Question 1

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 116 \
x ^ { 2 } - y ^ { 2 } = 84
\end{array}$$

Accepted Answer

A)  $( 10 , - 4 ) , ( 10,4 )$ 
B)  $( - 10 , - 4 ) , ( - 4 , - 10 )$ 
C)  $( 10,4 ) , ( - 10,4 ) , ( 10 , - 4 ) , ( - 10 , - 4 )$ 
D)  $( 10,4 ) , ( 4,10 ) , ( - 10 , - 4 ) , ( - 4 , - 10 )$ 
A)  $( 10 , - 4 ) , ( 10,4 )$ 
B)  $( - 10 , - 4 ) , ( - 4 , - 10 )$ 
C)  $( 10,4 ) , ( - 10,4 ) , ( 10 , - 4 ) , ( - 10 , - 4 )$ 
D)  $( 10,4 ) , ( 4,10 ) , ( - 10 , - 4 ) , ( - 4 , - 10 )$

Question 2

Solve the problem.
-A deli sells three sizes of chicken sandwiches: the small chicken sandwich contains 4 ounces of meat and sells for $3.00; the regular chicken sandwich contains 8 ounces of meat and sells for $3.50; and the large chicken sandwich contains 10 ounces of meat and sells for $4.00. A customer requests a selection of each size for a reception. She and the manager agree on a combination of 52 sandwiches made from 22 pounds 4 ounces of chicken for a total cost of $178. How many of each size sandwich will be in this combination? (Note: 1 pound = 16 ounces)

Accepted Answer

A) 24 small sandwiches, 10 medium sandwiches, 18 large sandwiches. 
B) 20 small sandwiches, 22 medium sandwiches, 10 large sandwiches. 
C) 22 small sandwiches, 16 medium sandwiches, 14 large sandwiches. 
D) 18 small sandwiches, 12 medium sandwiches, 22 large sandwiches. 
A) 24 small sandwiches, 10 medium sandwiches, 18 large sandwiches. 
B) 20 small sandwiches, 22 medium sandwiches, 10 large sandwiches. 
C) 22 small sandwiches, 16 medium sandwiches, 14 large sandwiches. 
D) 18 small sandwiches, 12 medium sandwiches, 22 large sandwiches.

Question 3

Graph the inequality.
-$$x + y < - 6$$

Accepted Answer

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

Question 4

Determine whether the system corresponding to the given augmented matrix is dependent or inconsistent. If it is
dependent, give the solution.
-$$\left[ \begin{array} { r r r | r } 
1 & 0 & 0 & - 8 \
0 & 1 & 0 & 4 \
0 & 0 & 0 & - 9
\end{array} \right]$$

Accepted Answer

A) dependent; (-8, 4) 
B) inconsistent 
C) dependent; (8, -4) 
D) dependent; (-8, 4, -9) 
A) dependent; (-8, 4) 
B) inconsistent 
C) dependent; (8, -4) 
D) dependent; (-8, 4, -9)

Question 5

Graph the system of inequalities.
-$\begin{array}{l}
3 x+y>6 \
3 x+y<1
\end{array}$

Accepted Answer

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

Question 6

Write the partial fraction decomposition of the rational expression.
-$$\frac { x } { ( x - 4 ) ( x - 5 ) }$$

Accepted Answer

A)  $\frac { - 5 } { x - 4 } + \frac { 4 } { x - 5 }$ 
B)  $\frac { 4 } { x - 4 } + \frac { - 5 } { x - 5 }$ 
C)  $\frac { - 4 } { x - 4 } + \frac { 5 } { x - 5 }$ 
D)  $\frac { - 4 } { x - 4 } + \frac { - 5 } { x - 5 }$ 
A)  $\frac { - 5 } { x - 4 } + \frac { 4 } { x - 5 }$ 
B)  $\frac { 4 } { x - 4 } + \frac { - 5 } { x - 5 }$ 
C)  $\frac { - 4 } { x - 4 } + \frac { 5 } { x - 5 }$ 
D)  $\frac { - 4 } { x - 4 } + \frac { - 5 } { x - 5 }$

Question 7

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.
-$$\begin{aligned}
4 x - y + 3 z & = 12 \
x + 4 y + 6 z & = - 32 \
5 x + 3 y + 9 z & = 20
\end{aligned}$$

Accepted Answer

A) (8, -7, -2) 
B) (-8, -7, 9) 
C) no solution 
D) (2, -7, -1) 
A) (8, -7, -2) 
B) (-8, -7, 9) 
C) no solution 
D) (2, -7, -1)

Question 8

Determine if the given ordered triple is a solution of the system.
-$$\begin{array} { l } 
( - 5 , - 1,5 ) \
3 x + 2 y + z = 8 \
2 x - 3 y - z = 18 \
4 x + y + 5 z = - 6
\end{array}$$

Accepted Answer

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

Question 9

Solve the problem.
-Find the values of $a$, $b$, and $c$ such that the graph of the quadratic equation $y = a x ^ { 2 } + b x + c$ passes through the points $( - 3,5 ) , ( 1,1 )$, and $( 2 , - 5 )$.

Accepted Answer

A)  $a = 1 ; b = - 3 ; c = 5$ 
B)  $a = 1 ; b = 5 ; c = - 3$ 
C)  $a = - 1 ; b = 5 ; c = - 3$ 
D)  $a = - 1 ; b = - 3 ; c = 5$ 
A)  $a = 1 ; b = - 3 ; c = 5$ 
B)  $a = 1 ; b = 5 ; c = - 3$ 
C)  $a = - 1 ; b = 5 ; c = - 3$ 
D)  $a = - 1 ; b = - 3 ; c = 5$

Question 10

Solve the problem.
-The Paperback Trader is a book store that takes in used paperbacks for 20% of their cover price and sells them for 50% of their cover price. Pat brings in a stack of 17 paperback books to trade and gets $17.17 credit. Some of the books had a cover price of $6.99, the rest $3.99. She wants to get some Tom Clancy books having a cover price of $6.99. How many $6.99 books did she bring in and how many Clancy books can she get without paying any additional cash?

Accepted Answer

A) 6 $6.99 books, 5 Clancy books 
B) 6 $6.99 books, 2 Clancy books 
C) 11 $6.99 books, 2 Clancy books 
D) 6 $6.99 books, 4 Clancy books 
A) 6 $6.99 books, 5 Clancy books 
B) 6 $6.99 books, 2 Clancy books 
C) 11 $6.99 books, 2 Clancy books 
D) 6 $6.99 books, 4 Clancy books

Question 11

Graph the inequality.
-$$x + 5 y \geq 6$$

Accepted Answer

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

Question 12

Graph the system of inequalities.
-$\begin{array}{c}
2 x+3 y \leq 6 \
x-y \geq 3 \
x \geq 1
\end{array}$

Accepted Answer

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

Question 13

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

Accepted Answer

A)  $( 2,1 ) , ( - 2 , - 1 )$ 
B)  $( - 1,2 ) , ( 1 , - 2 )$ 
C)  $( 1,2 ) , ( - 1,2 ) , ( 1 , - 2 ) , ( - 1 , - 2 )$ 
D)  $( 2,1 ) , ( 2 , - 1 ) , ( - 2,1 ) , ( - 2 , - 1 )$ 
A)  $( 2,1 ) , ( - 2 , - 1 )$ 
B)  $( - 1,2 ) , ( 1 , - 2 )$ 
C)  $( 1,2 ) , ( - 1,2 ) , ( 1 , - 2 ) , ( - 1 , - 2 )$ 
D)  $( 2,1 ) , ( 2 , - 1 ) , ( - 2,1 ) , ( - 2 , - 1 )$

Question 14

Graph the inequality.
-

Accepted Answer

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

Question 15

Use the substitution method or the elimination method to solve the system. If the system has infinitely many solutions, express the ordered pair in terms of x or y.
-x + 9y = 9 
5x - 6y = -6

Accepted Answer

A) (1, 1) 
B) (0, 0) 
C) (1, 0) 
D) (0, 1) 
A) (1, 1) 
B) (0, 0) 
C) (1, 0) 
D) (0, 1)

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.
-$$\begin{aligned}
4 x - y + 3 z & = 12 \
x + 4 y + 6 z & = - 32 \
5 x + 3 y + 9 z & = 20
\end{aligned}$$

Accepted Answer

A) no solution 
B) (2, -7, -1) 
C) (-8, -7, 9) 
D) (8, -7, -2) 
A) no solution 
B) (2, -7, -1) 
C) (-8, -7, 9) 
D) (8, -7, -2)

Question 17

Solve the problem.
-Three shrimp boats supply the shrimp wholesalers on Hilton Head with fresh catch. The Annabelle takes 50% of its catch to Hudson's, 20% to Captain J's, and 30% to Mainstreet. The Curly Q takes 40% of its catch to Hudson's, 40% to Captain J's, and 20% to Mainstreet. The SloJoe takes 30% of its catch to Hudson's, 40% to Captain J's, and 30% to Mainstreet. One week Hudson's received 228.7 pounds of shrimp, Captain J's received 201.8 pounds, and Mainstreet received 151.5 pounds. How many pounds of shrimp did each boat catch?

Accepted Answer

A) Annabelle 196 lbs, Curly Q 231 lbs, SloJoe 155 lbs 
B) Annabelle 196 lbs, Curly Q 155 lbs, SloJoe 231 lbs 
C) Annabelle 231 lbs, Curly Q 196 lbs, SloJoe 155 lbs 
D) Annabelle 155 lbs, Curly Q 231 lbs, SloJoe 196 lbs 
A) Annabelle 196 lbs, Curly Q 231 lbs, SloJoe 155 lbs 
B) Annabelle 196 lbs, Curly Q 155 lbs, SloJoe 231 lbs 
C) Annabelle 231 lbs, Curly Q 196 lbs, SloJoe 155 lbs 
D) Annabelle 155 lbs, Curly Q 231 lbs, SloJoe 196 lbs

Question 18

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

Accepted Answer

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

Question 19

A system of nonlinear equations is given. Sketch the graph of the equation of the system and then determine the number of real solutions to the system. Do not solve the system.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 25 \
x y = 1
\end{array}$$

Accepted Answer

A)  Two
  
B)  $\mathrm { Two }$
  
C)  Four
  
D)  Four
  
A)  Two
  
B)  $\mathrm { Two }$
  
C)  Four
  
D)  Four

Question 20

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
x ^ { 2 } - y ^ { 2 } = 39 \
x - y = 3
\end{array}$$
$x - y = 3$

Accepted Answer

A)  $( - 8,5 )$ 
B)  $( - 8 , - 5 )$ 
C)  $( 8,5 )$ 
D)  $( 8 , - 5 )$ 
A)  $( - 8,5 )$ 
B)  $( - 8 , - 5 )$ 
C)  $( 8,5 )$ 
D)  $( 8 , - 5 )$

Determine the real solutions to the system of nonlinear equations. - +=116 -=84

Graph the inequality. - $x + y < - 6$

Determine whether the system corresponding to the given augmented matrix is dependent or inconsistent. If it is dependent, give the solution. - $\left[ \begin{array} { r r r | r } 1 & 0 & 0 & - 8 \\0 & 1 & 0 & 4 \\0 & 0 & 0 & - 9\end{array} \right]$

Graph the system of inequalities. - 3x+y>6 3x+y<1 $Graph the system of inequalities. - \begin{array}{l} 3 x+y>6 \\ 3 x+y<1 \end{array}$

Write the partial fraction decomposition of the rational expression. - $\frac { x } { ( x - 4 ) ( x - 5 ) }$

Determine if the given ordered triple is a solution of the system. - (-5,-1,5) 3x+2y+z=8 2x-3y-z=18 4x+y+5z=-6

Solve the problem. -Find the values of $a$ , $b$ , and $c$ such that the graph of the quadratic equation $y = a x ^ { 2 } + b x + c$ passes through the points $( - 3,5 ) , ( 1,1 )$ , and $( 2 , - 5 )$ .

Graph the inequality. - $x + 5 y \geq 6$ $Graph the inequality. - x + 5 y \geq 6$

Graph the system of inequalities. - 2x+3y\leq6 x-y\geq3 x\geq1 $Graph the system of inequalities. - \begin{array}{c} 2 x+3 y \leq 6 \\ x-y \geq 3 \\ x \geq 1 \end{array}$

Determine the real solutions to the system of nonlinear equations. - -2=2 3+2=14

Graph the inequality. -

Use the substitution method or the elimination method to solve the system. If the system has infinitely many solutions, express the ordered pair in terms of x or y. -x + 9y = 9 5x - 6y = -6

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. - 4x-y+3z =12 x+4y+6z =-32 5x+3y+9z =20

Determine the real solutions to the system of nonlinear equations. - 4+=16 4-=16

Determine the real solutions to the system of nonlinear equations. - -=39 x-y=3 $x - y = 3$

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

Determine the real solutions to the system of nonlinear equations. - +=116 -=84

Graph the inequality. - x+y<−6x + y < - 6x+y<−6

Graph the system of inequalities. - 3x+y>6 3x+y<1

Write the partial fraction decomposition of the rational expression. - x(x−4)(x−5)\frac { x } { ( x - 4 ) ( x - 5 ) }(x−4)(x−5)x​

Determine if the given ordered triple is a solution of the system. - (-5,-1,5) 3x+2y+z=8 2x-3y-z=18 4x+y+5z=-6

Solve the problem. -Find the values of aaa , bbb , and ccc such that the graph of the quadratic equation y=ax2+bx+cy = a x ^ { 2 } + b x + cy=ax2+bx+c passes through the points (−3,5),(1,1)( - 3,5 ) , ( 1,1 )(−3,5),(1,1) , and (2,−5)( 2 , - 5 )(2,−5) .

Graph the inequality. - x+5y≥6x + 5 y \geq 6x+5y≥6

Graph the system of inequalities. - 2x+3y\leq6 x-y\geq3 x\geq1

Determine the real solutions to the system of nonlinear equations. - -2=2 3+2=14

Graph the inequality. -

Use the substitution method or the elimination method to solve the system. If the system has infinitely many solutions, express the ordered pair in terms of x or y. -x + 9y = 9 5x - 6y = -6

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. - 4x-y+3z =12 x+4y+6z =-32 5x+3y+9z =20

Determine the real solutions to the system of nonlinear equations. - 4+=16 4-=16

A system of nonlinear equations is given. Sketch the graph of the equation of the system and then determine the number of real solutions to the system. Do not solve the system. - +=25 xy=1

Determine the real solutions to the system of nonlinear equations. - -=39 x-y=3 x−y=3x - y = 3x−y=3

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

Graph the inequality. - $x + y < - 6$

Graph the system of inequalities. - 3x+y>6 3x+y<1 $Graph the system of inequalities. - \begin{array}{l} 3 x+y>6 \\ 3 x+y<1 \end{array}$

Write the partial fraction decomposition of the rational expression. - $\frac { x } { ( x - 4 ) ( x - 5 ) }$

Solve the problem. -Find the values of $a$ , $b$ , and $c$ such that the graph of the quadratic equation $y = a x ^ { 2 } + b x + c$ passes through the points $( - 3,5 ) , ( 1,1 )$ , and $( 2 , - 5 )$ .

Graph the inequality. - $x + 5 y \geq 6$ $Graph the inequality. - x + 5 y \geq 6$

Graph the system of inequalities. - 2x+3y\leq6 x-y\geq3 x\geq1 $Graph the system of inequalities. - \begin{array}{c} 2 x+3 y \leq 6 \\ x-y \geq 3 \\ x \geq 1 \end{array}$

Determine the real solutions to the system of nonlinear equations. - -=39 x-y=3 $x - y = 3$