Title: Final Exam
Course: Technical Math for Industry

Q: Evaluate the expression for .
- 20 (Incorrect. For , the quantity can be written as , or Does this help you think about the problem?)
- 40 (Correct. When you evaluate for you get 40.)
- 8 (Incorrect. For , the quantity can be written as , or Does this help you think about the problem?)
- 12 (Incorrect. For , the quantity can be written as , or Does this help you think about the problem?)
A: 40

Q: In which of the following equations is the Distributive Property correctly applied to the equation ?
A: (a choice with no text)
If wrong: Incorrect. When applying the Distributive Property, multiplication occurs with only the terms inside the parenthesis, not the other parts of the equation.
If right: Correct. All of the terms inside the parentheses, (7x + 5), have been multiplied by the value 3.
If wrong: Incorrect. When applying the Distributive Property, all of the terms inside the parentheses must be multiplied by the value outside. Here, you have multiplied but not .
If wrong: Incorrect. When applying the Distributive Property, multiplication occurs with only the terms inside the parenthesis, not the other parts of the equation. Here, you multiplied , but not .

Q: Which of the following number lines show the correct solution to the equation ?
A: (a choice with no text)
If right: Correct. When x equals -10 or 10, this is a true statement.
If wrong: Incorrect. is the same as -40, so you can rewrite this as . Now solve for x.
If wrong: Incorrect. is the same as -40, so you can rewrite this as . Now solve for x.
If wrong: Incorrect. is the same as -40, so you can rewrite this as . Now solve for x.

Q: Rewrite the formula for the area of a trapezoid to solve for the length of .
A: (a choice with no text)
If wrong: Incorrect. To solve for , begin by dividing both sides by h. What new expression does that create? How can you isolate from here?
If right: Correct. Dividing both sides by h, then multiplying by 2, and then subtracting will isolate on one side of the equation.
If wrong: Incorrect. To solve for , begin by dividing both sides by h. What new expression does that create? How can you isolate from here?
If wrong: Incorrect. To solve for , begin by dividing both sides by h. What new expression does that create? How can you isolate from here?

Q: What is the correct value of  ?
- 29 (Correct. You found that the expression can be rewritten , and then simplified to .)
- 59 (Incorrect. Simplify everything within the absolute value symbols first, and then evaluate. For example, can be rewritten as . Does this help you find the correct value?)
- 41 (Incorrect. Simplify everything within the absolute value symbols first, and then evaluate. For example, can be rewritten as . Does this help you find the correct value?)
- 65 (Incorrect. Simplify everything within the absolute value symbols first, and then evaluate. For example, can be rewritten as . Does this help you find the correct value?)
A: 29

Q: For which of the following sequences is it true that every term (after the first one) is 7 less than the previous term?
- 70, 63, 56, 49, ... (Correct. Every term is 7 less than the term before it (70 - 7 = 63, 63 - 7 = 56, 56 - 7 = 49).)
- 7, 14, 21, 28, ... (Incorrect. Each term after the first one is 7 more than the one before it, so the sequence does not match the description.)
- 35, 28, 35, 28, ... (Incorrect. The third term is 7 more than the second term (not 7 less than the second term), so the sequence does not match the description.)
- 14, 7, 0, 7, ... (Incorrect. The fourth term is 7 more than the third term (not 7 less than the third term), so the sequence does not match the description.)
A: 70, 63, 56, 49, ...

Q: Which of the following statements is correct about the function graphed below?
- This is the graph of the function . (Incorrect. The function is representd by a line. This graph is not a line, so it is not a linear function.)
- The ordered pair (0, 0) lies on the graph of the function. (Incorrect. Look at the graph; the ordered pair (0, 0) does not lie on the graph of the function.)
- The function is undefined when . (Correct. The equation for this inverse function is . Since division by 0 is undefined, the function itself will be undefined when .)
- The function is linear. (Incorrect. This graph is not a line, so it can not be a linear function.)
A: The function is undefined when .

Q: Which of the following tables represents the equation ?
- x | y
1 | 7
2 | 4
3 | 1
4 | -2
5 | -5 (Correct. In each row of the table, the y value equals 10 more than negative three times the corresponding x value.)
- x | y
1 | 13
2 | 16
3 | 19
4 | 22
5 | 25 (Incorrect. In order for the table to represent the equation, each y value in a row must equal 10 more than negative three times the corresponding x value.)
- x | y
7 | 1
4 | 2
1 | 3
-2 | 4
-5 | 5 (Incorrect. In order for the table to represent the equation, each y value in a row must equal 10 more than negative three times the corresponding x value.)
- x | y
1 | 11
2 | 14
3 | 17
4 | 20
5 | 23 (Incorrect. In order for the table to represent the equation, each y value in a row must equal 10 more than negative three times the corresponding x value.)
A: x | y
1 | 7
2 | 4
3 | 1
4 | -2
5 | -5

Q: To form Figure 1, 6 toothpicks are required, while Figure 2 requires 11 toothpicks.

Which table represents the relationship between x and y, where y is the number of toothpicks required to build Figure x?
- x | y
1 | 6
2 | 11
3 | 16
4 | 24 (Incorrect. For the table to represent the situation, in each row of the table the y value must equal the number of toothpicks required to form Figure x.)
- x | y
1 | 6
2 | 11
3 | 16
4 | 20 (Incorrect. For the table to represent the situation, in each row of the table the y value must equal the number of toothpicks required to form Figure x.)
- x | y
1 | 6
2 | 11
3 | 18
4 | 24 (Incorrect. For the table to represent the situation, in each row of the table the y value must equal the number of toothpicks required to form Figure x.)
- x | y
1 | 6
2 | 11
3 | 16
4 | 21 (Correct. The number of toothpicks required to form Figure 3 is 16 and Figure 4 requires 21 toothpicks; in each row of this table the y value equals the number of toothpicks required to form Figure x.)
A: x | y
1 | 6
2 | 11
3 | 16
4 | 21

Q: Which of the following statements is true about this graph?
- It does not represent a function. (Correct. This graph cannot represent a function because some x-values (for example, x=-3) correspond to more than one y-value.)
- It represents the function . (Incorrect. The graph is a parabola and no x-value has two corresponding y-values. What do you notice about the y-values at in this graph?)
- It goes through the origin. (Incorrect. The graph does not go through the origin, (0, 0).)
- It represents the function . (Incorrect. If the graph represented the line , it would go through the ordered pairs (0, 0), (1, 3), and (2, 6). Does it?)
A: It does not represent a function.

Q: Jean gets an allowance of $18 each month plus an extra $1.50 for each chore she completes around the house. How much allowance will she earn if she does chores in a month?
- dollars (Incorrect. The equation correctly shows that Jean earns $1.50 per chore, but fails to include the fact that she gets $18 per month without having to complete any chores.)
- dollars (Incorrect. This expression says that if Jean completes 0 chores, she will earn $1.50. Is this true?)
- dollars (Correct. Jean earns 18 dollars plus an additional $1.50 for each chore she completes, so she will earn dollars for completin g tasks.)
- dollars (Incorrect. Even though this equation gives the right answer when , the amount per chore is incorrect.)
A: dollars

Q: Erin has been saving money at a regular rate and noticed that months after her 15th birthday, she had saved a total of dollars. Which of the following statements correctly describes her savings plan?
- By her 15th birthday, she had saved 20 dollars and was able to save an additional 180 dollars each month afterwards. (Incorrect. One month later, when , how much money did Erin have? What does the +180 in the scenario refer to?)
- She had saved a total of 180 dollars by her 16th birthday. (Incorrect. One month later, when , how much money did Erin have? What does the +180 in the scenario refer to?)
- After her 15th birthday, she saved 180 dollars per month. (Incorrect. One month later, when , how much money did Erin have? What does the +180 in the scenario refer to?)
- By her 15th birthday, she had saved 180 dollars and was able to save an additional 20 dollars each month afterwards. (Correct. On her 15th birthday, (0 months after her 15th birthday) she had dollars and 1 month later (when ) she had dollars, so she saved an additional 20 dollars that month.)
A: By her 15th birthday, she had saved 180 dollars and was able to save an additional 20 dollars each month afterwards.

Q: Find the y-intercept of the line represented by the table.

x | y
2 | -6
3 | 0
4 | 6
5 | 12
- (0, 0) (Incorrect. The y-intercept of the line is the point (0, y) that lies on the line. Use the pattern in the table to find the value of the y-coordinate when x = 0.)
- (0, -18) (Correct. The y-intercept of the line is the point (0, y) that lies on the line. Using the pattern described in the table, the slope of the line is 6, so the points (1, -12) and (0, -18) are also on the line, showing that the y-intercept is (0, -18).)
- (0, -12) (Incorrect. The y-intercept of the line is the point (0, y) that lies on the line. Use the pattern in the table to find the value of the y-coordinate when x = 0.)
- (3, 0) (Incorrect. The y-intercept of the line is the point (0, y) that lies on the line. Use the pattern in the table to find the value of the y-coordinate when x = 0.)
A: (0, -18)

Q: Find the slope of the line represented by the table below.

x | y
1 | 20
3 | 16
5 | 12
9 | 4
- 8 (Incorrect. Identify two sets of values in this table, and then find the difference between the y-values and the difference between the x-values. This will lead you to the slope of the line.)
- -4 (Incorrect. Identify two sets of values in this table, and then find the difference between the y-values and the difference between the x-values. This will lead you to the slope of the line.)
- -2 (Correct. The slope between any two points represented by the table is -2. For example, the slope between (1, 20) and (3, 16) is , and the slope between (5, 12) and (9, 4) is .)
A: -2
If wrong: Incorrect. Identify two sets of values in this table, and then find the difference between the y-values and the difference between the x-values. This will lead you to the slope of the line.

Q: Which of the following equations is represented by the line shown below?
A: (a choice with no text)
If wrong: Incorrect. Find the y-intercept and slope of the line. Which equation represents this information?
If right: Correct. The y-intercept is (0, -2) and the points (0, -2) and (-2, 1) are on the line, so the slope is . Therefore the slope intercept form of the equation is .
If wrong: Incorrect. Find the y-intercept and slope of the line. Which equation represents this information?
If wrong: Incorrect. Find the y-intercept and slope of the line. Which equation represents this information?

Q: What is the x-intercept of the line with equation
A: (a choice with no text)
If wrong: Incorrect. The x-intercept of the line is the point on the line. Substitute into the equation to find the value of the x-coordinate.
If right: Correct. The x-intercept of the line is the point on the line. If then so and therefore, so the x-intercept is
If wrong: Incorrect. The x-intercept of the line is the point on the line. Substitute into the equation to find the value of the x-coordinate.
If wrong: Incorrect. The x-intercept of the line is the point on the line. Substitute into the equation to find the value of the x-coordinate.

Q: Which of the following equations represent the line that has slope 7 and goes through the point (2, 9)?
A: (a choice with no text)
If wrong: Incorrect. This equation would be the point slope form of the line with slope 7 going through the point Since the line has the correct slope, we should still check to see if this is an alternate way to represent the given line. To do this we need to check whether is on the line Replacing x with 2 and y with 9, but , so when and
If wrong: Incorrect. This equation would be the point slope form of the line with slope -7 going through the point
If wrong: Incorrect. This equation would be the point slope form of the line with slope -7 going through the point .
If right: Correct. The point slope form of the line with slope m going through the point is so the point slope form of the given line is

Q: Convert the point slope equation into standard form.
A: (a choice with no text)
If right: Correct. If then , so so and therefore
If wrong: To express the equation in standard form, multiply both sides of the equation by 5 to eliminate the fraction. Then distribute the -3 through and bring the x and y terms to one side of the equation and the constants to the other side.
If wrong: To express the equation in standard form, multiply both sides of the equation by 5 to eliminate the fraction. Then distribute the -3 through and bring the x and y terms to one side of the equation and the constants to the other side.
If wrong: To express the equation in standard form, multiply both sides of the equation by 5 to eliminate the fraction. Then distribute the -3 through and bring the x and y terms to one side of the equation and the constants to the other side.

Q: Which line is perpendicular to the line graphed below?
A: (a choice with no text)
If wrong: Incorrect. What is the slope of the graphed line? What should the slope of a perpendicular line be?
If wrong: Incorrect. What is the slope of the graphed line? What should the slope of a perpendicular line be?
If right: Correct. The graphed line has slope since it goes through the points (0, 1) and (-4, 2). Any line perpendicular to the graphed line must have slope 4 (the opposite reciprocal of ).
If wrong: Incorrect. What is the slope of the graphed line? What should the slope of a perpendicular line be?

Q: Solve the inequality for x.
A: (a choice with no text)
If wrong: Incorrect. Did you move all the non-variable terms to one side? Check your solution to see if it makes the inequality a true statement.
If wrong: Incorrect. Did you move all the non-variable terms to one side? Check your solution to see if it makes the inequality a true statement.
If wrong: Incorrect. Did you move all the non-variable terms to one side? Check your solution to see if it makes the inequality a true statement.
If right: Correct. Since solving the inequality requires you to isolate the variable x, use the Properties of Inequality to work out that .

Q: Select the inequality that represents the following example.
A: (a choice with no text)
If wrong: Incorrect. Check to make sure your answer has the correct line (solid or dotted), the correct orientation (vertical or horizontal), and the correct shading (above vs. below, left vs. right). Which values of does this graph represent?
If wrong: Incorrect. Check to make sure your answer has the correct line (solid or dotted), the correct orientation (vertical or horizontal), and the correct shading (above vs. below, left vs. right). Which values of does this graph represent?
If wrong: Incorrect. Check to make sure your answer has the correct line (solid or dotted), the correct orientation (vertical or horizontal), and the correct shading (above vs. below, left vs. right). Which values of does this graph represent?
If right: Correct. The line is dotted, implying either a > or a < sign. The line is vertical, so it's a single-variable inequality with .

Q: Solve the inequality for the variable x.
A: (a choice with no text)
If right: Correct. To solve the inequality, isolate the variable x by adding 2 to both sides and then multiply both sides by 5.
If wrong: Incorrect. Did you move all the non-variable terms to one side and use the correct mathematical operation(s) to simplify your inequality? Are you using the right inequality?
If wrong: Incorrect. Did you move all the non-variable terms to one side and use the correct mathematical operation(s) to simplify your inequality? Are you using the right inequality?
If wrong: Incorrect. Did you move all the non-variable terms to one side and use the correct mathematical operation(s) to simplify your inequality? Are you using the right inequality?

Q: The forecaster on TV said, "It's a cold day outside! Right now it's only 7 degrees but the temperature will change by up to 10 degrees by 3 PM. We'll tell you if we're getting warmer or colder in a minute!”

What is the range of possible temperatures it could be at 3 PM?
- Colder than -3 degrees or warmer than 17 degrees. (Incorrect. If the temperature gets exactly 10 degrees warmer or colder, what two temperatures could it be at 3 PM? What does it mean if the temperature difference is up to 10 degrees different?)
- Warmer than 17 degrees. (Incorrect. If the temperature gets exactly 10 degrees warmer or colder, what two temperatures could it be at 3 PM? What does it mean if the temperature difference is up to 10 degrees different?)
- Warmer than -3 degrees or colder than 17 degrees. (Correct. Since the temperature is forecast to be up to 10 degrees different, it could be either up to 10 degrees warmer or colder. This means that it could be warmer than -3 degrees or colder than 17 degrees.)
- Exactly 7 degrees. (Incorrect. If the temperature gets exactly 10 degrees warmer or colder, what two temperatures could it be at 3 PM? What does it mean if the temperature difference is up to 10 degrees different?)
A: Warmer than -3 degrees or colder than 17 degrees.

Q: Which set of points below are all solutions to the inequality ?
- (1, 2), (3, 8), (-1, 0) (Incorrect. Points that are solutions to the inequality will have a coordinate that is less than -1 times the coordinate. Check to make sure that you've included only values for x and y that fit this rule.)
- (2, 2), (3, 0), (-3, -5) (Incorrect. Points that are solutions to the inequality will have a coordinate that is less than -1 times the coordinate. Check to make sure that you've included only values for x and y that fit this rule.)
- (1, -2), (2, -3), (-3, -5) (Correct. All three points in this set have a coordinate that is less than -1 times the coordinate.)
- (9, -9), (2.75, -2.75), (5, -5) (Incorrect. Points that are solutions to the inequality will have a coordinate that is less than -1 times the coordinate. Check to make sure that you've included only values for x and y that fit this rule.)
A: (1, -2), (2, -3), (-3, -5)

Q: Solve the inequality .
- and (Incorrect. The distance between y and zero has to be greater than 7. Pick numbers that satisfy this requirement and then fit those numbers to an answer choice.)
- and (Incorrect. The distance between y and zero has to be greater than 7. Pick numbers that satisfy this requirement and then fit those numbers to an answer choice.)
- and (Incorrect. The distance between y and zero has to be greater than 7. Pick numbers that satisfy this requirement and then fit those numbers to an answer choice.)
- and (Correct. Create the two inequalities and . Solve the latter inequality by multiplying both sides by -1 and flipping the sign.)
A: and

Q: Ezra is graphing the inequality on a number line. What should his graph look like?
- A ray starting at -3 and continuing to , with a closed circle at -3. (Incorrect. What values of x make this inequality true? They must be between -3 and 3 or equal to 3. Does your line represent all these numbers and no others?)
- A segment from -3 to 3, with a closed circle at -3, and an open circle at 3. (Correct. There should be a closed circle at -3, an open circle at 3, and the line in between them should be shaded.)
- A segment from -3 to 3, with closed circles at both -3 and 3. (Incorrect. What values of x make this inequality true? They must be between -3 and 3 or equal to 3. Does your line represent all these numbers and no others?)
- A segment from -3 to 3, with open circles at both -3 and 3. (Incorrect. What values of x make this inequality true? They must be between -3 and 3 or equal to 3. Does your line represent all these numbers and no others?)
A: A segment from -3 to 3, with a closed circle at -3, and an open circle at 3.

Q: Consider the problem: Cecilia wants to buy a brand new pair of headphones that cost $139. While she already has $40 saved up, she is planning on working at a local grocery store for $10 an hour to make up the extra cash.

Which of the following inequalities will help her determine values of , the number of hours that Cecilia can work so she can afford the new headphones?
- $40 + $10 $139 (Incorrect. The amount of money that Cecilia can earn for hours of work is $10h. This amount of money added to her current savings ($40) needs to be greater than or equal to the cost for the headphones ($139). Which inequality best represents this situation?)
- $4 0 - $10 $139 (Incorrect. The amount of money that Cecilia can earn for hours of work is $10h. This amount of money added to her current savings ($40) needs to be greater than or equal to the cost for the headphones ($139). Which inequality best represents this situation?)
- $10 $139 (Incorrect. The amount of money that Cecilia can earn for hours of work is $10h. This amount of money added to her current savings ($40) needs to be greater than or equal to the cost for the headphones ($139). Which inequality best represents this situation?)
- $4 0 + $10 $139 (Correct. The amount of money that Jasmine can earn for hours of work is $10. This amount of money added to her current savings ($40) needs to be greater than or equal to the cost for the headphones ($139).)
A: $4 0 + $10 $139

Q: Brian and Hayden go out for dinner and the bill comes to $120.00. Hayden usually tips more than 10% of the bill and Brian usually tips at most 20% of the bill.

Given Brian and Hayden's tipping habits, what graph below best represents the range for a tip that the server should expect to see?
- $12 $24 (Incorrect. Make sure the signs are correct; could the server get exactly 10% or 20%?)
- $24 (Incorrect. Make sure the signs are correct; could the server get exactly 10% or 20%?)
- $12 $24 (Correct. Hayden tips more than 10%, meaning that the server should expect more than $12 as a tip, but Brian tips at most 20% of the bill, meaning that the server should expect less than or equal to $24.)
- $10 $20 (Incorrect. Make sure the signs are correct; could the server get exactly 10% or 20%?)
A: $12 $24

Q: Determine the number of solutions the following system of equations will have:
- One solution. (Incorrect. Rearrange the equations into form. What do you notice? Can you think of more than one set of values for x and y that would solve both equations?)
- No solutions. (Incorrect. Rearrange the equations into form. What do you notice? Can you think of more than one set of values for x and y that would solve both equations?)
- Infinite solutions. (Correct. Rearranging the equations into , you see that the lines are exactly the same and therefore have infinitely many solutions.)
- Impossible to determine. (Incorrect. Rearrange the equations into form. What do you notice? Can you think of more than one set of values for x and y that would solve both equations?)
A: Infinite solutions.

Q: Consider the system of inequalities and its non-shaded graph:

After graphing and shading the inequalities, which region in the grid below would represent the solution region?
- Region D (Incorrect. Pick an ordered pair from each region and substitute those values into the given inequalities. Which region produces an ordered pair that makes both inequalities true?)
- Region A (Incorrect. Pick an ordered pair from each region and substitute those values into the given inequalities. Which region produces an ordered pair that makes both inequalities true?)
- Region C (Correct. Region C is the solution because when any ordered pair from that region is substituted into both inequalities, they result in true statements.)
- Region B (Incorrect. Pick an ordered pair from each region and substitute those values into the given inequalities. Which region produces an ordered pair that makes both inequalities true?)
A: Region C

Q: Use the substitution method to determine whether the system of equations has one solution, no solution, or infinitely many solutions.
- It is impossible to determine from the information given. (Incorrect. Try rearranging the equations to compare the slopes and y-intercepts. What happens if you substitute in for x in the first equation?)
- The system has one solution; the two equations intersect at one point. (Correct. If you rearrange the equations and solve for y, you will find that . Substituting into one of the equations yields . Therefore, this system has one solution at (5, 0).)
- The system has no solution; the lines are parallel. (Incorrect. Try rearranging the equations to compare the slopes and y-intercepts. What happens if you substitute in for x in the first equation?)
- The system has infinitely many solutions; the two equations are the same line. (Incorrect. Try rearranging the equations to compare the slopes and y-intercepts. What happens if you substitute in for x in the first equation?)
A: The system has one solution; the two equations intersect at one point.

Q: Solve the system of equations using substitution.
A: (a choice with no text)
If wrong: Incorrect. Try substituting into the top equation for y. Use that x value in either equation to solve for y.
If wrong: Incorrect. Try substituting into the top equation for y. Use that x value in either equation to solve for y.
If right: Correct. When and , both equations are true. This means it is the solution of the system.
If wrong: Incorrect. Try substituting into the top equation for y. Use that x value in either equation to solve for y.

Q: Solve the system of equations using substitution.
A: (a choice with no text)
If right: Correct. When and , both equations are true. This means it is the solution of the system.
If wrong: Incorrect. Try rearranging so that it expresses the value of either x or y, and then substitute that value into the first equation.
If wrong: Incorrect. Try rearranging so that it expresses the value of either x or y, and then substitute that value into the first equation.
If wrong: Incorrect. Try rearranging so that it expresses the value of either x or y, and then substitute that value into the first equation.

Q: Use the elimination method to solve the system for x and y.
A: (a choice with no text)
If wrong: Incorrect. Adding the two equations together eliminates the variable y to create the equation , so . What is the value of y?
If wrong: Incorrect. Adding the two equations together eliminates the variable y to create the equation , so . What is the value of y?
If right: Correct. The point is a solution to both equations, and therefore is the solution to the system.
If wrong: Incorrect. Adding the two equations together eliminates the variable y to create the equation , so . What is the value of y?

Q: The drama club is selling tickets to their annual talent show. They sold adult tickets (a) for $12.50 each and student tickets (s) for $6. They sold a total of 30 tickets and made $264.50.

Which system of equations best represents the situation above?
- Tickets sold:

Money earned: (Correct. This system correctly relates the number of tickets sold and the amount of money earned.)
- Tickets sold:

Money earned: (Incorrect. The second equation says that the difference between the amount of money earned from sales of adult tickets and student tickets was 264.50. Is this true?)
- Money from student tickets:

Money from adult tickets: (Incorrect. Both equations are set equal to 264.50, the total amount of money that the club made. Did they earn that amount of money from each group (adults and students) or from the ticket sales to both groups combined?)
- Money from student tickets:

Money from adult tickets: (Incorrect. The first equation says that the number of student tickets is the total amount of money earned divided by the cost of one student ticket, $6. How do sales of adult tickets factor in?)
A: Tickets sold:

Money earned:

Q: A dessert restaurant sells a special blend of Mexican and Swiss chocolate that it uses in its famous hot chocolate drinks. Mexican chocolate costs $7.60 per pound, and Swiss chocolate costs $12 per pound.

How many pounds of Mexican chocolate must be mixed with 6 pounds of Swiss chocolate to make a mixture that costs $9.25 per pound?
- 12 pounds (Incorrect. Use a chart to create an equation to solve the problem. You want to know the amount of Meican chocolate, so label that x: | Total cost ($) | = | Price ($/pound) | * | Amount (pounds) Mexican | | = | 7.60 | * | Swiss | 72.00 | = | 12.00 | * | 6 Total Mix | | = | 9.25 | * | Create an equation that relates the Total Costs, and solve for x.)
- 10.5 pounds (Incorrect. Use a chart to create an equation to solve the problem. You want to know the amount of Meican chocolate, so label that x: | Total cost ($) | = | Price ($/pound) | * | Amount (pounds) Mexican | | = | 7.60 | * | Swiss | 72.00 | = | 12.00 | * | 6 Total Mix | | = | 9.25 | * | Create an equation that relates the Total Costs, and solve for x.)
- 10 pounds (Correct. You need 10 pounds of Mexican chocolate for this mixture.)
- 8 pounds (Incorrect. Use a chart to create an equation to solve the problem. You want to know the amount of Meican chocolate, so label that x: | Total cost ($) | = | Price ($/pound) | * | Amount (pounds) Mexican | | = | 7.60 | * | Swiss | 72.00 | = | 12.00 | * | 6 Total Mix | | = | 9.25 | * | Create an equation that relates the Total Costs, and solve for x.)
A: 10 pounds

Q: Consider the system of inequalities:

Which of the following graphs correctly represents this system?
A: (a choice with no text)
If wrong: Incorrect. The inequality is a solid line with shading above it, and the inequality is a dotted line with shading beneath it. Go back and check that the lines drawn are correctly dotted or solid in accordance with their inequality sign.
If right: Correct. The inequality is a dotted line with shading above it, and the inequality is a dotted line with shading beneath it.
If wrong: Incorrect. The inequality is a solid line with shading above it, and the inequality is a dotted line with shading beneath it. Go back and check that the lines drawn are correctly dotted or solid in accordance with their inequality sign.
If wrong: Incorrect. The inequality is a solid line with shading above it, and the inequality is a dotted line with shading beneath it. Go back and check that the lines drawn are correctly dotted or solid in accordance with their inequality sign.

Q: Which of the following inequalities is not a true statement?
A: (a choice with no text)
If right: Correct. is not true; 65 is not less than or equal to 56!
If wrong: Incorrect. Recall that an inequality like can be read "a is less than b", and can be read "a is less than or equal to b." Knowing this, which of the inequalities is false?
If wrong: Incorrect. Recall that an inequality like can be read "a is less than b", and can be read "a is less than or equal to b." Knowing this, which of the inequalities is false?
If wrong: Incorrect. Recall that an inequality like can be read "a is less than b", and can be read "a is less than or equal to b." Knowing this, which of the inequalities is false?

Q: Which of the following equations does not apply the Order of Operations correctly?
A: (a choice with no text)
If right: Correct. The one that is not solved correctly is . Since multiplication should be evaluated before subtraction, , which equals 6.
If wrong: Incorrect. Remember the order of operations: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. In one of these equations, subtraction occurs before multiplication. Which one is it?
If wrong: Incorrect. Remember the order of operations: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. In one of these equations, subtraction occurs before multiplication. Which one is it?
If wrong: Incorrect. Remember the order of operations: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. In one of these equations, subtraction occurs before multiplication. Which one is it?

Q: Use the order of operations to evaluate this expression:
- 0 (Incorrect. To evaluate this expression, first evaluate the exponents; this means that the expression can be rewritten . Remember that multiplication comes before subtraction in the order of operations.)
- 32 (Correct. You evaluated this expression correctly by applying the order of operations.)
- 48 (Incorrect. To evaluate this expression, first evaluate the exponents; this means that the expression can be rewritten . Remember that multiplication comes before subtraction in the order of operations.)
- 256 (Incorrect. To evaluate this expression, first evaluate the exponents; this means that the expression can be rewritten . Remember that multiplication comes before subtraction in the order of operations.)
A: 32