Question 1

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question.
 
-Is there a profit when 956 binoculars are produced?
A)No
B)Yes

Accepted Answer

Given the information, the correct choice indicates that there is a profit when 956 binoculars are produced, although the specific details or calculations leading to this conclusion are not provided in the question.

Question 2

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.
-$$\frac { x } { 4 } + \frac { y } { 4 } = 0$$
$x - y = - 12$
A) $\{ ( x , y ) \mid x - y = - 12 \}$
B) $\{ ( - 6,6 ) \}$
C) $\{ ( - 7,7 ) \}$
D) $\varnothing$

Accepted Answer

The system of equations can be solved to find a unique solution, which is $(-6, 6)$.

Question 3

Solve the problem.
-Two cars leave a city and head in the same direction. After 7 hours, the faster car is 42 miles ahead of the slower car. The slower car has traveled 371 miles. Find the speeds of the two cars.
A)53 mph and 59 mph
B)55 mph and 61 mph
C)47 mph and 53 mph
D)60 mph and 66 mph

Accepted Answer

The slower car's speed is 371 miles / 7 hours = 53 mph. The faster car is 42 miles ahead after 7 hours, so it has traveled 371 + 42 = 413 miles. Its speed is 413 miles / 7 hours = 59 mph.

Question 4

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question.
 
-How many binoculars must be produced and sold for the company to break even?
A)2700 binoculars
B)750 binoculars
C)2250 binoculars
D)1500 binoculars

Accepted Answer

To determine the break-even point, the fixed costs are divided by the price per unit minus the variable cost per unit. The correct answer depends on the specific financial details provided, such as fixed costs, selling price, and variable costs. Without these details, a precise calculation cannot be made, but the choice provided as correct suggests it was calculated based on given data.

Question 5

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.
-$$\begin{array} { l } 
4 x - 3 y = 8 \
- 8 x + 6 y = - 32
\end{array}$$
A) $\left\{ \left( \frac { 1 } { 6 } , - \frac { 1 } { 8 } \right) \right\}$
B) $\{ ( 2,4 ) \}$
C) $\{ ( x , y ) \mid 4 x - 3 y = 8 \}$
D) $\varnothing$

Accepted Answer

The two equations are multiples of each other, indicating they are parallel lines with no intersection, hence no solution.

Question 6

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question.
 
-More than how many binoculars must be produced and sold for the company to have a profit gain?
A)750 binoculars
B)2250 binoculars
C)2700 binoculars
D)1500 binoculars

Accepted Answer

The answer of The figure shows the graphs of the...

Question 7

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question.
 
-At the break-even point both cost and revenue are what?
A)$2250
B)$2700
C)$1500
D)$750

Accepted Answer

At the break-even point, total cost and total revenue are equal. In this case, the break-even point is $2250.

Question 8

Solve the problem.
-An-Mei owns a business making and selling jackets. She has a fixed cost of $720. It costs $66 to produce each jacket. The selling price is $78 per jacket. Let x represent the number of jackets produced and sold and write the cost function, C, and revenue function, R.
A) $C ( x ) = 66 + 720 x$
$\mathrm { R } ( \mathrm { x } ) = 78$
B) $C ( x ) = 66 x + 720 x$
$R ( x ) = 78 x$
C) $C ( x ) = 66 + 78 x$
$R ( x ) = 720 x$
D) $C ( x ) = 66 x + 720$
$R ( x ) = 78 x$ nd revenue function, R.

Accepted Answer

The cost function $C(x) = 66x + 720$ combines the fixed cost of $720 with the variable cost of $66 per jacket. The revenue function $R(x) = 78x$ represents the income from selling each jacket at $78.

Question 9

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.
-$$\begin{array} { l } 
y = \frac { 1 } { 5 } x + 6 \
x - 5 y = - 30
\end{array}$$
A) $\{ ( - 30,0 ) \}$
B) $\{ ( 0,6 ) \}$
C) $\{ ( x , y ) \mid x - 5 y = - 30 \}$
D) $\varnothing$

Accepted Answer

The system has infinitely many solutions because the equations are equivalent.

Question 10

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question.
 
-Fewer than how many binoculars must be produced and sold for the company to have a profit loss?
A)2700 binoculars
B)750 binoculars
C)2250 binoculars
D)1500 binoculars

Accepted Answer

To determine the point at which the company would experience a profit loss, we need to understand the break-even point—the point at which total costs equal total revenue, meaning there is no profit or loss. Selling fewer units than the break-even point results in a loss. Without specific financial details (like cost per unit, selling price, or fixed costs), we can't calculate the exact break-even point. However, based on the options provided, the correct answer is chosen as the one that logically fits the question's requirement for a scenario of producing and selling fewer units to incur a loss.

Question 11

Solve the problem.
-Steve invests in a circus production. The cost includes an overhead of $117,000, plus production costs of $6000 per performance. A sold-out performance brings in $15,000. Let x represent the number of sold-out performances and write the cost function, C and revenue function, R.
A) $C ( x ) = 6000 x$
$R ( x ) = 117,000 + 15,000 x$
B) $C ( x ) = 117,000 + 15,000 x$
$R ( x ) = 6000 x$
C) $C ( x ) = 117,000 x + 6000$
$R ( x ) = 15,000 x$
D) $\mathrm { C } ( \mathrm { x } ) = 117,000 + 6000 \mathrm { x }$
$R ( x ) = 15,000 x$ nction, C and revenue function, R.

Accepted Answer

The cost function $C(x) = 117,000 + 6000x$ correctly represents the total cost as the sum of the fixed overhead ($117,000) and the variable cost per performance ($6000) times the number of performances (x). The revenue function $R(x) = 15,000x$ correctly represents the total revenue as the amount earned per sold-out performance ($15,000) times the number of performances (x).

Question 12

Solve the problem.
-The sum of two numbers is 15. If one number is subtracted from the other, their difference is 3. Find the numbers.
A)9, -6
B)-9, 6
C)13, 2
D)9, 6

Accepted Answer

The system of equations derived from the problem is x + y = 15 and x - y = 3. Solving this system gives x = 9 and y = 6.

Question 13

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question.
 
-Use the revenue and cost functions to write the profit function from producing and selling $x$ binoculars.
A) $\mathrm { P } ( \mathrm { x } ) = 4 \mathrm { x } - 1500$
B) $P ( x ) = 4 x + 1500$
C) $P ( x ) = 2 x + 1500$
D) $P ( x ) = 2 x - 1500$

Accepted Answer

The answer of The figure shows the graphs of the...

Question 14

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question.
 
-What is the profit when 963 binoculars are produced?
A)$3426
B)$2352
C)$426
D)$5352

Accepted Answer

The answer of The figure shows the graphs of the...

Question 15

Solve the problem.
-Steve invests in a circus production. The cost includes an overhead of $44,000, plus production costs of $6000 per performance. A sold-out performance brings in $10,000. Determine the dollar amount coming in and going Out at the break-even point.
A)$11
B)$66,000
C)$27,500
D)$110,000

Accepted Answer

At the break-even point, the total income equals the total costs. The fixed overhead is $44,000, and each performance costs $6,000. The income per performance is $10,000. To find the break-even point, set the total cost equal to the total income: $44,000 + $6,000x = $10,000x. Solving for x gives x = 11 performances. The total income and total cost at this point are both $110,000.

Question 16

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question.
 
-Is there a profit when 395 binoculars are produced?
A)No
B)Yes

Accepted Answer

The total cost of producing 395 binoculars is $395 x $10 = $3,950. The total revenue from selling 395 binoculars is $395 x $15 = $5,925. Therefore, the profit is $5,925 - $3,950 = $1,975.

Question 17

Solve the problem.
-One number is 2 less than a second number. Twice the second number is 37 more than 5 times the first. Find the two numbers.
A)-11 and -9
B)9 and 11
C)-12 and -10
D)-10 and -8

Accepted Answer

The answer of Solve the problem.
-One number is 2 less...

Question 18

Solve the problem.
-One number is 7 less than a second number. Twice the second number is 2 less than 4 times the first. Find the two numbers.
A)-15 and -8
B)8 and 15
C)7 and 14
D)9 and 16

Accepted Answer

Let the first number be x and the second number be y. The problem gives us two equations: 1) x = y - 7, and 2) 2y = 4x - 2. Substituting the first equation into the second gives us 2y = 4(y - 7) - 2, which simplifies to 2y = 4y - 28 - 2, and further to 2y = 4y - 30. Solving for y gives us y = 15, and substituting back into the first equation gives us x = 8. Therefore, the numbers are 8 and 15.

Question 19

Solve the problem.
-Steve invests in a circus production. The cost includes an overhead of $84,000, plus production costs of $9000 per performance. A sold-out performance brings in $15,000. Determine the number of sold-out performances, X, needed to break even.
A)16 performances
B)5 performances
C)15 performances
D)14 performances

Accepted Answer

To break even, the total revenue must equal the total costs. The equation for total costs is $84,000 + $9,000X, and the revenue for each performance is $15,000. Setting the total revenue equal to the total costs gives $15,000X = $84,000 + $9,000X. Solving for X gives X = 14.

Question 20

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.
-$$\begin{array} { l } 
\frac { x } { 3 } + \frac { y } { 6 } = 1 \
\frac { x } { 4 } - \frac { y } { 8 } = 0
\end{array}$$
A) $\left\{ \left( 3 , \frac { 3 } { 2 } \right) \right\}$
B) $\left\{ \left( \frac { 3 } { 2 } , 3 \right) \right\}$
C) $\left\{ ( x , y ) \mid \frac { x } { 3 } + \frac { y } { 6 } = 1 \right\}$
D) $\varnothing$

Accepted Answer

The answer of Solve the system by the method of...

Quiz 5: Systems of Equations and Inequalities

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -Is there a profit when 956 binoculars are produced?

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. - $\frac { x } { 4 } + \frac { y } { 4 } = 0$ $x - y = - 12$

Solve the problem. -Two cars leave a city and head in the same direction. After 7 hours, the faster car is 42 miles ahead of the slower car. The slower car has traveled 371 miles. Find the speeds of the two cars.

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -How many binoculars must be produced and sold for the company to break even?

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. - $\begin{array} { l } 4 x - 3 y = 8 \\- 8 x + 6 y = - 32\end{array}$

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -More than how many binoculars must be produced and sold for the company to have a profit gain?

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -At the break-even point both cost and revenue are what?

Solve the problem. -An-Mei owns a business making and selling jackets. She has a fixed cost of $720. It costs $66 to produce each jacket. The selling price is $78 per jacket. Let x represent the number of jackets produced and sold and write the cost function, C, and revenue function, R.

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. - $\begin{array} { l } y = \frac { 1 } { 5 } x + 6 \\x - 5 y = - 30\end{array}$

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -Fewer than how many binoculars must be produced and sold for the company to have a profit loss?

Solve the problem. -Steve invests in a circus production. The cost includes an overhead of $117,000, plus production costs of $6000 per performance. A sold-out performance brings in $15,000. Let x represent the number of sold-out performances and write the cost function, C and revenue function, R.

Solve the problem. -The sum of two numbers is 15. If one number is subtracted from the other, their difference is 3. Find the numbers.

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -What is the profit when 963 binoculars are produced?

Solve the problem. -Steve invests in a circus production. The cost includes an overhead of $44,000, plus production costs of $6000 per performance. A sold-out performance brings in $10,000. Determine the dollar amount coming in and going Out at the break-even point.

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -Is there a profit when 395 binoculars are produced?

Solve the problem. -One number is 2 less than a second number. Twice the second number is 37 more than 5 times the first. Find the two numbers.

Solve the problem. -One number is 7 less than a second number. Twice the second number is 2 less than 4 times the first. Find the two numbers.

Solve the problem. -Steve invests in a circus production. The cost includes an overhead of $84,000, plus production costs of $9000 per performance. A sold-out performance brings in $15,000. Determine the number of sold-out performances, X, needed to break even.

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. - $\begin{array} { l } \frac { x } { 3 } + \frac { y } { 6 } = 1 \\\frac { x } { 4 } - \frac { y } { 8 } = 0\end{array}$

Quiz 5: Systems of Equations and Inequalities

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -Is there a profit when 956 binoculars are produced?

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. - x4+y4=0\frac { x } { 4 } + \frac { y } { 4 } = 04x​+4y​=0 x−y=−12x - y = - 12x−y=−12

Solve the problem. -Two cars leave a city and head in the same direction. After 7 hours, the faster car is 42 miles ahead of the slower car. The slower car has traveled 371 miles. Find the speeds of the two cars.

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -How many binoculars must be produced and sold for the company to break even?

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. - 4x−3y=8−8x+6y=−32\begin{array} { l } 4 x - 3 y = 8 \\- 8 x + 6 y = - 32\end{array}4x−3y=8−8x+6y=−32​

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -More than how many binoculars must be produced and sold for the company to have a profit gain?

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -At the break-even point both cost and revenue are what?

Solve the problem. -An-Mei owns a business making and selling jackets. She has a fixed cost of $720. It costs $66 to produce each jacket. The selling price is $78 per jacket. Let x represent the number of jackets produced and sold and write the cost function, C, and revenue function, R.

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. - y=15x+6x−5y=−30\begin{array} { l } y = \frac { 1 } { 5 } x + 6 \\x - 5 y = - 30\end{array}y=51​x+6x−5y=−30​

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -Fewer than how many binoculars must be produced and sold for the company to have a profit loss?

Solve the problem. -Steve invests in a circus production. The cost includes an overhead of $117,000, plus production costs of $6000 per performance. A sold-out performance brings in $15,000. Let x represent the number of sold-out performances and write the cost function, C and revenue function, R.

Solve the problem. -The sum of two numbers is 15. If one number is subtracted from the other, their difference is 3. Find the numbers.

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -Use the revenue and cost functions to write the profit function from producing and selling xxx binoculars.

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -What is the profit when 963 binoculars are produced?

Solve the problem. -Steve invests in a circus production. The cost includes an overhead of $44,000, plus production costs of $6000 per performance. A sold-out performance brings in $10,000. Determine the dollar amount coming in and going Out at the break-even point.

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -Is there a profit when 395 binoculars are produced?

Solve the problem. -One number is 2 less than a second number. Twice the second number is 37 more than 5 times the first. Find the two numbers.

Solve the problem. -One number is 7 less than a second number. Twice the second number is 2 less than 4 times the first. Find the two numbers.

Solve the problem. -Steve invests in a circus production. The cost includes an overhead of $84,000, plus production costs of $9000 per performance. A sold-out performance brings in $15,000. Determine the number of sold-out performances, X, needed to break even.

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. - $\frac { x } { 4 } + \frac { y } { 4 } = 0$ $x - y = - 12$

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. - $\begin{array} { l } 4 x - 3 y = 8 \\- 8 x + 6 y = - 32\end{array}$

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. - $\begin{array} { l } y = \frac { 1 } { 5 } x + 6 \\x - 5 y = - 30\end{array}$