Question 1

Determine if the ordered pair is a solution to the system of linear inequalities in two variables.
-$$\begin{array} { l } 
3 x + 3 y  11
\end{array}$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 2

Determine whether the given ordered pair is a solution of the system.
-(2, -5) 4x - y = 3 3x - 4y = -14

Accepted Answer

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

Question 3

Write the partial fraction decomposition of the rational expression.
-$\frac { 3 x ^ { 3 } + 3 x ^ { 2 } } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$

Accepted Answer

A)  $\frac { 3 x - 3 } { x ^ { 2 } + 5 } + \frac { - 15 x + 15 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
B)  $\frac { 3 x + 3 } { x ^ { 2 } + 5 } + \frac { 15 x - 15 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
C)  $\frac { 3 x + 3 } { x ^ { 2 } + 5 } + \frac { 15 x + 15 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
D)  $\frac { 3 x + 3 } { x ^ { 2 } + 5 } + \frac { - 15 x - 15 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
A)  $\frac { 3 x - 3 } { x ^ { 2 } + 5 } + \frac { - 15 x + 15 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
B)  $\frac { 3 x + 3 } { x ^ { 2 } + 5 } + \frac { 15 x - 15 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
C)  $\frac { 3 x + 3 } { x ^ { 2 } + 5 } + \frac { 15 x + 15 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$ 
D)  $\frac { 3 x + 3 } { x ^ { 2 } + 5 } + \frac { - 15 x - 15 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$

Question 4

Determine whether the given ordered pair is a solution of the system.
-(6, -3) 2x - y = 9 4x + 2y = 18

Accepted Answer

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

Question 5

Graph the inequality.
-

Accepted Answer

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

Question 6

Solve the problem.
-A right triangle has an area of 11 square inches. The square of the hypotenuse is 125. Find the lengths of the legs of the triangle. Round your answer to the nearest inch.

Accepted Answer

A) 4 inches and 121 inches 
B) 4 inches and 5.5 inches 
C) 1 inches and 22 inches 
D) 2 inches and 11 inches 
A) 4 inches and 121 inches 
B) 4 inches and 5.5 inches 
C) 1 inches and 22 inches 
D) 2 inches and 11 inches

Question 7

Solve the system of equations by substitution.
-x + y = 0 2x + 3y = -7

Accepted Answer

A) (6, -6) 
B) (-7, 7) 
C) (-6, 6) 
D) (7, -7) 
A) (6, -6) 
B) (-7, 7) 
C) (-6, 6) 
D) (7, -7)

Question 8

Graph the system of inequalities.
-$\begin{array}{l}
x+9 y \leq 9 \
x+9 y \geq 0
\end{array}$

Accepted Answer

A)  No solution
  
B) 
  
C) 
  
D) 
  
A)  No solution
  
B) 
  
C) 
  
D)

Question 9

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
y = ( x + 5 ) ^ { 2 } + 1 \
2 x - y + 10 = 0
\end{array}$$

Accepted Answer

A)  $( - 5,0 )$ 
B)  $( 0,10 ) , ( 0,26 )$ 
C)  $( - 4,2 ) , ( 4,18 )$ 
D)  $( - 4,2 )$ 
A)  $( - 5,0 )$ 
B)  $( 0,10 ) , ( 0,26 )$ 
C)  $( - 4,2 ) , ( 4,18 )$ 
D)  $( - 4,2 )$

Question 10

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

Accepted Answer

A)  $\frac { 5 } { x } + \frac { - 5 } { x - 1 } + \frac { 11 } { ( x - 1 ) ^ { 2 } }$ 
B)  $\frac { 5 } { x } + \frac { - 5 } { x - 1 } + \frac { 6 } { ( x - 1 ) ^ { 2 } }$ 
C)  $\frac { - 5 } { x } + \frac { 5 } { x - 1 } + \frac { 6 } { ( x - 1 ) ^ { 2 } }$ 
D)  $\frac { 5 } { x } + \frac { 6 } { x - 1 } + \frac { - 5 } { ( x - 1 ) ^ { 2 } }$ 
A)  $\frac { 5 } { x } + \frac { - 5 } { x - 1 } + \frac { 11 } { ( x - 1 ) ^ { 2 } }$ 
B)  $\frac { 5 } { x } + \frac { - 5 } { x - 1 } + \frac { 6 } { ( x - 1 ) ^ { 2 } }$ 
C)  $\frac { - 5 } { x } + \frac { 5 } { x - 1 } + \frac { 6 } { ( x - 1 ) ^ { 2 } }$ 
D)  $\frac { 5 } { x } + \frac { 6 } { x - 1 } + \frac { - 5 } { ( x - 1 ) ^ { 2 } }$

Question 11

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
x y = 16 \
x ^ { 2 } + y ^ { 2 } = 68
\end{array}$$

Accepted Answer

A)  $( 2,8 ) , ( 8,2 ) , ( 2 , - 8 ) , ( 8 , - 2 )$ 
B)  $( 2 , - 2 ) , ( - 2 , - 8 ) , ( 8,2 ) , ( - 8 , - 2 )$ 
C)  $( - 2 , - 8 ) , ( - 8 , - 2 ) , ( - 2,8 ) , ( - 8,2 )$ 
D)  $( 2,8 ) , ( - 2 , - 8 ) , ( 2 , - 8 ) , ( - 2,8 )$ 
A)  $( 2,8 ) , ( 8,2 ) , ( 2 , - 8 ) , ( 8 , - 2 )$ 
B)  $( 2 , - 2 ) , ( - 2 , - 8 ) , ( 8,2 ) , ( - 8 , - 2 )$ 
C)  $( - 2 , - 8 ) , ( - 8 , - 2 ) , ( - 2,8 ) , ( - 8,2 )$ 
D)  $( 2,8 ) , ( - 2 , - 8 ) , ( 2 , - 8 ) , ( - 2,8 )$

Question 12

Solve the system of linear equations. If the system has infinitely many solutions, describe the solution with an ordered triple in terms of variable z.
-x + 8y + 8z = 8 
7x + 7y + z = 1 
8x + 15y + 9z = -9

Accepted Answer

A) (0, 0, 1) 
B) (1, -1, 1) 
C) no solution 
D) (-1, 0, 1) 
A) (0, 0, 1) 
B) (1, -1, 1) 
C) no solution 
D) (-1, 0, 1)

Question 13

Use Gaussian elimination to solve the linear system by finding an equivalent system in triangular form.
-$$\begin{array} { r } 
x + y + z = - 10 \
x - y + 5 z = - 24 \
3 x + y + z = - 14
\end{array}$$

Accepted Answer

A) (-5, -3, -2) 
B) (-2, -3, -5) 
C) (-5, -2, -3) 
D) no solution 
A) (-5, -3, -2) 
B) (-2, -3, -5) 
C) (-5, -2, -3) 
D) no solution

Question 14

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
x y - x ^ { 2 } = - 20 \
x - 2 y = 3
\end{array}$$

Accepted Answer

A)  $( 5,1 ) , \left( - \frac { 11 } { 2 } , - 8 \right)$ 
B)  $( - 5 , - 1 ) , \left( 8 , \frac { 11 } { 2 } \right)$ 
C)  $( - 5 , - 1 ) , \left( - \frac { 11 } { 2 } , 8 \right)$ 
D)  $( 5,1 ) , \left( - 8 , - \frac { 11 } { 2 } \right)$ 
A)  $( 5,1 ) , \left( - \frac { 11 } { 2 } , - 8 \right)$ 
B)  $( - 5 , - 1 ) , \left( 8 , \frac { 11 } { 2 } \right)$ 
C)  $( - 5 , - 1 ) , \left( - \frac { 11 } { 2 } , 8 \right)$ 
D)  $( 5,1 ) , \left( - 8 , - \frac { 11 } { 2 } \right)$

Question 15

Use Gaussian elimination and matrices to solve the system of linear equations. Write your final augmented matrix in triangular form and then solve for each variable using back substitution.
-$$\begin{aligned}
x - y + 4 z & = 16 \
4 x + z & = 5 \
x + 5 y + z & = 25
\end{aligned}$$

Accepted Answer

A) (0, 4, 5) 
B) (5, 4, 0) 
C) (0, 5, 4) 
D) (5, 0, 4) 
A) (0, 4, 5) 
B) (5, 4, 0) 
C) (0, 5, 4) 
D) (5, 0, 4)

Question 16

Solve the system of linear equations. If the system has infinitely many solutions, describe the solution with an ordered triple in terms of variable z.
-$$\begin{array} { r r } 
x + y + z & = 7 \
x - y + 2 z & = 7 \
2 x + 3 z & = 14
\end{array}$$

Accepted Answer

A)  $\left( - \frac { 3 z } { 2 } - 7,2 z , z \right)$ 
B)  $\left( - \frac { 3 z } { 2 } + 7 , \frac { z } { 2 } , z \right)$ 
C)  $\left( - \frac { 3 z } { 2 } - 7 , \frac { z } { 2 } , z \right)$ 
D)  $\left( - \frac { 3 z } { 2 } + 7,2 z , z \right)$ 
A)  $\left( - \frac { 3 z } { 2 } - 7,2 z , z \right)$ 
B)  $\left( - \frac { 3 z } { 2 } + 7 , \frac { z } { 2 } , z \right)$ 
C)  $\left( - \frac { 3 z } { 2 } - 7 , \frac { z } { 2 } , z \right)$ 
D)  $\left( - \frac { 3 z } { 2 } + 7,2 z , z \right)$

Question 17

Solve the system of equations by elimination.
-$$\begin{array} { l } 
\frac { 7 } { 12 } x - y = 10 \
\frac { 5 } { 9 } x + 2 y = 11
\end{array}$$

Accepted Answer

A)  $\left( 16 , \frac { 1 } { 2 } \right)$ 
B)  $\left( - 16 , - \frac { 1 } { 2 } \right)$ 
C)  $\left( - 18 , - \frac { 1 } { 2 } \right)$ 
D)  $\left( 18 , \frac { 1 } { 2 } \right)$ 
A)  $\left( 16 , \frac { 1 } { 2 } \right)$ 
B)  $\left( - 16 , - \frac { 1 } { 2 } \right)$ 
C)  $\left( - 18 , - \frac { 1 } { 2 } \right)$ 
D)  $\left( 18 , \frac { 1 } { 2 } \right)$

Question 18

Solve the problem.
-Ron attends a cocktail party (with his graphing calculator in his pocket). He wants to limit his food intake to 136 g protein, 125 g fat, and 174 g carbohydrate. According to the health conscious hostess, the marinated mushroom caps have 3 g protein, 5 g fat, and 9 g carbohydrate; the spicy meatballs have 14 g protein, 7 g fat, and 15 g carbohydrate; and the deviled eggs have 13 g protein, 15 g fat, and 6 g carbohydrate. How many of each snack can he eat to obtain his goal?

Accepted Answer

A) 3 mushrooms, 9 meatballs, 5 eggs 
B) 10 mushrooms, 6 meatballs, 4 eggs 
C) 5 mushrooms, 3 meatballs, 9 eggs 
D) 9 mushrooms, 5 meatballs, 3 eggs 
A) 3 mushrooms, 9 meatballs, 5 eggs 
B) 10 mushrooms, 6 meatballs, 4 eggs 
C) 5 mushrooms, 3 meatballs, 9 eggs 
D) 9 mushrooms, 5 meatballs, 3 eggs

Question 19

Solve the system of equations by elimination.
-x + y = -6 x - y = 16

Accepted Answer

A) (5, 11) 
B) (6, 5) 
C) (6, -11) 
D) (5, -11) 
A) (5, 11) 
B) (6, 5) 
C) (6, -11) 
D) (5, -11)

Question 20

Solve the problem.
-A ceramics workshop makes serving bowls, platters, and bread baskets to sell at its Winter Festival. A serving bowl takes 3 hours to prepare, 2 hours to paint, and 9 hours to fire. A platter takes 16 hours to prepare, 3 hours to paint, and 4 hours to fire. A bread basket takes 4 hours to prepare, 17 hours to paint, and 7 hours to fire. If the workshop has 119 hours for prep time, 84 hours for painting, and 122 hours for firing, how many of each can be made?

Accepted Answer

A) 9 serving bowls, 5 platters, 3 bread baskets 
B) 3 serving bowls, 9 platters, 5 bread baskets 
C) 10 serving bowls, 6 platters, 4 bread baskets 
D) 5 serving bowls, 3 platters, 9 bread baskets 
A) 9 serving bowls, 5 platters, 3 bread baskets 
B) 3 serving bowls, 9 platters, 5 bread baskets 
C) 10 serving bowls, 6 platters, 4 bread baskets 
D) 5 serving bowls, 3 platters, 9 bread baskets

Determine if the ordered pair is a solution to the system of linear inequalities in two variables. - 3x+3y<11 -3x+3y>11

Determine whether the given ordered pair is a solution of the system. -(2, -5) 4x - y = 3 3x - 4y = -14

Write the partial fraction decomposition of the rational expression. - $\frac { 3 x ^ { 3 } + 3 x ^ { 2 } } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$

Determine whether the given ordered pair is a solution of the system. -(6, -3) 2x - y = 9 4x + 2y = 18

Graph the inequality. -

Solve the problem. -A right triangle has an area of 11 square inches. The square of the hypotenuse is 125. Find the lengths of the legs of the triangle. Round your answer to the nearest inch.

Solve the system of equations by substitution. -x + y = 0 2x + 3y = -7

Graph the system of inequalities. - x+9y\leq9 x+9y\geq0 $Graph the system of inequalities. - \begin{array}{l} x+9 y \leq 9 \\ x+9 y \geq 0 \end{array}$

Determine the real solutions to the system of nonlinear equations. - y=(x+5+1 2x-y+10=0

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

Determine the real solutions to the system of nonlinear equations. - xy=16 +=68

Solve the system of linear equations. If the system has infinitely many solutions, describe the solution with an ordered triple in terms of variable z. -x + 8y + 8z = 8 7x + 7y + z = 1 8x + 15y + 9z = -9

Use Gaussian elimination to solve the linear system by finding an equivalent system in triangular form. - x+y+z=-10 x-y+5z=-24 3x+y+z=-14

Determine the real solutions to the system of nonlinear equations. - xy-=-20 x-2y=3

Use Gaussian elimination and matrices to solve the system of linear equations. Write your final augmented matrix in triangular form and then solve for each variable using back substitution. - x-y+4z =16 4x+z =5 x+5y+z =25

Solve the system of linear equations. If the system has infinitely many solutions, describe the solution with an ordered triple in terms of variable z. - x+y+z =7 x-y+2z =7 2x+3z =14

Solve the system of equations by elimination. - x-y=10 x+2y=11

Solve the system of equations by elimination. -x + y = -6 x - y = 16

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

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Exam 7: Systems of Equations and Inequalities