Question 1

Graph the inequality.
-$$x > - 2$$

Accepted Answer

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

Question 2

Determine whether the given ordered pair is a solution of the system.
-$$\begin{array} { l } 
( - 1 , - 6 ) \
2 x - y = - 8 \
3 x - 2 y = - 15
\end{array}$$

Accepted Answer

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

Question 3

Solve Problems Using Systems in Three Variables
-Three trains - one eastbound, one westbound, and one northbound - leave a city at the same time. The speed of the northbound train is 20 miles per hour greater than the speed of the eastbound train. After 3 hours, the distance between the westbound train and the eastbound train is 300 miles. Twice the speed of the westbound train is 60 miles per hour more than the speed of the northbound train. Find the speeds of the three trains.

Accepted Answer

A)  eastbound, $40 \mathrm { mph }$; westbound, $60 \mathrm { mph }$; northbound, $60 \mathrm { mph }$ 
B)  eastbound, $50 \mathrm { mph }$; westbound, $60 \mathrm { mph }$; northbound, $70 \mathrm { mph }$ 
C)  eastbound, $30 \mathrm { mph }$; westbound, $70 \mathrm { mph }$; northbound, $60 \mathrm { mph }$ 
D)  eastbound, $60 \mathrm { mph }$; westbound, $60 \mathrm { mph }$; northbound, $40 \mathrm { mph }$ 
A)  eastbound, $40 \mathrm { mph }$; westbound, $60 \mathrm { mph }$; northbound, $60 \mathrm { mph }$ 
B)  eastbound, $50 \mathrm { mph }$; westbound, $60 \mathrm { mph }$; northbound, $70 \mathrm { mph }$ 
C)  eastbound, $30 \mathrm { mph }$; westbound, $70 \mathrm { mph }$; northbound, $60 \mathrm { mph }$ 
D)  eastbound, $60 \mathrm { mph }$; westbound, $60 \mathrm { mph }$; northbound, $40 \mathrm { mph }$

Question 4

Determine whether the given ordered pair is a solution of the system.
-$$\begin{array} { l } 
( - 5 , - 5 ) \
4 x = 15 - y \
3 x = - 5 - 4 y
\end{array}$$

Accepted Answer

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

Question 5

Solve Problems Using Systems of Linear Equations
-The sum of two numbers is 9 . If one number is subtracted from the other, their difference is $- 1$. Find the numbers.

Accepted Answer

A)  4,5 
B)  $4 , - 5$ 
C)  $- 4,5$ 
D)  6,3 
A)  4,5 
B)  $4 , - 5$ 
C)  $- 4,5$ 
D)  6,3

Question 6

Solve Problems Using Systems in Three Variables
-The table shows the percentage of people living below the poverty line in one U.S. city in the years 2000 through $2003 .$
 
 The data in the table can be written as ordered pairs (x, y) where x is the number of years after 2000 and y is the percentage of people living below the poverty line in that year. Use the data for 2000, 2002, and 2003 to find the quadratic function y = ax2 + bx + c that models the percentage, y, of people in this city living below the poverty line x years after 2000. [Hint: Find a, b, and c by substituting each of three ordered pairs into the function and writing and solving a system of linear equations in three variables.]

Accepted Answer

A)  $y = - 0.3 x ^ { 2 } + 1.8 x + 9.3$ 
B)  $y = - 0.2 x ^ { 2 } + 1.6 x + 9.3$ 
C)  $y = - 0.4 x ^ { 2 } + 2 x + 9.3$ 
D)  $y = - 0.2 x ^ { 2 } + 1.5 x + 9.3$ 
A)  $y = - 0.3 x ^ { 2 } + 1.8 x + 9.3$ 
B)  $y = - 0.2 x ^ { 2 } + 1.6 x + 9.3$ 
C)  $y = - 0.4 x ^ { 2 } + 2 x + 9.3$ 
D)  $y = - 0.2 x ^ { 2 } + 1.5 x + 9.3$

Question 7

Solve Problems Using Systems of Linear Equations
-How many binoculars must be produced and sold for the company to break even?

Accepted Answer

A)  750 binoculars 
B)  2250 binoculars 
C)  1500 binoculars 
D)  2700 binoculars 
A)  750 binoculars 
B)  2250 binoculars 
C)  1500 binoculars 
D)  2700 binoculars

Question 8

Systems of Linear Equations in Three Variables
1 Verify the Solution of a System of Linear Equations in Three Variables
-$$\begin{array} { l } 
( 4 , - 3,5 ) \
x - y + z = - 4 \
x + y + z = 6 \
x + y - z = - 2
\end{array}$$

Accepted Answer

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

Question 9

Graph the solution set of the system of inequalities or indicate that the system has no solution.
-$$- 1 \leq y < 3$$

Accepted Answer

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

Question 10

Solve Problems Using Systems of Linear Equations
-Fewer than how many binoculars must be produced and sold for the company to have a profit loss?

Accepted Answer

A)  750 binoculars 
B)  2250 binoculars 
C)  1500 binoculars 
D)  2700 binoculars 
A)  750 binoculars 
B)  2250 binoculars 
C)  1500 binoculars 
D)  2700 binoculars

Question 11

Solve Nonlinear Systems By Substitution
-$$\begin{array} { l } 
x ^ { 2 } = y ^ { 2 } + 39 \
x - y = 3
\end{array}$$

Accepted Answer

A)  $\{ ( 8,5 ) \}$ 
B)  $\{ ( 8 , - 5 ) \}$ 
C)  $\{ ( - 8,5 ) \}$ 
D)  $\{ ( - 8 , - 5 ) \}$ 
A)  $\{ ( 8,5 ) \}$ 
B)  $\{ ( 8 , - 5 ) \}$ 
C)  $\{ ( - 8,5 ) \}$ 
D)  $\{ ( - 8 , - 5 ) \}$

Question 12

Solve Nonlinear Systems By Substitution
-$$\begin{array} { l } 
2 y - x = 10 \
x ^ { 2 } + y ^ { 2 } - 100 = 0
\end{array}$$

Accepted Answer

A)  $\{ ( - 10,0 ) , ( 6,8 ) \}$ 
B)  $\{ ( 10,0 ) , ( - 10,0 ) , ( 6,8 ) \}$ 
C)  $\{ ( 0,5 ) , ( 8,9 ) \}$ 
D)  $\{ ( 0,5 ) , ( 0 , - 5 ) , ( 8,9 ) \}$ 
A)  $\{ ( - 10,0 ) , ( 6,8 ) \}$ 
B)  $\{ ( 10,0 ) , ( - 10,0 ) , ( 6,8 ) \}$ 
C)  $\{ ( 0,5 ) , ( 8,9 ) \}$ 
D)  $\{ ( 0,5 ) , ( 0 , - 5 ) , ( 8,9 ) \}$

Question 13

Use Linear Programming to Solve Problems
-An office manager is buying used filing cabinets. Each small file cabinet costs $\$ 5$, takes up 7 square feet of floor space, and holds 8 cubic feet of files. Each large file cabinet costs $\$ 10$, takes up 9 square feet of floor space, and holds 14 cubic feet of files. The total cost cannot exceed $\$ 90$, and the office has no more than 101 square feet of floor space available for the cabinets. How many of each file cabinet should the manager buy to maximize storage capacity? What is the maximum storage capacity?

Accepted Answer

A)  8 small file cabinets and 5 large file cabinets; 134 cubic feet 
B)  5 small file cabinets and 8 large file cabinets; 176 cubic feet 
C)  0 small file cabinets and 13 large file cabinets; 182 cubic feet 
D)  13 small file cabinets and 0 large file cabinets; 104 cubic feet 
A)  8 small file cabinets and 5 large file cabinets; 134 cubic feet 
B)  5 small file cabinets and 8 large file cabinets; 176 cubic feet 
C)  0 small file cabinets and 13 large file cabinets; 182 cubic feet 
D)  13 small file cabinets and 0 large file cabinets; 104 cubic feet

Question 14

Use Linear Programming to Solve Problems
-Objective Function: $z = 9 x + 10 y$
Find minimum.

Accepted Answer

A)  minimum: 56 
B)  minimum: 57 
C)  minimum: 68 
D)  no minimum 
A)  minimum: 56 
B)  minimum: 57 
C)  minimum: 68 
D)  no minimum

Question 15

Graph a Nonlinear Inequality in Two Variables
-$y>x^{2}-7$

Accepted Answer

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

Question 16

Solve Problems Using Systems of Nonlinear Equations
-The diagonal of the floor of a rectangular office cubicle is $2 \mathrm { ft }$ longer than the length of the cubicle and $5 \mathrm { ft }$ longer than twice the width. Find the dimensions of the cubicle. Round to the nearest tenth, if necessary.

Accepted Answer

A)  width $= 9.7 \mathrm { ft }$, length $= 22.4 \mathrm { ft }$ 
B)  width $= 4 \mathrm { ft }$, length $= 11 \mathrm { ft }$ 
C)  width $= 2 \mathrm { ft }$, length $= 9 \mathrm { ft }$ 
D)  width $= 3.9 \mathrm { ft }$, length $= 9.7 \mathrm { ft }$ 
A)  width $= 9.7 \mathrm { ft }$, length $= 22.4 \mathrm { ft }$ 
B)  width $= 4 \mathrm { ft }$, length $= 11 \mathrm { ft }$ 
C)  width $= 2 \mathrm { ft }$, length $= 9 \mathrm { ft }$ 
D)  width $= 3.9 \mathrm { ft }$, length $= 9.7 \mathrm { ft }$

Question 17

Solve Problems Using Systems of Linear Equations
-What is the profit when 964 binoculars are produced?

Accepted Answer

A)  $\$ 428$ 
B)  $\$ 3428$ 
C)  $\$ 2356$ 
D)  $\$ 5356$ 
A)  $\$ 428$ 
B)  $\$ 3428$ 
C)  $\$ 2356$ 
D)  $\$ 5356$

Question 18

Solve Problems Using Systems in Three Variables
-Ron attends a cocktail party (with his graphing calculator in his pocket). He wants to limit his food intake to 127 g protein, 110 g fat, and 147 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)  6 mushrooms; 5 meatballs; 3 eggs 
B)  5 mushrooms; 3 meatballs; 6 eggs 
C)  3 mushrooms; 6 meatballs; 5 eggs 
D)  7 mushrooms; 6 meatballs; 4 eggs 
A)  6 mushrooms; 5 meatballs; 3 eggs 
B)  5 mushrooms; 3 meatballs; 6 eggs 
C)  3 mushrooms; 6 meatballs; 5 eggs 
D)  7 mushrooms; 6 meatballs; 4 eggs

Question 19

Solve Problems Using Systems of Nonlinear Equations
-A system for tracking ships indicated that a ship lies on a hyperbolic path described by $6 \mathrm { x } ^ { 2 } - \mathrm { y } ^ { 2 } = 18$. The process is repeated and the ship is found to lie on a hyperbolic path described by $y ^ { 2 } - 3 x ^ { 2 } = 9$. If it is known that the ship is located in the first quadrant of the coordinate system, determine its exact location.

Accepted Answer

A)  $( 3,6 )$ 
B)  $( - 3 , - 6 )$ 
C)  $( 6,3 )$ 
D)  $( - 6 , - 3 )$ 
A)  $( 3,6 )$ 
B)  $( - 3 , - 6 )$ 
C)  $( 6,3 )$ 
D)  $( - 6 , - 3 )$

Question 20

Solve Problems Using Systems of Linear Equations
-In 1985, in the town of Appleby, $20.3 \%$ of Hispanics were overweight, increasing by an average of $0.43 \%$ per year. In 1985, in the town of Appleby, $0.18 \%$ of whites were overweight, increasing by an average of $31.6 \%$ per year. If these trends continue, in which year will the percentage of Hispanics who are overweight be the same as the percentage of whites who are overweight? Round to the nearest year. What percentage of Hispanics (to the nearest whole percent) will be overweight at that time?

Accepted Answer

A)  $1986 ; 21 \%$ 
B)  $1988 ; 21 \%$ 
C)  $1984 ; 20 \%$ 
D)  $1982 ; 19 \%$ 
A)  $1986 ; 21 \%$ 
B)  $1988 ; 21 \%$ 
C)  $1984 ; 20 \%$ 
D)  $1982 ; 19 \%$

Graph the inequality. - $x > - 2$

Determine whether the given ordered pair is a solution of the system. - (-1,-6) 2x-y=-8 3x-2y=-15

Determine whether the given ordered pair is a solution of the system. - (-5,-5) 4x=15-y 3x=-5-4y

Solve Problems Using Systems of Linear Equations -The sum of two numbers is 9 . If one number is subtracted from the other, their difference is $- 1$ . Find the numbers.

Solve Problems Using Systems of Linear Equations -How many binoculars must be produced and sold for the company to break even?

Systems of Linear Equations in Three Variables 1 Verify the Solution of a System of Linear Equations in Three Variables - (4,-3,5) x-y+z=-4 x+y+z=6 x+y-z=-2

Graph the solution set of the system of inequalities or indicate that the system has no solution. - $- 1 \leq y < 3$ $Graph the solution set of the system of inequalities or indicate that the system has no solution. - - 1 \leq y < 3$

Solve Problems Using Systems of Linear Equations -Fewer than how many binoculars must be produced and sold for the company to have a profit loss?

Solve Nonlinear Systems By Substitution - =+39 x-y=3

Solve Nonlinear Systems By Substitution - 2y-x=10 +-100=0

Use Linear Programming to Solve Problems -Objective Function: $z = 9 x + 10 y$ Find minimum.

Graph a Nonlinear Inequality in Two Variables - $y>x^{2}-7$ $Graph a Nonlinear Inequality in Two Variables - y>x^{2}-7$

Solve Problems Using Systems of Nonlinear Equations -The diagonal of the floor of a rectangular office cubicle is $2 \mathrm { ft }$ longer than the length of the cubicle and $5 \mathrm { ft }$ longer than twice the width. Find the dimensions of the cubicle. Round to the nearest tenth, if necessary.

Solve Problems Using Systems of Linear Equations -What is the profit when 964 binoculars are produced?

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Matrices and Determinants

Conic Sections and Analytic Geometry

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Exam 8: Systems of Equations and Inequalities

Graph the inequality. - x>−2x > - 2x>−2

Determine whether the given ordered pair is a solution of the system. - (-1,-6) 2x-y=-8 3x-2y=-15

Determine whether the given ordered pair is a solution of the system. - (-5,-5) 4x=15-y 3x=-5-4y

Solve Problems Using Systems of Linear Equations -The sum of two numbers is 9 . If one number is subtracted from the other, their difference is −1- 1−1 . Find the numbers.

Solve Problems Using Systems of Linear Equations -How many binoculars must be produced and sold for the company to break even?

Systems of Linear Equations in Three Variables 1 Verify the Solution of a System of Linear Equations in Three Variables - (4,-3,5) x-y+z=-4 x+y+z=6 x+y-z=-2

Graph the solution set of the system of inequalities or indicate that the system has no solution. - −1≤y<3- 1 \leq y < 3−1≤y<3

Solve Problems Using Systems of Linear Equations -Fewer than how many binoculars must be produced and sold for the company to have a profit loss?

Solve Nonlinear Systems By Substitution - =+39 x-y=3

Solve Nonlinear Systems By Substitution - 2y-x=10 +-100=0

Use Linear Programming to Solve Problems -Objective Function: z=9x+10yz = 9 x + 10 yz=9x+10y Find minimum.

Graph a Nonlinear Inequality in Two Variables - y>x2−7y>x^{2}-7y>x2−7

Solve Problems Using Systems of Linear Equations -What is the profit when 964 binoculars are produced?

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Matrices and Determinants

Conic Sections and Analytic Geometry

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Graph the inequality. - $x > - 2$

Solve Problems Using Systems of Linear Equations -The sum of two numbers is 9 . If one number is subtracted from the other, their difference is $- 1$ . Find the numbers.

Graph the solution set of the system of inequalities or indicate that the system has no solution. - $- 1 \leq y < 3$ $Graph the solution set of the system of inequalities or indicate that the system has no solution. - - 1 \leq y < 3$

Use Linear Programming to Solve Problems -Objective Function: $z = 9 x + 10 y$ Find minimum.

Graph a Nonlinear Inequality in Two Variables - $y>x^{2}-7$ $Graph a Nonlinear Inequality in Two Variables - y>x^{2}-7$