Question 1

Determine if each ordered pair is a solution to the given system of inequalities in two variables.
-$$\begin{array} { l } 
x + y = 13 \
y = x ^ { 2 } - 14 x + 49
\end{array}$$
(i) $( - 4,17 )$; (ii) $( 9,4 )$

Accepted Answer

A)  (i) Yes; (ii) No 
B)  (i) Yes; (ii) Yes 
C)  (i) No; (ii) Yes 
D)  (i) No; (ii) No 
A)  (i) Yes; (ii) No 
B)  (i) Yes; (ii) Yes 
C)  (i) No; (ii) Yes 
D)  (i) No; (ii) No

Question 2

Solve the problem.
-A flat rectangular piece of aluminum has a perimeter of 62 inches. The length is 9 inches longer than the width. Find the width.

Accepted Answer

A) 29 in. 
B) 31 in. 
C) 11 in. 
D) 20 in. 
A) 29 in. 
B) 31 in. 
C) 11 in. 
D) 20 in.

Question 3

Determine whether the given ordered pair is a solution of the system.
-(-6, -4) 4x + y = -28 2x + 4y = -28

Accepted Answer

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

Question 4

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
y = x ^ { 2 } - 14 x + 49 \
x + y = 19
\end{array}$$
$x + y = 19$

Accepted Answer

A)  $( 7,12 )$ 
B)  $( 3,16 ) , ( 10,9 )$ 
C)  $( - 3,22 ) , ( - 10,29 )$ 
D)  $( 3,22 ) , ( 10,9 )$ 
A)  $( 7,12 )$ 
B)  $( 3,16 ) , ( 10,9 )$ 
C)  $( - 3,22 ) , ( - 10,29 )$ 
D)  $( 3,22 ) , ( 10,9 )$

Question 5

Solve the system of equations by substitution.
-$$\begin{array} { c } 
\frac { 1 } { 5 } x - y = - \frac { 4 } { 5 } \
x + 8 y = - 4
\end{array}$$

Accepted Answer

A) (0, -4) 
B) (0, 4) 
C) (-4, 0) 
D) (4, 0) 
A) (0, -4) 
B) (0, 4) 
C) (-4, 0) 
D) (4, 0)

Question 6

Solve the system of equations by elimination.
-3x + 6y = 39 3x + 2y = 47

Accepted Answer

A) (-17, 6) 
B) (-2, 17) 
C) ( -17, 3) 
D) (17, -2) 
A) (-17, 6) 
B) (-2, 17) 
C) ( -17, 3) 
D) (17, -2)

Question 7

Graph the system of inequalities.
-$\begin{array}{l}
x^{2}+y^{2} \leq 49 \
-10 x+2 y \leq-20
\end{array}$

Accepted Answer

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

Question 8

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 4 \
x + y = 2
\end{array}$$

Accepted Answer

A)  $( 0,0 ) , ( 2 , - 2 )$ 
B)  $( 2 , - 2 ) , ( - 2 , - 2 )$ 
C)  $( 0 , - 2 ) , ( - 2,0 )$ 
D)  $( 0,2 ) , ( 2,0 )$ 
A)  $( 0,0 ) , ( 2 , - 2 )$ 
B)  $( 2 , - 2 ) , ( - 2 , - 2 )$ 
C)  $( 0 , - 2 ) , ( - 2,0 )$ 
D)  $( 0,2 ) , ( 2,0 )$

Question 9

Graph the system of inequalities.
-$\begin{array}{l}
x^{2}+y^{2} \leq 36 \
-6 x+4 y \leq-24
\end{array}$

Accepted Answer

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

Question 10

Graph the system of inequalities.
-$\begin{array}{l}
y \geq x^{2} \
x+y>6
\end{array}$

Accepted Answer

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

Question 11

Write the partial fraction decomposition of the rational expression.
-$\frac { 12 x + 3 } { ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) }$

Accepted Answer

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

Question 12

Graph the system of inequalities.
-$\begin{array}{l}
x^{2}+y^{2} \leq 4 \
x^{2}+y^{2} \geq 1
\end{array}$

Accepted Answer

A) 
  
B) 
  
C) 
  
D)  no solution
  
A) 
  
B) 
  
C) 
  
D)  no solution

Question 13

Determine if each ordered pair is a solution to the given system of inequalities in two variables.
-$$\begin{array} { l } 
x y = 54 \
x ^ { 2 } + y ^ { 2 } = 117
\end{array}$$
(i) $( 6 , - 9 )$; (ii) $( - 9 , - 6 )$

Accepted Answer

A)  (i) Yes; (ii) Yes 
B)  (i) $\mathrm { No }$; (ii) Yes 
C)  (i) No; (ii) No 
D)  (i) Yes; (ii) No 
A)  (i) Yes; (ii) Yes 
B)  (i) $\mathrm { No }$; (ii) Yes 
C)  (i) No; (ii) No 
D)  (i) Yes; (ii) No

Question 14

Graph the inequality.
-

Accepted Answer

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

Question 15

Write the partial fraction decomposition of the rational expression.
-$\frac { 8 x ^ { 2 } + 12 x + 19 } { x ^ { 3 } + 2 x ^ { 2 } + 5 x + 10 }$

Accepted Answer

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

Question 16

Write the partial fraction decomposition of the rational expression.
-$\frac { 8 x + 3 } { ( x - 8 ) ^ { 2 } }$

Accepted Answer

A)  $\frac { 8 } { x - 8 } + \frac { 128 } { ( x - 8 ) ^ { 2 } }$ 
B)  $\frac { 8 } { x - 8 } + \frac { 67 } { ( x - 8 ) ^ { 2 } }$ 
C)  $\frac { 8 } { x - 8 } + \frac { x + 67 } { ( x - 8 ) ^ { 2 } }$ 
D)  $\frac { 1 } { x - 8 } + \frac { x + 67 } { ( x - 8 ) ^ { 2 } }$ 
A)  $\frac { 8 } { x - 8 } + \frac { 128 } { ( x - 8 ) ^ { 2 } }$ 
B)  $\frac { 8 } { x - 8 } + \frac { 67 } { ( x - 8 ) ^ { 2 } }$ 
C)  $\frac { 8 } { x - 8 } + \frac { x + 67 } { ( x - 8 ) ^ { 2 } }$ 
D)  $\frac { 1 } { x - 8 } + \frac { x + 67 } { ( x - 8 ) ^ { 2 } }$

Question 17

Write the partial fraction decomposition of the rational expression.
-$$\frac { 7 x ^ { 2 } - 36 x + 38 } { ( x - 6 ) \left( x ^ { 2 } + 1 \right) }$$

Accepted Answer

A)  $\frac { 2 } { x - 6 } + \frac { 5 x - 6 } { x ^ { 2 } + 1 }$ 
B)  $\frac { 2 } { x - 6 } + \frac { 5 x + 6 } { x ^ { 2 } + 1 }$ 
C)  $\frac { 2 } { x - 6 } + \frac { 5 } { x ^ { 2 } + 1 }$ 
D)  $\frac { 2 } { x - 6 } + \frac { 5 } { x + 1 } + \frac { - 6 } { ( x + 1 ) ^ { 2 } }$ 
A)  $\frac { 2 } { x - 6 } + \frac { 5 x - 6 } { x ^ { 2 } + 1 }$ 
B)  $\frac { 2 } { x - 6 } + \frac { 5 x + 6 } { x ^ { 2 } + 1 }$ 
C)  $\frac { 2 } { x - 6 } + \frac { 5 } { x ^ { 2 } + 1 }$ 
D)  $\frac { 2 } { x - 6 } + \frac { 5 } { x + 1 } + \frac { - 6 } { ( x + 1 ) ^ { 2 } }$

Question 18

Determine the real solutions to the system of nonlinear equations.
-$$x + y = 2$$
$x ^ { 2 } + y ^ { 2 } = - 6 y + 8$

Accepted Answer

A)  $( - 2,4 ) , ( 1,1 )$ 
B)  $( 0,2 ) , ( 3 , - 1 )$ 
C)  $( 4 , - 2 ) , ( 1,1 )$ 
D)  $( 2,0 ) , ( - 1,3 )$ 
A)  $( - 2,4 ) , ( 1,1 )$ 
B)  $( 0,2 ) , ( 3 , - 1 )$ 
C)  $( 4 , - 2 ) , ( 1,1 )$ 
D)  $( 2,0 ) , ( - 1,3 )$

Question 19

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered
triple involving variable z.
-$$\begin{array} { l } 
x + y + z = 9 \
2 x - 3 y + 4 z = 7
\end{array}$$

Accepted Answer

A)  $\left( \frac { 27 } { 5 } , \frac { 13 } { 5 } , 1 \right)$ 
B)  $\left( - \frac { 7 } { 5 } z + \frac { 34 } { 5 } , \frac { 2 } { 5 } z + \frac { 11 } { 5 } , z \right)$ 
C)  no solution 
D)  $\left( \frac { 3 } { 5 } z + \frac { 16 } { 5 } , - \frac { 8 } { 5 } z + \frac { 29 } { 5 } , z \right)$ 
A)  $\left( \frac { 27 } { 5 } , \frac { 13 } { 5 } , 1 \right)$ 
B)  $\left( - \frac { 7 } { 5 } z + \frac { 34 } { 5 } , \frac { 2 } { 5 } z + \frac { 11 } { 5 } , z \right)$ 
C)  no solution 
D)  $\left( \frac { 3 } { 5 } z + \frac { 16 } { 5 } , - \frac { 8 } { 5 } z + \frac { 29 } { 5 } , z \right)$

Question 20

Write the partial fraction decomposition of the rational expression.
-$\frac { 7 x ^ { 2 } - x - 20 } { x ^ { 3 } - x }$

Accepted Answer

A)  $\frac { 20 } { x } + \frac { - 6 } { x + 1 } + \frac { 7 } { x - 1 }$ 
B)  $\frac { 20 } { x } + \frac { 6 } { x + 1 } + \frac { - 7 } { x - 1 }$ 
C)  $\frac { 20 } { x } + \frac { - 6 } { x + 1 } + \frac { - 7 } { x - 1 }$ 
D)  $\frac { 20 } { x } + \frac { - 7 } { x + 1 } + \frac { 6 } { x - 1 }$ 
A)  $\frac { 20 } { x } + \frac { - 6 } { x + 1 } + \frac { 7 } { x - 1 }$ 
B)  $\frac { 20 } { x } + \frac { 6 } { x + 1 } + \frac { - 7 } { x - 1 }$ 
C)  $\frac { 20 } { x } + \frac { - 6 } { x + 1 } + \frac { - 7 } { x - 1 }$ 
D)  $\frac { 20 } { x } + \frac { - 7 } { x + 1 } + \frac { 6 } { x - 1 }$

Determine if each ordered pair is a solution to the given system of inequalities in two variables. - x+y=13 y=-14x+49 (i) $( - 4,17 )$ ; (ii) $( 9,4 )$

Solve the problem. -A flat rectangular piece of aluminum has a perimeter of 62 inches. The length is 9 inches longer than the width. Find the width.

Determine whether the given ordered pair is a solution of the system. -(-6, -4) 4x + y = -28 2x + 4y = -28

Determine the real solutions to the system of nonlinear equations. - y=-14x+49 x+y=19 $x + y = 19$

Solve the system of equations by substitution. - x-y=- x+8y=-4

Solve the system of equations by elimination. -3x + 6y = 39 3x + 2y = 47

Graph the system of inequalities. - +\leq49 -10x+2y\leq-20 $Graph the system of inequalities. - \begin{array}{l} x^{2}+y^{2} \leq 49 \\ -10 x+2 y \leq-20 \end{array}$

Determine the real solutions to the system of nonlinear equations. - +=4 x+y=2

Graph the system of inequalities. - +\leq36 -6x+4y\leq-24 $Graph the system of inequalities. - \begin{array}{l} x^{2}+y^{2} \leq 36 \\ -6 x+4 y \leq-24 \end{array}$

Graph the system of inequalities. - y\geq x+y>6 $Graph the system of inequalities. - \begin{array}{l} y \geq x^{2} \\ x+y>6 \end{array}$

Write the partial fraction decomposition of the rational expression. - $\frac { 12 x + 3 } { ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) }$

Graph the system of inequalities. - +\leq4 +\geq1 $Graph the system of inequalities. - \begin{array}{l} x^{2}+y^{2} \leq 4 \\ x^{2}+y^{2} \geq 1 \end{array}$

Determine if each ordered pair is a solution to the given system of inequalities in two variables. - xy=54 +=117 (i) $( 6 , - 9 )$ ; (ii) $( - 9 , - 6 )$

Graph the inequality. -

Write the partial fraction decomposition of the rational expression. - $\frac { 8 x ^ { 2 } + 12 x + 19 } { x ^ { 3 } + 2 x ^ { 2 } + 5 x + 10 }$

Write the partial fraction decomposition of the rational expression. - $\frac { 8 x + 3 } { ( x - 8 ) ^ { 2 } }$

Write the partial fraction decomposition of the rational expression. - $\frac { 7 x ^ { 2 } - 36 x + 38 } { ( x - 6 ) \left( x ^ { 2 } + 1 \right) }$

Determine the real solutions to the system of nonlinear equations. - $x + y = 2$ $x ^ { 2 } + y ^ { 2 } = - 6 y + 8$

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered triple involving variable z. - x+y+z=9 2x-3y+4z=7

Write the partial fraction decomposition of the rational expression. - $\frac { 7 x ^ { 2 } - x - 20 } { x ^ { 3 } - x }$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

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Exponential and Logarithmic Functions and Equations

Conic Sections

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Math Exercises: Sets, Intervals, Absolute Value, and Properties

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Exam 7: Systems of Equations and Inequalities

Determine if each ordered pair is a solution to the given system of inequalities in two variables. - x+y=13 y=-14x+49 (i) (−4,17)( - 4,17 )(−4,17) ; (ii) (9,4)( 9,4 )(9,4)

Solve the problem. -A flat rectangular piece of aluminum has a perimeter of 62 inches. The length is 9 inches longer than the width. Find the width.

Determine whether the given ordered pair is a solution of the system. -(-6, -4) 4x + y = -28 2x + 4y = -28

Determine the real solutions to the system of nonlinear equations. - y=-14x+49 x+y=19 x+y=19x + y = 19x+y=19

Solve the system of equations by substitution. - x-y=- x+8y=-4

Solve the system of equations by elimination. -3x + 6y = 39 3x + 2y = 47

Graph the system of inequalities. - +\leq49 -10x+2y\leq-20

Determine the real solutions to the system of nonlinear equations. - +=4 x+y=2

Graph the system of inequalities. - +\leq36 -6x+4y\leq-24

Graph the system of inequalities. - y\geq x+y>6

Write the partial fraction decomposition of the rational expression. - 12x+3(x−1)(x2+x+1)\frac { 12 x + 3 } { ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) }(x−1)(x2+x+1)12x+3​

Graph the system of inequalities. - +\leq4 +\geq1

Determine if each ordered pair is a solution to the given system of inequalities in two variables. - xy=54 +=117 (i) (6,−9)( 6 , - 9 )(6,−9) ; (ii) (−9,−6)( - 9 , - 6 )(−9,−6)

Graph the inequality. -

Write the partial fraction decomposition of the rational expression. - 8x2+12x+19x3+2x2+5x+10\frac { 8 x ^ { 2 } + 12 x + 19 } { x ^ { 3 } + 2 x ^ { 2 } + 5 x + 10 }x3+2x2+5x+108x2+12x+19​

Write the partial fraction decomposition of the rational expression. - 8x+3(x−8)2\frac { 8 x + 3 } { ( x - 8 ) ^ { 2 } }(x−8)28x+3​

Write the partial fraction decomposition of the rational expression. - 7x2−36x+38(x−6)(x2+1)\frac { 7 x ^ { 2 } - 36 x + 38 } { ( x - 6 ) \left( x ^ { 2 } + 1 \right) }(x−6)(x2+1)7x2−36x+38​

Determine the real solutions to the system of nonlinear equations. - x+y=2x + y = 2x+y=2 x2+y2=−6y+8x ^ { 2 } + y ^ { 2 } = - 6 y + 8x2+y2=−6y+8

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered triple involving variable z. - x+y+z=9 2x-3y+4z=7

Write the partial fraction decomposition of the rational expression. - 7x2−x−20x3−x\frac { 7 x ^ { 2 } - x - 20 } { x ^ { 3 } - x }x3−x7x2−x−20​

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Determine if each ordered pair is a solution to the given system of inequalities in two variables. - x+y=13 y=-14x+49 (i) $( - 4,17 )$ ; (ii) $( 9,4 )$

Determine the real solutions to the system of nonlinear equations. - y=-14x+49 x+y=19 $x + y = 19$

Graph the system of inequalities. - +\leq49 -10x+2y\leq-20 $Graph the system of inequalities. - \begin{array}{l} x^{2}+y^{2} \leq 49 \\ -10 x+2 y \leq-20 \end{array}$

Graph the system of inequalities. - +\leq36 -6x+4y\leq-24 $Graph the system of inequalities. - \begin{array}{l} x^{2}+y^{2} \leq 36 \\ -6 x+4 y \leq-24 \end{array}$

Graph the system of inequalities. - y\geq x+y>6 $Graph the system of inequalities. - \begin{array}{l} y \geq x^{2} \\ x+y>6 \end{array}$

Write the partial fraction decomposition of the rational expression. - $\frac { 12 x + 3 } { ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) }$

Graph the system of inequalities. - +\leq4 +\geq1 $Graph the system of inequalities. - \begin{array}{l} x^{2}+y^{2} \leq 4 \\ x^{2}+y^{2} \geq 1 \end{array}$

Determine if each ordered pair is a solution to the given system of inequalities in two variables. - xy=54 +=117 (i) $( 6 , - 9 )$ ; (ii) $( - 9 , - 6 )$

Write the partial fraction decomposition of the rational expression. - $\frac { 8 x ^ { 2 } + 12 x + 19 } { x ^ { 3 } + 2 x ^ { 2 } + 5 x + 10 }$

Write the partial fraction decomposition of the rational expression. - $\frac { 8 x + 3 } { ( x - 8 ) ^ { 2 } }$

Write the partial fraction decomposition of the rational expression. - $\frac { 7 x ^ { 2 } - 36 x + 38 } { ( x - 6 ) \left( x ^ { 2 } + 1 \right) }$

Determine the real solutions to the system of nonlinear equations. - $x + y = 2$ $x ^ { 2 } + y ^ { 2 } = - 6 y + 8$

Write the partial fraction decomposition of the rational expression. - $\frac { 7 x ^ { 2 } - x - 20 } { x ^ { 3 } - x }$