Math 112 Final Review 1

1. Simplify by combining like terms: 4(x – 6 ) – 8x

X - 16

-4x - 24

X-4

7x+5

The given expression is 4(x - 6) - 8x. To simplify this expression, we can distribute the 4 to both terms inside the parentheses: 4x - 24 - 8x. Combining like terms, we have -4x - 24.

Explanation

The given expression is 4(x - 6) - 8x. To simplify this expression, we can distribute the 4 to both terms inside the parentheses: 4x - 24 - 8x. Combining like terms, we have -4x - 24.

2. Solve: 4x + 2 = 3x + 8

1

5

6

-2

To solve the equation 4x + 2 = 3x + 8, we need to isolate the variable x. We can do this by subtracting 3x from both sides of the equation. This will give us x + 2 = 8. Next, we subtract 2 from both sides to get x = 6. Therefore, the correct answer is 6.

Explanation

To solve the equation 4x + 2 = 3x + 8, we need to isolate the variable x. We can do this by subtracting 3x from both sides of the equation. This will give us x + 2 = 8. Next, we subtract 2 from both sides to get x = 6. Therefore, the correct answer is 6.

3. If y = 3, then y³(y³-y)=

300

459

648

999

1099

When y = 3, we can substitute this value into the equation to find the result. So, y3(y3-y) becomes 3^3(3^3-3), which simplifies to 27(27-3). Further simplifying, we get 27(24), which equals 648.

Explanation

When y = 3, we can substitute this value into the equation to find the result. So, y3(y3-y) becomes 3^3(3^3-3), which simplifies to 27(27-3). Further simplifying, we get 27(24), which equals 648.

4. Solve: - 4(x – 2) = - 12

5

3

-3

7

To solve the equation -4(x-2) = -12, we first distribute the -4 to both terms inside the parentheses: -4x + 8 = -12. Then, we subtract 8 from both sides to isolate the variable: -4x = -20. Finally, we divide both sides by -4 to solve for x: x = 5.

Explanation

To solve the equation -4(x-2) = -12, we first distribute the -4 to both terms inside the parentheses: -4x + 8 = -12. Then, we subtract 8 from both sides to isolate the variable: -4x = -20. Finally, we divide both sides by -4 to solve for x: x = 5.

5. The x , y-intercepts for the linear equation y - 6x = 6 are

( 3, 0),( 0, 5)

(0, 4), (-3, 0)

(-1, 0),(0, 6)

(9, 3),(0, 12)

The answer (-1, 0),(0, 6) is correct because it satisfies the equation y - 6x = 6. When x = -1, y = 0, and when x = 0, y = 6. Therefore, these points are the x and y-intercepts of the given linear equation.

Explanation

The answer (-1, 0),(0, 6) is correct because it satisfies the equation y - 6x = 6. When x = -1, y = 0, and when x = 0, y = 6. Therefore, these points are the x and y-intercepts of the given linear equation.

6. Lee worked 22 hours this week and made $132. If she works 15 hours next week at the same pay rate, how much will she make?

$57

$90

$104

$112

$122

If Lee worked 22 hours this week and made $132, we can calculate her hourly rate by dividing her total earnings by the number of hours worked. Therefore, her hourly rate is $132/22 = $6. Now, if she works 15 hours next week at the same pay rate of $6 per hour, she will make 15 * $6 = $90.

Explanation

If Lee worked 22 hours this week and made $132, we can calculate her hourly rate by dividing her total earnings by the number of hours worked. Therefore, her hourly rate is $132/22 = $6. Now, if she works 15 hours next week at the same pay rate of $6 per hour, she will make 15 * $6 = $90.

7. If 5 is added to 3 times a number, the result is 17. Find the number.

2

13

9

4

If 5 is added to 3 times a number and the result is 17, we can set up the equation 3x + 5 = 17, where x represents the number. To solve for x, we subtract 5 from both sides of the equation, giving us 3x = 12. Then, we divide both sides by 3, resulting in x = 4. Therefore, the number is 4.

Explanation

If 5 is added to 3 times a number and the result is 17, we can set up the equation 3x + 5 = 17, where x represents the number. To solve for x, we subtract 5 from both sides of the equation, giving us 3x = 12. Then, we divide both sides by 3, resulting in x = 4. Therefore, the number is 4.

8. If x = -1 and y = 2, what is the value of the expression 2x ³ - 3xy ?

8

4

-1

-4

The expression 2x^3 - 3xy can be simplified by substituting the given values of x and y. Plugging in x = -1 and y = 2, we get 2(-1)^3 - 3(-1)(2). Simplifying further, we have 2(-1) - 3(-2), which becomes -2 + 6, resulting in a final value of 4.

Explanation

The expression 2x^3 - 3xy can be simplified by substituting the given values of x and y. Plugging in x = -1 and y = 2, we get 2(-1)^3 - 3(-1)(2). Simplifying further, we have 2(-1) - 3(-2), which becomes -2 + 6, resulting in a final value of 4.

9. You need to purchase a textbook for nursing school. The book cost $80.00, and the sales tax where you are purchasing the book is 8.25%. You have $100. How much change will you receive back?

$5.20

$7.35

$13.40

$19.95

$21.25

The cost of the textbook is $80.00 and the sales tax is 8.25% of the cost. To calculate the sales tax, we multiply $80.00 by 8.25% (0.0825), which gives us $6.60. So the total cost of the textbook including sales tax is $80.00 + $6.60 = $86.60.
You have $100, so to find the change you subtract the total cost from the amount you have: $100 - $86.60 = $13.40. Therefore, you will receive $13.40 back as change.

Explanation

The cost of the textbook is $80.00 and the sales tax is 8.25% of the cost. To calculate the sales tax, we multiply $80.00 by 8.25% (0.0825), which gives us $6.60. So the total cost of the textbook including sales tax is $80.00 + $6.60 = $86.60.
You have $100, so to find the change you subtract the total cost from the amount you have: $100 - $86.60 = $13.40. Therefore, you will receive $13.40 back as change.

10. Perform the Operation:3 + 2 [18 – (5+3)]

48

23

-32

24

None of these

The given expression involves the operation of addition, subtraction, and multiplication. According to the order of operations, we need to perform the operations inside the parentheses first. (5+3) equals 8. Then, we subtract 8 from 18, which gives us 10. Next, we multiply 2 by 10, resulting in 20. Finally, we add 3 to 20, giving us the final answer of 23.

Explanation

The given expression involves the operation of addition, subtraction, and multiplication. According to the order of operations, we need to perform the operations inside the parentheses first. (5+3) equals 8. Then, we subtract 8 from 18, which gives us 10. Next, we multiply 2 by 10, resulting in 20. Finally, we add 3 to 20, giving us the final answer of 23.

11. A student has earned scores of 87, 81, and 88 on the first 3 of 4 tests. If the student wants an average (arithmetic mean) of exactly 87, what score must she earn on the fourth test?

85

86

87

92

To find the score the student must earn on the fourth test, we need to calculate the total score the student should have after all four tests. The desired average is 87, and since there are four tests, the total score should be 87 multiplied by 4, which equals 348. The student has already earned scores of 87, 81, and 88 on the first three tests, which sum up to 256. To reach a total score of 348, the student must earn 348 - 256 = 92 on the fourth test. Therefore, the correct answer is 92.

Explanation

To find the score the student must earn on the fourth test, we need to calculate the total score the student should have after all four tests. The desired average is 87, and since there are four tests, the total score should be 87 multiplied by 4, which equals 348. The student has already earned scores of 87, 81, and 88 on the first three tests, which sum up to 256. To reach a total score of 348, the student must earn 348 - 256 = 92 on the fourth test. Therefore, the correct answer is 92.

12. The order pair (2, 3 ) satisfies which of the following equation

Y = 2x - 5

X = y + 2

X = 2y - 4

Y = 2x

The given ordered pair (2, 3) satisfies the equation x = 2y - 4. By substituting x = 2 and y = 3 into the equation, we get 2 = 2(3) - 4, which simplifies to 2 = 6 - 4 and further simplifies to 2 = 2. Since the equation is true, we can conclude that the ordered pair (2, 3) satisfies the equation x = 2y - 4.

Explanation

The given ordered pair (2, 3) satisfies the equation x = 2y - 4. By substituting x = 2 and y = 3 into the equation, we get 2 = 2(3) - 4, which simplifies to 2 = 6 - 4 and further simplifies to 2 = 2. Since the equation is true, we can conclude that the ordered pair (2, 3) satisfies the equation x = 2y - 4.

13. The sales price of a car is $12,590, which is 20% off the original price. What is the original price?

$14,310.40

$14,990.90

$15,290.70

$15,737.50

$16,935.80

The original price can be calculated by dividing the sales price by (1 - discount percentage). In this case, the discount percentage is 20%, so we divide $12,590 by (1 - 0.20) which equals $15,737.50.

Explanation

The original price can be calculated by dividing the sales price by (1 - discount percentage). In this case, the discount percentage is 20%, so we divide $12,590 by (1 - 0.20) which equals $15,737.50.

14. Ben is making wooden toys for the next arts and crafts sale. Each toy costs Ben $1.80 to make. If he sells the toys for $3.00 each, how many will he have to sell to make a profit of exactly $36.00?

12

20

30

60

Ben makes a profit of $1.20 per toy ($3.00 - $1.80). To make a profit of $36.00, he needs to sell 30 toys ($36.00 / $1.20).

Explanation

Ben makes a profit of $1.20 per toy ($3.00 - $1.80). To make a profit of $36.00, he needs to sell 30 toys ($36.00 / $1.20).

15. If Leah is 6 years older than Sue, and John is 5 years older than Leah, and the total of their ages is 41. Then how old is Sue?

8

10

14

19

21

Leah is 6 years older than Sue, and John is 5 years older than Leah. If we let Sue's age be x, then Leah's age would be x+6, and John's age would be x+6+5=x+11. The total of their ages is 41, so we can set up the equation x + (x+6) + (x+11) = 41. Simplifying this equation gives us 3x + 17 = 41. Solving for x, we get x = 8. Therefore, Sue is 8 years old.

Explanation

Leah is 6 years older than Sue, and John is 5 years older than Leah. If we let Sue's age be x, then Leah's age would be x+6, and John's age would be x+6+5=x+11. The total of their ages is 41, so we can set up the equation x + (x+6) + (x+11) = 41. Simplifying this equation gives us 3x + 17 = 41. Solving for x, we get x = 8. Therefore, Sue is 8 years old.

16. Phillip charged $400 worth of goods on his credit card. On his first bill, he was not charged any interest, and he made a payment of $20. He then charged another $18 worth of goods. On his second bill a month later, he was charged 2% interest on his entire unpaid balance. How much interest was Phillip charged on his second bill?

$8.76

$7.96

$7.60

$7.24

Phillip was charged 2% interest on his entire unpaid balance on his second bill. On his first bill, he made a payment of $20, so his unpaid balance was $400 - $20 = $380. He then charged another $18 worth of goods, making his total unpaid balance $380 + $18 = $398. 2% of $398 is $7.96, which is the amount of interest Phillip was charged on his second bill.

Explanation

Phillip was charged 2% interest on his entire unpaid balance on his second bill. On his first bill, he made a payment of $20, so his unpaid balance was $400 - $20 = $380. He then charged another $18 worth of goods, making his total unpaid balance $380 + $18 = $398. 2% of $398 is $7.96, which is the amount of interest Phillip was charged on his second bill.

17. Which of the following expressions represents the product of 3 less than twice x and 2 more than the quantity 3 times x?

-6x 2 + 25x + 6

6x 2 + 5x + 6

6x 2 - 5x + 6

6x 2 - 5x - 6

The expression 6x^2 - 5x - 6 represents the product of 3 less than twice x and 2 more than the quantity 3 times x. This can be determined by breaking down the given information. "Twice x" can be represented as 2x, and "3 less than twice x" can be written as 2x - 3. Similarly, "3 times x" can be represented as 3x, and "2 more than the quantity 3 times x" can be written as 3x + 2. Multiplying these two expressions together gives us 6x^2 - 5x - 6.

Explanation

The expression 6x^2 - 5x - 6 represents the product of 3 less than twice x and 2 more than the quantity 3 times x. This can be determined by breaking down the given information. "Twice x" can be represented as 2x, and "3 less than twice x" can be written as 2x - 3. Similarly, "3 times x" can be represented as 3x, and "2 more than the quantity 3 times x" can be written as 3x + 2. Multiplying these two expressions together gives us 6x^2 - 5x - 6.

18. What is the average (arithmetic mean) of 8, 7, 7, 5, 3, 2, and 2?

3 4/7

4 5/6

4 6/7

5

To find the average of a set of numbers, you add up all the numbers and then divide the sum by the total number of numbers. In this case, the sum of the numbers 8, 7, 7, 5, 3, 2, and 2 is 34. There are a total of 7 numbers. Dividing 34 by 7 gives us a quotient of 4 and a remainder of 6. Therefore, the average is 4 6/7.

Explanation

To find the average of a set of numbers, you add up all the numbers and then divide the sum by the total number of numbers. In this case, the sum of the numbers 8, 7, 7, 5, 3, 2, and 2 is 34. There are a total of 7 numbers. Dividing 34 by 7 gives us a quotient of 4 and a remainder of 6. Therefore, the average is 4 6/7.

19. Simon arrived at work at 8:15 A.M. and left work at 10: 30 P.M. If Simon gets paid by the hour at a rate of $10 and time and ½ for any hours worked over 8 in a day. How much did Simon get paid?

$120.25

$160.75

$173.75

$180

$182.50

Simon worked for a total of 14 hours and 15 minutes. He worked 8 hours at his regular rate of $10 per hour, earning $80. For the remaining 6 hours and 15 minutes, he worked at time and a half, earning $15 per hour. Therefore, he earned an additional $15 * 1.5 * 6.25 = $93.75. Adding this to his regular pay, Simon earned a total of $80 + $93.75 = $173.75.

Explanation

Simon worked for a total of 14 hours and 15 minutes. He worked 8 hours at his regular rate of $10 per hour, earning $80. For the remaining 6 hours and 15 minutes, he worked at time and a half, earning $15 per hour. Therefore, he earned an additional $15 * 1.5 * 6.25 = $93.75. Adding this to his regular pay, Simon earned a total of $80 + $93.75 = $173.75.