Question 1

Graph the inequality.
-$x+y<-3$

Accepted Answer

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

Question 2

2x + 3y ≥6
-$$\begin{array} { l } 
2 x + 3 y \leq 6 \
x - y \geq 3 \
x \geq 1
\end{array}$$

Accepted Answer

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

Question 3

Solve the system of equations using elimination.
-$$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 81 \
x ^ { 2 } - y ^ { 2 } = 81
\end{array} \right.$$

Accepted Answer

A)  $x = 9 , y = 9 ; x = - 9 , y = 9$ 
B)  $x = - 9 , y = 0 ; x = - 9 , y = 9$ 
C)  $x = 9 , y = 0 ; x = - 9 , y = 0$ 
D)  $x = 9 , y = 0 ; x = 9 , y = 9$ 
A)  $x = 9 , y = 9 ; x = - 9 , y = 9$ 
B)  $x = - 9 , y = 0 ; x = - 9 , y = 9$ 
C)  $x = 9 , y = 0 ; x = - 9 , y = 0$ 
D)  $x = 9 , y = 0 ; x = 9 , y = 9$ C

Question 4

Find the value of the determinant.
-$$\left| \begin{array} { r r r } 
- 2 & 5 & 4 \
3 & - 2 & 1 \
1 & 6 & - 3
\end{array} \right|$$

Accepted Answer

A)  $- 90$ 
B)  130 
C)  80 
D)  $- 12$ 
A)  $- 90$ 
B)  130 
C)  80 
D)  $- 12$

Question 5

Choose the one alternative that best completes the statement or answers the question.
Use a graphing utility to find the inverse of the matrix, if it exists. Round answers to two decimal places, if necessary.
-$\left[\begin{array}{rrr}
-16 & 3 & 28 \
5 & -14 & 15 \
34 & 25 & 2
\end{array}\right]$

Accepted Answer

A)  $\left[ \begin{array} { r r r } - 0.02 & 0.03 & 0.02 \ 0.02 & - 0.04 & 0.01 \ 0.02 & 0.02 & 0.00 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } - 0.02 & 0.03 & 0.02 \ 0.02 & - 0.04 & 0.02 \ 0.02 & 0.02 & 0.01 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } - 0.01 & 0.03 & 0.02 \ 0.02 & - 0.03 & 0.01 \ 0.02 & 0.02 & 0.01 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } - 0.01 & 0.02 & 0.01 \ 0.02 & - 0.03 & 0.01 \ 0.02 & 0.02 & 0.01 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r } - 0.02 & 0.03 & 0.02 \ 0.02 & - 0.04 & 0.01 \ 0.02 & 0.02 & 0.00 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } - 0.02 & 0.03 & 0.02 \ 0.02 & - 0.04 & 0.02 \ 0.02 & 0.02 & 0.01 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } - 0.01 & 0.03 & 0.02 \ 0.02 & - 0.03 & 0.01 \ 0.02 & 0.02 & 0.01 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } - 0.01 & 0.02 & 0.01 \ 0.02 & - 0.03 & 0.01 \ 0.02 & 0.02 & 0.01 \end{array} \right]$

Question 6

Choose the one alternative that best completes the statement or answers the question.
Use Cramer's rule to solve the linear system.
-$$\left\{ \begin{array} { c } 
2 x + 5 y = 21 \
2 x + y = 1
\end{array} \right.$$

Accepted Answer

A)  $x = 5 , y = - 2$ 
B)  $x = - 5 , y = - 2$ 
C)  $x = - 2 , y = 5$ 
D)  $x = 2 , y = - 5$ 
A)  $x = 5 , y = - 2$ 
B)  $x = - 5 , y = - 2$ 
C)  $x = - 2 , y = 5$ 
D)  $x = 2 , y = - 5$

Question 7

Graph the inequality.
-$-3 x-4 y \leq-12$

Accepted Answer

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

Question 8

Use the properties of determinants to find the value of the second determinant, given the value of the first.
-$\left| \begin{array} { r r r } x & y & z \ u & v & w \ 1 & - 2 & 3 \end{array} \right| = 22 \left| \begin{array} { c c c } x & y & z - x \ u & v & w - u \ 1 & - 2 & 2 \end{array} \right| = ?$

Accepted Answer

A)  0 
B)  $- 22$ 
C)  22 
D)  Cannot determine 
A)  0 
B)  $- 22$ 
C)  22 
D)  Cannot determine

Question 9

Write the partial fraction decomposition of the rational expression.
-$$\frac { 2 x - 5 } { x ^ { 2 } - 5 x - 6 }$$

Accepted Answer

A)  $\frac { 17 } { x + 6 } - \frac { 3 } { x - 1 }$ 
B)  $\frac { 1 } { x - 3 } + \frac { 1 } { x - 2 }$ 
C)  $\frac { 9 } { x + 2 } + \frac { 1 } { x - 3 }$ 
D)  $\frac { 1 } { x - 6 } + \frac { 1 } { x + 1 }$ 
A)  $\frac { 17 } { x + 6 } - \frac { 3 } { x - 1 }$ 
B)  $\frac { 1 } { x - 3 } + \frac { 1 } { x - 2 }$ 
C)  $\frac { 9 } { x + 2 } + \frac { 1 } { x - 3 }$ 
D)  $\frac { 1 } { x - 6 } + \frac { 1 } { x + 1 }$

Question 10

Find the value of the determinant.
-$\left| \begin{array} { l l l } 3 & 5 & 5 \ 6 & 3 & 2 \ 1 & 1 & 5 \end{array} \right|$

Accepted Answer

A)  $- 106$ 
B)  256 
C)  $- 86$ 
D)  86 
A)  $- 106$ 
B)  256 
C)  $- 86$ 
D)  86

Question 11

Perform the indicated operations and simplify.
-Let $\mathrm { A } = \left[ \begin{array} { r r } 3 & - 4 \ - 2 & 5 \end{array} \right] , \mathrm { B } = \left[ \begin{array} { r r r } 5 & - 2 & 8 \ 1 & 0 & - 3 \end{array} \right]$, and $\mathrm { C } = \left[ \begin{array} { r r r } 7 & - 9 & 0 \ 3 & - 5 & 1 \ - 1 & 6 & 2 \end{array} \right]$. Find $\mathrm { AB } + \mathrm { BC }$.

Accepted Answer

A)  $\left[ \begin{array} { r r r } 68 & 3 & 31 \ 8 & - 2 & - 5 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 32 & 7 & 50 \ 5 & - 23 & - 37 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } - 10 & - 19 & 12 \ - 15 & 31 & - 25 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 32 & 19 & 40 \ - 15 & 31 & - 37 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r } 68 & 3 & 31 \ 8 & - 2 & - 5 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 32 & 7 & 50 \ 5 & - 23 & - 37 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } - 10 & - 19 & 12 \ - 15 & 31 & - 25 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 32 & 19 & 40 \ - 15 & 31 & - 37 \end{array} \right]$

Question 12

Write the augmented matrix for the system.
-$$\left\{ \begin{array} { l } 
9 x + 8 y = 50 \
5 x + 6 y = 34
\end{array} \right.$$

Accepted Answer

A)  $\left[ \begin{array} { l l | l } 2 & 6 & 26 \ 5 & 9 & 35 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l | l } 26 & 6 & 2 \ 35 & 5 & 9 \end{array} \right]$ 
C)  $\left[ \begin{array} { l | l } 2 & 6 \end{array} \right.$ 
D)  $\left[ \begin{array} { l l | l } 2 & 5 & 26 \ 6 & 9 & 35 \end{array} \right]$ 
A)  $\left[ \begin{array} { l l | l } 2 & 6 & 26 \ 5 & 9 & 35 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l | l } 26 & 6 & 2 \ 35 & 5 & 9 \end{array} \right]$ 
C)  $\left[ \begin{array} { l | l } 2 & 6 \end{array} \right.$ 
D)  $\left[ \begin{array} { l l | l } 2 & 5 & 26 \ 6 & 9 & 35 \end{array} \right]$

Question 13

Solve the system using the inverse method.
-$$\left\{ \begin{aligned}
x + 2 y + 3 z & = 11 \
x + y + z & = 3 \
2 x + 2 y + z & = 10
\end{aligned} \right.$$

Accepted Answer

A)  $x = - 8 , y = 49 , z = 7$ 
B)  $x = 33 , y = 46 , z = 16$ 
C)  $x = - 9 , y = 16 , z = - 4$ 
D)  $x = 44 , y = - 6 , z = 10$ 
A)  $x = - 8 , y = 49 , z = 7$ 
B)  $x = 33 , y = 46 , z = 16$ 
C)  $x = - 9 , y = 16 , z = - 4$ 
D)  $x = 44 , y = - 6 , z = 10$

Question 14

Write the word or phrase that best completes each statement or answers the question.
-$$\left\{ \begin{array} { r } 
3 x ^ { 2 } + 2 y ^ { 2 } = 89 \
x ^ { 2 } - 2 y ^ { 2 } = - 21
\end{array} \right.$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 15

Choose the one alternative that best completes the statement or answers the question.
-In a 1-mile race, the winner crosses the finish line 10 feet ahead of the second-place runner and 30 feet ahead of the third-place runner. Assuming that each runner maintains a constant speed throughout the race, by how
Many feet does the second-place runner beat the third-place runner? (5280 feet in 1 mile.)

Accepted Answer

A)  -10.06 ft 
B)  10.02 ft 
C)  20.04 ft 
D)  -20.11 ft 
A)  -10.06 ft 
B)  10.02 ft 
C)  20.04 ft 
D)  -20.11 ft

Question 16

2x + 3y ≥6
-$\begin{array}{l}
y>x^{2} \
2 x+5 y \leq 10
\end{array}$

Accepted Answer

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

Question 17

Write the word or phrase that best completes each statement or answers the question.
-$\mathrm{R}_{3}=4 \mathrm{r}_{1}+\mathrm{r}_{3}$

$$\begin{array} { l } 
\
{ \left[ \begin{array} { r r r | r } 
- 7 & - 5 & - 1 & - 10 \
6 & - 2 & 9 & 5 \
28 & - 6 & 6 & 18
\end{array} \right] }
\end{array}$$

Accepted Answer

\[\left[ \begin{array} { c c r

Question 18

Verify that the values of the variables listed are solutions of the system of equations.
-$$\left\{ \begin{array} { l } 
x + y = 8 \
x - y = 4 \
\end{array} \right.$$
x = 6 , y = 2

Accepted Answer

A)  not a solution 
B)  solution 
A)  not a solution 
B)  solution

Question 19

Solve the system.
-$$\left\{ \begin{array} { l } 
4 x - 7 y = 8 \
4 x - 7 y = - 5
\end{array} \right.$$

Accepted Answer

A)  $\left( \frac { 8 } { 7 } , - \frac { 5 } { 4 } \right)$ 
B)  inconsistent (no solution) 
C)  $( 8 , - 5 )$ 
D)  consistent (many solutions) 
A)  $\left( \frac { 8 } { 7 } , - \frac { 5 } { 4 } \right)$ 
B)  inconsistent (no solution) 
C)  $( 8 , - 5 )$ 
D)  consistent (many solutions)

Question 20

Perform the indicated matrix operations.
-Let $C = \left[ \begin{array} { r } 1 \ - 3 \ 2 \end{array} \right]$ and $D = \left[ \begin{array} { r } - 1 \ 3 \ - 2 \end{array} \right]$. Find $C - 3 D$

Accepted Answer

A)  $\left[ \begin{array} { c } - 4 \ 12 \ - 8 \end{array} \right]$ 
B)  $\left[ \begin{array} { r } 4 \ - 6 \ 4 \end{array} \right]$ 
C)  $\left[ \begin{array} { r } - 2 \ 6 \ - 4 \end{array} \right]$ 
D)  $\left[ \begin{array} { r } 4 \ - 12 \ 8 \end{array} \right]$ 
A)  $\left[ \begin{array} { c } - 4 \ 12 \ - 8 \end{array} \right]$ 
B)  $\left[ \begin{array} { r } 4 \ - 6 \ 4 \end{array} \right]$ 
C)  $\left[ \begin{array} { r } - 2 \ 6 \ - 4 \end{array} \right]$ 
D)  $\left[ \begin{array} { r } 4 \ - 12 \ 8 \end{array} \right]$

Graph the inequality. - $x+y<-3$

2x + 3y ≥6 - 2x+3y\leq6 x-y\geq3 x\geq1 $2x + 3y ≥6 - \begin{array} { l } 2 x + 3 y \leq 6 \\ x - y \geq 3 \\ x \geq 1 \end{array}$

Solve the system of equations using elimination. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 81 \\x ^ { 2 } - y ^ { 2 } = 81\end{array} \right.$

Find the value of the determinant. - $\left| \begin{array} { r r r } - 2 & 5 & 4 \\3 & - 2 & 1 \\1 & 6 & - 3\end{array} \right|$

Choose the one alternative that best completes the statement or answers the question. Use a graphing utility to find the inverse of the matrix, if it exists. Round answers to two decimal places, if necessary. - $\left[\begin{array}{rrr}-16 & 3 & 28 \\5 & -14 & 15 \\34 & 25 & 2\end{array}\right]$

Choose the one alternative that best completes the statement or answers the question. Use Cramer's rule to solve the linear system. - $\left\{ \begin{array} { c } 2 x + 5 y = 21 \\2 x + y = 1\end{array} \right.$

Graph the inequality. - $-3 x-4 y \leq-12$ $Graph the inequality. - -3 x-4 y \leq-12$

Write the partial fraction decomposition of the rational expression. - $\frac { 2 x - 5 } { x ^ { 2 } - 5 x - 6 }$

Find the value of the determinant. - $\left| \begin{array} { l l l } 3 & 5 & 5 \\ 6 & 3 & 2 \\ 1 & 1 & 5 \end{array} \right|$

Write the augmented matrix for the system. - $\left\{ \begin{array} { l } 9 x + 8 y = 50 \\5 x + 6 y = 34\end{array} \right.$

Solve the system using the inverse method. - $\left\{ \begin{aligned}x + 2 y + 3 z & = 11 \\x + y + z & = 3 \\2 x + 2 y + z & = 10\end{aligned} \right.$

Write the word or phrase that best completes each statement or answers the question. - $\left\{ \begin{array} { r } 3 x ^ { 2 } + 2 y ^ { 2 } = 89 \\x ^ { 2 } - 2 y ^ { 2 } = - 21\end{array} \right.$

2x + 3y ≥6 - y> 2x+5y\leq10 $2x + 3y ≥6 - \begin{array}{l} y>x^{2} \\ 2 x+5 y \leq 10 \end{array}$

Write the word or phrase that best completes each statement or answers the question. - $\mathrm{R}_{3}=4 \mathrm{r}_{1}+\mathrm{r}_{3}$ -7 -5 -1 -10 6 -2 9 5 28 -6 6 18

Verify that the values of the variables listed are solutions of the system of equations. - $\left\{ \begin{array} { l } x + y = 8 \\x - y = 4 \\\end{array} \right.$ x = 6 , y = 2

Solve the system. - $\left\{ \begin{array} { l } 4 x - 7 y = 8 \\4 x - 7 y = - 5\end{array} \right.$

Perform the indicated matrix operations. -Let $C = \left[ \begin{array} { r } 1 \\ - 3 \\ 2 \end{array} \right]$ and $D = \left[ \begin{array} { r } - 1 \\ 3 \\ - 2 \end{array} \right]$ . Find $C - 3 D$

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

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 10: Systems of Equations and Inequalities

Graph the inequality. - x+y<−3x+y<-3x+y<−3

2x + 3y ≥6 - 2x+3y\leq6 x-y\geq3 x\geq1

Solve the system of equations using elimination. - {x2+y2=81x2−y2=81\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 81 \\x ^ { 2 } - y ^ { 2 } = 81\end{array} \right.{x2+y2=81x2−y2=81​

Find the value of the determinant. - ∣−2543−2116−3∣\left| \begin{array} { r r r } - 2 & 5 & 4 \\3 & - 2 & 1 \\1 & 6 & - 3\end{array} \right|​−231​5−26​41−3​​

Choose the one alternative that best completes the statement or answers the question. Use Cramer's rule to solve the linear system. - {2x+5y=212x+y=1\left\{ \begin{array} { c } 2 x + 5 y = 21 \\2 x + y = 1\end{array} \right.{2x+5y=212x+y=1​

Graph the inequality. - −3x−4y≤−12-3 x-4 y \leq-12−3x−4y≤−12

Write the partial fraction decomposition of the rational expression. - 2x−5x2−5x−6\frac { 2 x - 5 } { x ^ { 2 } - 5 x - 6 }x2−5x−62x−5​

Find the value of the determinant. - ∣355632115∣\left| \begin{array} { l l l } 3 & 5 & 5 \\ 6 & 3 & 2 \\ 1 & 1 & 5 \end{array} \right|​361​531​525​​

Write the augmented matrix for the system. - {9x+8y=505x+6y=34\left\{ \begin{array} { l } 9 x + 8 y = 50 \\5 x + 6 y = 34\end{array} \right.{9x+8y=505x+6y=34​

Solve the system using the inverse method. - {x+2y+3z=11x+y+z=32x+2y+z=10\left\{ \begin{aligned}x + 2 y + 3 z & = 11 \\x + y + z & = 3 \\2 x + 2 y + z & = 10\end{aligned} \right.⎩⎨⎧​x+2y+3zx+y+z2x+2y+z​=11=3=10​

Write the word or phrase that best completes each statement or answers the question. - {3x2+2y2=89x2−2y2=−21\left\{ \begin{array} { r } 3 x ^ { 2 } + 2 y ^ { 2 } = 89 \\x ^ { 2 } - 2 y ^ { 2 } = - 21\end{array} \right.{3x2+2y2=89x2−2y2=−21​

2x + 3y ≥6 - y> 2x+5y\leq10

Write the word or phrase that best completes each statement or answers the question. - R3=4r1+r3\mathrm{R}_{3}=4 \mathrm{r}_{1}+\mathrm{r}_{3}R3​=4r1​+r3​ -7 -5 -1 -10 6 -2 9 5 28 -6 6 18

Verify that the values of the variables listed are solutions of the system of equations. - {x+y=8x−y=4\left\{ \begin{array} { l } x + y = 8 \\x - y = 4 \\\end{array} \right.{x+y=8x−y=4​ x = 6 , y = 2

Solve the system. - {4x−7y=84x−7y=−5\left\{ \begin{array} { l } 4 x - 7 y = 8 \\4 x - 7 y = - 5\end{array} \right.{4x−7y=84x−7y=−5​

Perform the indicated matrix operations. -Let C=[1−32]C = \left[ \begin{array} { r } 1 \\ - 3 \\ 2 \end{array} \right]C=​1−32​​ and D=[−13−2]D = \left[ \begin{array} { r } - 1 \\ 3 \\ - 2 \end{array} \right]D=​−13−2​​ . Find C−3DC - 3 DC−3D