Question 1

Find the measure of angles x and y.
-(The figure is not necessarily drawn to scale.) 
A) $x = 61 ^ { \circ } ; y = 84 ^ { \circ }$
B) $x = 82 ^ { \circ } ; y = 86 ^ { \circ }$
C) $x = 84 ^ { \circ } ; y = 61 ^ { \circ }$
D) $x = 86 ^ { \circ } ; y = 82 ^ { \circ }$

Accepted Answer

The answer of Find the measure of angles x and...

Question 2

Solve the problem.
-Nail polish remover is essentially a mixture of water and a chemical called acetone. How much pure acetone must be combined with a solution that is 28% acetone to make 24 oz of a 58% solution?
A) 14 oz
B) 12 oz
C) 10 oz
D) 17 oz

Accepted Answer

The answer of Solve the problem.
-Nail polish remover is essentially...

Question 3

Solve the problem.
-Find $C$ and $D$ so that the solution set to the system is $\{ ( - 4,2 ) \}$.
$$\begin{array} { l } 
C x - 2 y = - 16 \
2 x + D y = - 16
\end{array}$$
A) $C = - 4 ; \mathrm { D } = - 3$
B) $C = 3 ; \mathrm { D } = - 4$
C) $C = - 3 ; \mathrm { D } = 4$
D) $C = - 4 ; \mathrm { D } = 3$

Accepted Answer

The answer of Solve the problem.
-Find $C$ and $D$ so...

Question 4

Solve the problem.
-Find the area of the triangle bounded by the lines $$y = x + 2 , y = - \frac { 1 } { 6 } x + 2$$ , and the x-axis.
A) 4 square units
B) 2 square units
C) 28 square units
D) 14 square units

Accepted Answer

The answer of Solve the problem.
-Find the area of the...

Question 5

Solve the problem.
-To reach a sales meeting, Carrie traveled by plane for 2 hours and by car for an additional 2 hours. The plane travels 54 mph faster than the car. If the total distance traveled is 308 miles, what are the
Speeds of the plane and the car? (Assume that the plane and the car travel at constant rates.)
A) plane: 109 mph; car: 45 mph
B) plane: 104 mph; car: 50 mph
C) plane: 99 mph; car: 55 mph
D) plane: 94 mph; car: 40 mph

Accepted Answer

The answer of Solve the problem.
-To reach a sales meeting,...

Question 6

Determine if the ordered triple is a solution to the system of equations.
-$$\begin{array} { l } 
- 4 x + 8 y + 2 z = - 40 \
- 9 x + 8 y + 8 z = - 27 ; ( - 4 , - 6 , - 1 ) \
- 8 x + 6 y - 8 z = 14
\end{array}$$
A) No
B) Yes

Accepted Answer

Substituting $x = -4$, $y = -6$, and $z = -1$ into each equation does not satisfy all three equations, indicating the ordered triple is not a solution to the system.

Question 7

Use the substitution $u = \frac { 1 } { x } \text { and } v = \frac { 1 } { y }$ to rewrite the equations in the system in terms of the variables u and
v. Solve the system in terms of u and v. Then back substitute to determine the solution set to the original
system in terms of x and y.
-$$\begin{array} { l } 
\frac { 2 } { x } + \frac { 1 } { y } = - 4 \
\frac { 2 } { x } - \frac { 3 } { y } = 20
\end{array}$$
A) $\{ ( 1 , - 6 ) \}$
B) $\left\{ \left( - \frac { 5 } { 2 } , 1 \right) \right\}$
C) $\left\{ \left( 1 , - \frac { 1 } { 6 } \right) \right\}$
D) $\left\{ \left( - \frac { 2 } { 5 } , 1 \right) \right\}$

Accepted Answer

The answer of Use the substitution \(u = \frac {...

Question 8

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-An equation of the form $$A x + B y + C z = D$$ (where A, B, and C are not all zero) is called a________equation in three variables.

Accepted Answer

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

Question 9

Solve the problem.
-Two angles are supplementary. The measure of one angle is 68° more than 3 times the measure of the other angle. Find the measure of each angle.
A) 62° and 118°
B) 107° and 253°
C) 28° and 152°
D) 73° and 287°

Accepted Answer

Supplementary angles add up to 180°. Let x be the measure of one angle, then the other angle is 3x + 68. Solving x + (3x + 68) = 180 gives x = 28°, so the other angle is 152°.

Question 10

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-A solution to a system of linear equations in three variables is an ordered________ that satisfies each equation in the system. Graphically, this is the point of ________of three planes.

Accepted Answer

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

Question 11

Solve the problem.
-A vendor at a carnival sells cotton candy and caramel apples for $2.00 each. The vendor is charged $60 to set up his booth. Furthermore, the vendor's average cost for each product he produces is Approximately $0.80.

a.Write a linear cost function representing the cost C(x) (in $) to produce x products.
b. Write a linear revenue function representing the revenue R(x) (in $) for selling x products.
c. Determine the number of products to be produced and sold for the vendor to break even. 
A) a. $C ( x ) = 60$
b. $R ( x ) = 1.2 x$
c. products $= 75$

B) a. $C ( x ) = 60$
b. $R ( x ) = 1.2 x$
c. products $= 50$

C) a. $C ( x ) = 0.8 x + 60$
b. $R ( x ) = 2 x$
c. products $= 75$

D) a. $C ( x ) = 0.8 x + 60$
b. $R ( x ) = 2 x$
c. products $= 50$

Accepted Answer

The cost function $C(x) = 0.8x + 60$ includes both the variable cost of $0.80 per product and the fixed cost of $60 for setting up the booth. The revenue function $R(x) = 2x$ comes from selling each product for $2.00. To find the break-even point, set $C(x) = R(x)$: $0.8x + 60 = 2x$, solving this gives $x = 50$ products.

Question 12

Solve the system by substitution.
-9x - 5y = 16 y = - 12 x + 6
A) 2023, 12823
B) { }
C) {(-4, -4)}
D) {(4, 4)}

Accepted Answer

The answer of Solve the system by substitution.
-9x - 5y...

Question 13

Solve the problem.
-Given $f ( x ) = m x + b$, find $m$ and $b$ if $f ( - 6 ) = - 7$ and $f ( - 12 ) = - 11$.
A) $m = \frac { 3 } { 2 } ; b = - 3$
B) $m = \frac { 3 } { 2 } ; b = 3$
C) $m = \frac { 2 } { 3 } ; b = 3$
D) $m = \frac { 2 } { 3 } ; b = - 3$

Accepted Answer

To find $m$ and $b$, we can use the given points $(-6, -7)$ and $(-12, -11)$ in the equation $f(x) = mx + b$. Substituting the first point gives us $-7 = m(-6) + b$, and the second point gives us $-11 = m(-12) + b$. Solving these two equations simultaneously for $m$ and $b$ yields $m = \frac{2}{3}$ and $b = -3$.

Question 14

Solve the problem.
-A helicopter flies 168 miles against the wind in 2 hours; with the wind, it can fly 252 miles in the same amount of time. Find the speed of the helicopter in still air.
A) 21 miles per hour
B) 63 miles per hour
C) 105 miles per hour
D) 84 miles per hour

Accepted Answer

The speed of the helicopter in still air is the average of its speed with and against the wind. Speed against the wind = 168 miles / 2 hours = 84 mph, speed with the wind = 252 miles / 2 hours = 126 mph. Average speed = (84 mph + 126 mph) / 2 = 105 mph.

Question 15

Solve the problem.
-The points shown in the graph represent the per capita consumption of chicken and beef in a country x years after the year 2000. Yearly Per Capita Consumption of Chicken and Beef

a. Use the given data points to write a linear function that approximates per capita consumption of Chicken C(x) (in lb) at a time x years since the year 2000.
b. Use the given data points to write a linear function that approximates per capita consumption of Beef B(x) (in lb) at a time x years since the year 2000.
c. Approximate the solution to the system of linear equations defined by the functions from parts (a)
And (b). Round to 1 decimal place. Interpret the meaning of the solution to the system.

A) a. $C ( x ) = 1.25 x + 55.5$
b. $B ( x ) = - 0.33 x + 65.6$
c. $\{ ( 6.5,63.4 ) \}$ Midyear in 2,006 , the per capita consumption of beef and chicken was approximately equal at $63.4 \mathrm { lb }$ each

B) a. $C ( x ) = 1.2 x + 55.6$;
b. $B ( x ) = - 0.34 x + 65.6$
c. $\{ ( 6.5,63.4 ) \}$ Midyear in 2,006 , the per capita consumption of beef and chicken was approximately equal at $63.4 \mathrm { lb }$ each

C) a. $C ( x ) = 1.25 x + 55.5$
b. $B ( x ) = - 0.33 x + 65.6$
c. $\{ ( 6.6,63.5 ) \}$ Midyear in 2,007 , the per capita consumption of beef and chicken was approximately equal at $63.5 \mathrm { lb }$ each

D) a. $C ( x ) = 1.2 x + 55.6$;
b. $B ( x ) = - 0.34 x + 65.6$
c. $\{ ( 6.6,63.5 ) \}$ Midyear in 2,007 , the per capita consumption of beef and chicken was approximately equal at $63.5 \mathrm { lb }$ each

Accepted Answer

The answer of Solve the problem.
-The points shown in the...

Question 16

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-A solution to a linear equation in three variables is an ordered________ (x, y, z) that satisfiesb the equation.

Accepted Answer

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

Question 17

Solve the problem.
-Abram and Fred leave opposite ends of a bike trail 8.5 miles apart and travel toward each other. Abram is traveling 3 mph faster than Fred. Find each of their speeds if they meet after 30 minutes.
A) Abram: 17 mph; Fred: 20 mph
B) Abram: 10 mph; Fred: 7 mph
C) Abram: 7 mph; Fred: 10 mph
D) Abram: 20 mph; Fred: 17 mph

Accepted Answer

Since they meet after 30 minutes (or 0.5 hours), the total distance they cover together is 8.5 miles. Let Fred's speed be $x$ mph, then Abram's speed is $x + 3$ mph. The equation based on distance = speed × time for both combined is $x(0.5) + (x + 3)(0.5) = 8.5$. Solving this equation gives $x = 7$ and $x + 3 = 10$, so Fred's speed is 7 mph and Abram's is 10 mph.

Question 18

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The graph of a linear equation in two variables is a line in a two-dimensional coordinate system.The graph of a linear equation in three variables is a________ in a three-dimensional coordinate system.

Accepted Answer

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

Question 19

Solve the problem.
-One angle measures 27° more than 2 times another. If the two angles are complementary, find the measures of the angles.
A) 26°; 64°
B) 23°; 67°
C) 21°; 69°
D) 31°; 59°

Accepted Answer

Let the smaller angle be x degrees. Then, the larger angle is 27° + 2x. Since they are complementary, their sum is 90°. So, x + 27° + 2x = 90°, leading to 3x = 63°, and x = 21°. The other angle is 69°.

Question 20

Choose the one alternative that best completes the statement or answers the question.
Find three ordered triples that are solutions to the linear equation in three variables.
-$$4 x - 4 y - 2 z = 32$$
A) $\{ ( - 4,0,0 ) , ( 0,4,0 ) , ( 0,0,2 ) \}$
B) $\{ ( 8,0,0 ) , ( 0 , - 8,0 ) , ( 0,0 , - 16 ) \}$
C) $\{ ( 4,0,0 ) , ( 0 , - 4,0 ) , ( 0,0 , - 2 ) \}$
D) $\{ ( 28,0,0 ) , ( 0,36,0 ) , ( 0,0,34 ) \}$

Accepted Answer

The answer of Choose the one alternative that best completes...

Quiz 5: Systems of Equations and Inequalities

Solve the problem. -Nail polish remover is essentially a mixture of water and a chemical called acetone. How much pure acetone must be combined with a solution that is 28% acetone to make 24 oz of a 58% solution?

Solve the problem. -Find $C$ and $D$ so that the solution set to the system is $\{ ( - 4,2 ) \}$ . $\begin{array} { l } C x - 2 y = - 16 \\2 x + D y = - 16\end{array}$

Solve the problem. -Find the area of the triangle bounded by the lines $y = x + 2 , y = - \frac { 1 } { 6 } x + 2$ , and the x-axis.

Determine if the ordered triple is a solution to the system of equations. - $\begin{array} { l } - 4 x + 8 y + 2 z = - 40 \\- 9 x + 8 y + 8 z = - 27 ; ( - 4 , - 6 , - 1 ) \\- 8 x + 6 y - 8 z = 14\end{array}$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An equation of the form $A x + B y + C z = D$ (where A, B, and C are not all zero) is called a________equation in three variables.

Solve the problem. -Two angles are supplementary. The measure of one angle is 68° more than 3 times the measure of the other angle. Find the measure of each angle.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A solution to a system of linear equations in three variables is an ordered that satisfies each equation in the system. Graphically, this is the point of of three planes.

Solve the system by substitution. -9x - 5y = 16 y = - 12 x + 6

Solve the problem. -Given $f ( x ) = m x + b$ , find $m$ and $b$ if $f ( - 6 ) = - 7$ and $f ( - 12 ) = - 11$ .

Solve the problem. -A helicopter flies 168 miles against the wind in 2 hours; with the wind, it can fly 252 miles in the same amount of time. Find the speed of the helicopter in still air.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A solution to a linear equation in three variables is an ordered________ (x, y, z) that satisfiesb the equation.

Solve the problem. -Abram and Fred leave opposite ends of a bike trail 8.5 miles apart and travel toward each other. Abram is traveling 3 mph faster than Fred. Find each of their speeds if they meet after 30 minutes.

Solve the problem. -One angle measures 27° more than 2 times another. If the two angles are complementary, find the measures of the angles.

Choose the one alternative that best completes the statement or answers the question. Find three ordered triples that are solutions to the linear equation in three variables. - $4 x - 4 y - 2 z = 32$

Quiz 5: Systems of Equations and Inequalities

Find the measure of angles x and y. -(The figure is not necessarily drawn to scale.)

Solve the problem. -Nail polish remover is essentially a mixture of water and a chemical called acetone. How much pure acetone must be combined with a solution that is 28% acetone to make 24 oz of a 58% solution?

Solve the problem. -Find CCC and DDD so that the solution set to the system is {(−4,2) }\{ ( - 4,2 ) \}{(−4,2) } . Cx−2y=−162x+Dy=−16\begin{array} { l } C x - 2 y = - 16 \\2 x + D y = - 16\end{array}Cx−2y=−162x+Dy=−16​

Solve the problem. -Find the area of the triangle bounded by the lines y=x+2,y=−16x+2y = x + 2 , y = - \frac { 1 } { 6 } x + 2y=x+2,y=−61​x+2 , and the x-axis.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An equation of the form Ax+By+Cz=DA x + B y + C z = DAx+By+Cz=D (where A, B, and C are not all zero) is called a________equation in three variables.

Solve the problem. -Two angles are supplementary. The measure of one angle is 68° more than 3 times the measure of the other angle. Find the measure of each angle.

Solve the system by substitution. -9x - 5y = 16 y = - 12 x + 6

Solve the problem. -Given f(x) =mx+bf ( x ) = m x + bf(x) =mx+b , find mmm and bbb if f(−6) =−7f ( - 6 ) = - 7f(−6) =−7 and f(−12) =−11f ( - 12 ) = - 11f(−12) =−11 .

Solve the problem. -A helicopter flies 168 miles against the wind in 2 hours; with the wind, it can fly 252 miles in the same amount of time. Find the speed of the helicopter in still air.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A solution to a linear equation in three variables is an ordered________ (x, y, z) that satisfiesb the equation.

Solve the problem. -Abram and Fred leave opposite ends of a bike trail 8.5 miles apart and travel toward each other. Abram is traveling 3 mph faster than Fred. Find each of their speeds if they meet after 30 minutes.

Solve the problem. -One angle measures 27° more than 2 times another. If the two angles are complementary, find the measures of the angles.

Choose the one alternative that best completes the statement or answers the question. Find three ordered triples that are solutions to the linear equation in three variables. - 4x−4y−2z=324 x - 4 y - 2 z = 324x−4y−2z=32

Solve the problem. -Find $C$ and $D$ so that the solution set to the system is $\{ ( - 4,2 ) \}$ . $\begin{array} { l } C x - 2 y = - 16 \\2 x + D y = - 16\end{array}$

Solve the problem. -Find the area of the triangle bounded by the lines $y = x + 2 , y = - \frac { 1 } { 6 } x + 2$ , and the x-axis.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An equation of the form $A x + B y + C z = D$ (where A, B, and C are not all zero) is called a________equation in three variables.

Solve the problem. -Given $f ( x ) = m x + b$ , find $m$ and $b$ if $f ( - 6 ) = - 7$ and $f ( - 12 ) = - 11$ .

Choose the one alternative that best completes the statement or answers the question. Find three ordered triples that are solutions to the linear equation in three variables. - $4 x - 4 y - 2 z = 32$