted Answer

A)  $7 \mathrm { P } _ { 1 }$ planes and $11 \mathrm { P } _ { 2 }$ planes 
B)  $9 \mathrm { P } _ { 1 }$ planes and $13 \mathrm { P } _ { 2 }$ planes 
C)  $5 \mathrm { P } _ { 1 }$ planes and $17 \mathrm { P } _ { 2 }$ planes 
D)  $11 \mathrm { P } _ { 1 }$ planes and $7 \mathrm { P } _ { 2 }$ planes 
A)  $7 \mathrm { P } _ { 1 }$ planes and $11 \mathrm { P } _ { 2 }$ planes 
B)  $9 \mathrm { P } _ { 1 }$ planes and $13 \mathrm { P } _ { 2 }$ planes 
C)  $5 \mathrm { P } _ { 1 }$ planes and $17 \mathrm { P } _ { 2 }$ planes 
D)  $11 \mathrm { P } _ { 1 }$ planes and $7 \mathrm { P } _ { 2 }$ planes

Question 6

Solve the problem using matrices.
-Find the function $f ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + d$ for which $f ( 0 ) = - 2 , f ( 1 ) = 5 , f ( - 1 ) = 3$, $f ( 2 ) = 4$.

Accepted Answer

A)  $f ( x ) = 10 x ^ { 3 } - 18 x ^ { 2 } - 13 x + 6$ 
B)  $f ( x ) = - 8 x ^ { 3 } + 12 x ^ { 2 } + 5 x - 6$ 
C)  $f ( x ) = - \frac { 10 } { 3 } x ^ { 3 } + 6 x ^ { 2 } + \frac { 13 } { 3 } x - 2$ 
D)  $f ( x ) = \frac { 8 } { 3 } x ^ { 3 } + 4 x ^ { 2 } + \frac { 5 } { 3 } x - 2$ 
A)  $f ( x ) = 10 x ^ { 3 } - 18 x ^ { 2 } - 13 x + 6$ 
B)  $f ( x ) = - 8 x ^ { 3 } + 12 x ^ { 2 } + 5 x - 6$ 
C)  $f ( x ) = - \frac { 10 } { 3 } x ^ { 3 } + 6 x ^ { 2 } + \frac { 13 } { 3 } x - 2$ 
D)  $f ( x ) = \frac { 8 } { 3 } x ^ { 3 } + 4 x ^ { 2 } + \frac { 5 } { 3 } x - 2$

Question 7

Solve the system of equations using elimination.
-$$\left\{ \begin{array} { l } 
2 x ^ { 2 } + x y - y ^ { 2 } = 3 \
x ^ { 2 } + 2 x y + y ^ { 2 } = 3
\end{array} \right.$$

Accepted Answer

A)  $x = - \frac { 2 } { 3 } , y = \frac { 1 } { 3 } ; x = \frac { 2 \sqrt { 3 } } { 3 } , y = - \frac { 1 } { 3 }$ 
B)  $x = \frac { 2 \sqrt { 3 } } { 3 } , y = \frac { \sqrt { 3 } } { 3 } ; x = - \frac { 2 \sqrt { 3 } } { 3 } , y = - \frac { \sqrt { 3 } } { 3 }$ 
C)  $x = - \frac { 2 } { 3 } , y = - \frac { 1 } { 3 } ; x = \frac { 2 \sqrt { 3 } } { 3 } , y = \frac { 1 } { 3 }$ 
D)  $x = \frac { 2 \sqrt { 3 } } { 3 } , y = - \frac { \sqrt { 3 } } { 3 } ; x = - \frac { 2 \sqrt { 3 } } { 3 } , y = \frac { \sqrt { 3 } } { 3 }$ 
A)  $x = - \frac { 2 } { 3 } , y = \frac { 1 } { 3 } ; x = \frac { 2 \sqrt { 3 } } { 3 } , y = - \frac { 1 } { 3 }$ 
B)  $x = \frac { 2 \sqrt { 3 } } { 3 } , y = \frac { \sqrt { 3 } } { 3 } ; x = - \frac { 2 \sqrt { 3 } } { 3 } , y = - \frac { \sqrt { 3 } } { 3 }$ 
C)  $x = - \frac { 2 } { 3 } , y = - \frac { 1 } { 3 } ; x = \frac { 2 \sqrt { 3 } } { 3 } , y = \frac { 1 } { 3 }$ 
D)  $x = \frac { 2 \sqrt { 3 } } { 3 } , y = - \frac { \sqrt { 3 } } { 3 } ; x = - \frac { 2 \sqrt { 3 } } { 3 } , y = \frac { \sqrt { 3 } } { 3 }$

Question 8

Graph the inequality.
-$y \leq-8$

A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 9

Find the maximum or minimum value of the objective function, subject to the constraints graphed in this feasible region.  
-z = x + 7y + 9 Find minimum.

Accepted Answer

A)  Minimum 34 
B)  No Minimum 
C)  Minimum 46 
D)  Minimum 27 
A)  Minimum 34 
B)  No Minimum 
C)  Minimum 46 
D)  Minimum 27

Question 10

Solve the problem using matrices.
-Find real numbers a, b, and c such that the graph of the function $$y = a x ^ { 2 } + b x + c$$ c contains the points (-2, -4), (1,
-1), and (3, -19).

Accepted Answer

a = -2 , b

Question 11

Graph the system of inequalities.
-$$\begin{aligned}
2 x + 3 y & \geq 6 \
x - y & \geq 3 \
y & \leq 2
\end{aligned}$$

A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 12

Solve the problem.
-The Family Arts Center charges $22 for adults, $12 for senior citizens, and $7 for children under 12 for their live performances on Sunday afternoon. This past Sunday, the paid revenue was $10,134 for 757 tickets sold. There
Were 41 more children than adults. How many children attended?

Accepted Answer

A)  200 children 
B)  244 children 
C)  234 children 
D)  208 children 
A)  200 children 
B)  244 children 
C)  234 children 
D)  208 children

Question 13

Use Cramer's rule to solve the linear system.
-$$\left\{ \begin{array} { l } 
- 4 x - 6 y - 8 z = - 84 \
- 4 x + 4 y - 3 z = 11 \
- 9 x - 5 y - 9 z = - 94
\end{array} \right.$$

Accepted Answer

A)  x = 3, y = 8, z = 3 
B)  x = 4, y = 6, z = 3 
C)  x = 8, y = 3, z = 8 
D)  x = 3, y = -8, z = -3 
A)  x = 3, y = 8, z = 3 
B)  x = 4, y = 6, z = 3 
C)  x = 8, y = 3, z = 8 
D)  x = 3, y = -8, z = -3

Question 14

Write a system of linear inequalities that has the given graph.
-  A)
$\left\{\begin{array}{r}
x \geq 0 \
y \geq 2 \
y \leq x \
y+x \leq 9
\end{array}\right.$

Accepted Answer

B) 
$\left\{\begin{array}{r}
y \geq 2 \
y \geq x \
y+x \leq 9
\end{array}\right.$ 
C) 
$\left\{\begin{array}{r}
y \geq 0 \
x \geq 0 \
y \leq 2 \
y+x \leq 9
\end{array}\right.$ 
D) 
$\left\{\begin{array}{r}
y \geq 0 \
x \geq 0 \
y \leq 2 \
y+x \leq 9
\end{array}\right.$ 
B) 
$\left\{\begin{array}{r}
y \geq 2 \
y \geq x \
y+x \leq 9
\end{array}\right.$ 
C) 
$\left\{\begin{array}{r}
y \geq 0 \
x \geq 0 \
y \leq 2 \
y+x \leq 9
\end{array}\right.$ 
D) 
$\left\{\begin{array}{r}
y \geq 0 \
x \geq 0 \
y \leq 2 \
y+x \leq 9
\end{array}\right.$

Question 15

Solve the system of equations.
-$$\left\{ \begin{aligned}
- x + y + 2 z & = 0 \
x + 2 y + z & = 6 \
- 2 x - y + z & = - 6
\end{aligned} \right.$$

Accepted Answer

A)  inconsistent (no solution) 
B)  $x = 2 - z$
$y = z + 2$
$z =$ any real number 
C)  $x = z + 2$
$y = 2 - z$
$z =$ any real number 
D)  $x = z + 2$
$y = z - 2$
$z =$ any real number 
A)  inconsistent (no solution) 
B)  $x = 2 - z$
$y = z + 2$
$z =$ any real number 
C)  $x = z + 2$
$y = 2 - z$
$z =$ any real number 
D)  $x = z + 2$
$y = z - 2$
$z =$ any real number

Question 16

Solve the system of equations using elimination.
-$$\left\{ \begin{aligned}
3 x ^ { 2 } + 2 y ^ { 2 } & = 89 \
x ^ { 2 } - 2 y ^ { 2 } & = - 21
\end{aligned} \right.$$

Accepted Answer

The answer of Solve the system of equations using elimination.
-\[\left\{...

Question 17

Solve the system of equations using substitution.
-$$\left\{ \begin{array} { l } 
\ln x = 3 \ln y \
3 ^ { x } = 27 y
\end{array} \right.$$

Accepted Answer

A)  $x = \sqrt { 3 } , y = 9$ 
B)  $x = 3 \sqrt { 3 } , y = \sqrt { 3 }$ 
C)  $x = \sqrt { 3 } , y = 3 \sqrt { 3 }$ 
D)  $x = 9 , y = \sqrt { 3 }$ 
A)  $x = \sqrt { 3 } , y = 9$ 
B)  $x = 3 \sqrt { 3 } , y = \sqrt { 3 }$ 
C)  $x = \sqrt { 3 } , y = 3 \sqrt { 3 }$ 
D)  $x = 9 , y = \sqrt { 3 }$

Question 18

Perform the indicated operation, whenever possible.
-Let $A = \left[ \begin{array} { r r r } 7 & - 4 & 8 \ - 6 & 5 & - 1 \ 0 & 6 & - 3 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } - 2 & - 6 & - 1 \ - 7 & - 4 & 3 \ - 3 & - 9 & - 5 \end{array} \right] . \quad$ Find $A - B$

Accepted Answer

A)  $\left[ \begin{array} { r r r } 9 & 2 & 9 \ 1 & 9 & - 4 \ 3 & 15 & 2 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 5 & - 10 & 7 \ - 13 & 1 & - 8 \ - 3 & - 3 & 2 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 9 & 2 & 9 \ 1 & 9 & 2 \ 3 & 15 & - 4 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 5 & - 10 & 7 \ - 13 & 1 & 2 \ - 3 & - 3 & - 8 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r } 9 & 2 & 9 \ 1 & 9 & - 4 \ 3 & 15 & 2 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 5 & - 10 & 7 \ - 13 & 1 & - 8 \ - 3 & - 3 & 2 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 9 & 2 & 9 \ 1 & 9 & 2 \ 3 & 15 & - 4 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 5 & - 10 & 7 \ - 13 & 1 & 2 \ - 3 & - 3 & - 8 \end{array} \right]$

Question 19

Write the partial fraction decomposition of the rational expression.
-$$\frac { 3 x - 2 } { x ^ { 3 } - 1 }$$

Accepted Answer

A)  $\frac { 3 } { x - 1 } + \frac { - 3 ( x - 7 ) } { x ^ { 2 } + x + 1 }$ 
B)  $\frac { \frac { 1 } { 3 } } { x - 1 } + \frac { - \frac { 1 } { 3 } x + \frac { 7 } { 3 } } { \left( x ^ { 2 } + x + 1 \right) }$ 
C)  $\frac { 3 } { ( x - 1 ) ^ { 2 } } + \frac { 1 } { ( x - 1 ) ^ { 3 } }$ 
D)  $\frac { \frac { 1 } { 2 } } { x - 1 } + \frac { \frac { 5 } { 2 } } { x + 1 }$ 
A)  $\frac { 3 } { x - 1 } + \frac { - 3 ( x - 7 ) } { x ^ { 2 } + x + 1 }$ 
B)  $\frac { \frac { 1 } { 3 } } { x - 1 } + \frac { - \frac { 1 } { 3 } x + \frac { 7 } { 3 } } { \left( x ^ { 2 } + x + 1 \right) }$ 
C)  $\frac { 3 } { ( x - 1 ) ^ { 2 } } + \frac { 1 } { ( x - 1 ) ^ { 3 } }$ 
D)  $\frac { \frac { 1 } { 2 } } { x - 1 } + \frac { \frac { 5 } { 2 } } { x + 1 }$

Question 20

Find the inverse of the matrix.
-$$\left[ \begin{array} { l l l } 
1 & 1 & 1 \
2 & 1 & 1 \
2 & 2 & 3
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { l l l } - 1 & - 1 & - 1 \ - 2 & - 1 & - 1 \ - 2 & - 2 & - 3 \end{array} \right]$

В) $\left[ \begin{array} { r r r } - 1 & 1 & 0 \ 4 & - 1 & - 1 \ - 2 & 0 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } 1 & 1 & 1 \ \frac { 1 } { 2 } & 1 & 1 \ \frac { 1 } { 2 } & \frac { 1 } { 2 } & \frac { 1 } { 3 } \end{array} \right]$ 
D)  No inverse 
A)  $\left[ \begin{array} { l l l } - 1 & - 1 & - 1 \ - 2 & - 1 & - 1 \ - 2 & - 2 & - 3 \end{array} \right]$

В) $\left[ \begin{array} { r r r } - 1 & 1 & 0 \ 4 & - 1 & - 1 \ - 2 & 0 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { c c c } 1 & 1 & 1 \ \frac { 1 } { 2 } & 1 & 1 \ \frac { 1 } { 2 } & \frac { 1 } { 2 } & \frac { 1 } { 3 } \end{array} \right]$ 
D)  No inverse

Use the elimination method to solve the system. - $\left\{ \begin{array} { r } 3 x + 48 y = 48 \\3 x - 6 y = - 6\end{array} \right.$

Perform the indicated matrix operations. -Let $A = \left[ \begin{array} { l l } - 4 & 2 \end{array} \right]$ and $B = \left[ \begin{array} { l l } 1 & 0 \end{array} \right]$ . Find $3 A + 4 B$ .

Solve the system of equations using elimination. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 61 \\x ^ { 2 } - y ^ { 2 } = 11\end{array} \right.$

Solve the problem using matrices. -Find the function $f ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + d$ for which $f ( 0 ) = - 2 , f ( 1 ) = 5 , f ( - 1 ) = 3$ , $f ( 2 ) = 4$ .

Solve the system of equations using elimination. - $\left\{ \begin{array} { l } 2 x ^ { 2 } + x y - y ^ { 2 } = 3 \\x ^ { 2 } + 2 x y + y ^ { 2 } = 3\end{array} \right.$

Graph the inequality. - $y \leq-8$ $Graph the inequality. - y \leq-8 A) B) C) D)$ A) $Graph the inequality. - y \leq-8 A) B) C) D)$ B) $Graph the inequality. - y \leq-8 A) B) C) D)$ C) $Graph the inequality. - y \leq-8 A) B) C) D)$ D) $Graph the inequality. - y \leq-8 A) B) C) D)$

Find the maximum or minimum value of the objective function, subject to the constraints graphed in this feasible region. -z = x + 7y + 9 Find minimum.

Solve the problem using matrices. -Find real numbers a, b, and c such that the graph of the function $y = a x ^ { 2 } + b x + c$ c contains the points (-2, -4), (1, -1), and (3, -19).

Use Cramer's rule to solve the linear system. - $\left\{ \begin{array} { l } - 4 x - 6 y - 8 z = - 84 \\- 4 x + 4 y - 3 z = 11 \\- 9 x - 5 y - 9 z = - 94\end{array} \right.$

Solve the system of equations. - $\left\{ \begin{aligned}- x + y + 2 z & = 0 \\x + 2 y + z & = 6 \\- 2 x - y + z & = - 6\end{aligned} \right.$

Solve the system of equations using elimination. - $\left\{ \begin{aligned}3 x ^ { 2 } + 2 y ^ { 2 } & = 89 \\x ^ { 2 } - 2 y ^ { 2 } & = - 21\end{aligned} \right.$

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } \ln x = 3 \ln y \\3 ^ { x } = 27 y\end{array} \right.$

Perform the indicated operation, whenever possible. -Let $A = \left[ \begin{array} { r r r } 7 & - 4 & 8 \\ - 6 & 5 & - 1 \\ 0 & 6 & - 3 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } - 2 & - 6 & - 1 \\ - 7 & - 4 & 3 \\ - 3 & - 9 & - 5 \end{array} \right] . \quad$ Find $A - B$

Write the partial fraction decomposition of the rational expression. - $\frac { 3 x - 2 } { x ^ { 3 } - 1 }$

Find the inverse of the matrix. - $\left[ \begin{array} { l l l } 1 & 1 & 1 \\2 & 1 & 1 \\2 & 2 & 3\end{array} \right]$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Exam 10: Systems of Equations and Inequalities

Use the elimination method to solve the system. - {3x+48y=483x−6y=−6\left\{ \begin{array} { r } 3 x + 48 y = 48 \\3 x - 6 y = - 6\end{array} \right.{3x+48y=483x−6y=−6​

Perform the indicated matrix operations. -Let A=[−42]A = \left[ \begin{array} { l l } - 4 & 2 \end{array} \right]A=[−4​2​] and B=[10]B = \left[ \begin{array} { l l } 1 & 0 \end{array} \right]B=[1​0​] . Find 3A+4B3 A + 4 B3A+4B .

Solve the system of equations using elimination. - {x2+y2=61x2−y2=11\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 61 \\x ^ { 2 } - y ^ { 2 } = 11\end{array} \right.{x2+y2=61x2−y2=11​

Solve the problem using matrices. -Find the function f(x)=ax3+bx2+cx+df ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + df(x)=ax3+bx2+cx+d for which f(0)=−2,f(1)=5,f(−1)=3f ( 0 ) = - 2 , f ( 1 ) = 5 , f ( - 1 ) = 3f(0)=−2,f(1)=5,f(−1)=3 , f(2)=4f ( 2 ) = 4f(2)=4 .

Solve the system of equations using elimination. - {2x2+xy−y2=3x2+2xy+y2=3\left\{ \begin{array} { l } 2 x ^ { 2 } + x y - y ^ { 2 } = 3 \\x ^ { 2 } + 2 x y + y ^ { 2 } = 3\end{array} \right.{2x2+xy−y2=3x2+2xy+y2=3​

Graph the inequality. - y≤−8y \leq-8y≤−8 A) B) C) D)