Question

1. what is the value of a? \\(7a - 8 = 4a + 10\\)

a. 6
b. 7
c. 8
d. 9
e. 10

1. change the subject of the formula \\(y = 3x - 2\\) to \\(x\\).

a. \\(x = 3y - 2\\)
b. \\(x = \frac{y - 2}{3}\\)
c. \\(x = \frac{3y}{2}\\)
d. \\(x = \frac{y + 2}{3}\\)
e. none of these

1. if two sides of a right-angled triangle are \\(7\text{ cm}\\) and \\(24\text{ cm}\\), then the hypotenuse is

a. \\(23\text{ cm}\\)
b. \\(24\text{ cm}\\)
c. \\(25\text{ cm}\\)
d. \\(27\text{ cm}\\)
e. \\(31\text{ cm}\\)

1. when doing a series of additions on a calculator, a student noted that she added \\(35,095\\) instead of \\(35.95\\). in order to obtain the correct total in a single step she should now

a. add \\(35.95\\)
b. subtract \\(35,059.05\\)
c. subtract \\(35,130.95\\)
d. add \\(35,130.95\\)
e. none of these

1. after \\(20\\%\\) of a bill is paid, \\(\\$60\\) still remains to be paid. how much was the total bill?

a. \\(\\$12\\)
b. \\(\\$20\\)
c. \\(\\$63\\)
d. \\(\\$72\\)
e. none of these

Explanation:

Solve the linear equation for a

We start with the equation:

$$7a - 8 = 4a + 10$$

Subtract \(4a\) from both sides:

$$3a - 8 = 10$$

Add \(8\) to both sides:

$$3a = 18$$

Divide by \(3\):

$$a = 6$$

This matches option A.

Rearrange the formula for x

We start with the formula:

$$y = 3x - 2$$

Add \(2\) to both sides to isolate the term with \(x\):

$$y + 2 = 3x$$

Divide both sides by \(3\):

$$x = \frac{y + 2}{3}$$

This matches option D.

Find the hypotenuse of the right triangle

Using the Pythagorean theorem:

$$c^2 = a^2 + b^2$$

Substitute the given side lengths \(7\text{ cm}\) and \(24\text{ cm}\):

$$c^2 = 7^2 + 24^2 = 49 + 576 = 625$$

Take the square root of both sides:

$$c = \sqrt{625} = 25\text{ cm}$$

This matches option C.

Correct the calculator addition error

The student added \(35,095\) instead of \(35.95\).
To find the correction needed, calculate the difference:

$$35,095 - 35.95 = 35,059.05$$

Since the student added too much, they must subtract this difference to get the correct total:
Subtract \(35,059.05\).
This matches option B.

Calculate the total bill amount

Let \(x\) be the total bill.
After paying \(20\%\), the remaining percentage is:

$$100\% - 20\% = 80\%$$

We are given that this remaining amount is \(\$60\):

$$0.80x = 60$$

Solve for \(x\):

$$x = \frac{60}{0.80} = 75$$

Since \(\$75\) is not listed in options A, B, C, or D, the correct choice is "none of these".
This matches option E.

Answer:

Question 9

• (A) 6 (Correct answer)
• (B) 7
• (C) 8
• (D) 9
• (E) 10

Question 10

• (A) \(x = 3y - 2\)
• (B) \(x = \frac{y - 2}{3}\)
• (C) \(x = \frac{3y}{2}\)
• (D) \(x = \frac{y + 2}{3}\) (Correct answer)
• (E) none of these

Question 11

• (A) 23 cm
• (B) 24 cm
• (C) 25 cm (Correct answer)
• (D) 27 cm
• (E) 31 cm

Question 12

• (A) add 35.95
• (B) subtract 35,059.05 (Correct answer)
• (C) subtract 35,130.95
• (D) add 35,130.95
• (E) none of these

Question 13

• (A) $12
• (B) $20
• (C) $63
• (D) $72
• (E) none of these (Correct answer)