1. The length of a rectangular box is 2 units less than its width.

If the area of the box is 15 units square.

Find the perimeter of the box.

B. 16(Correct Answer)

Explanation

These are the formulas for the box.

A= L x W

P = 2( L + W)

We know that the area is 15

15= L x W

Also,

L= W-2

Now we can use both formulas

(W)(W-2) = 15

W² - 2W= 15

W²- 2W-15= 0

(W-5) (W+3) = 0

W= 5 , W= -3

We can find the Length,

L = W-2 = 5- 2= 3

L= 3

Finally the perimeter:

P = 2( 3+ 5)

P = 2(8)

P= 16

2. Evaluate the following expression

if X=-2, Y= 3, Z= -5

2X²-3Y-3Z

D. 14(Correct Answer)

Explanation

2(-2)² -3(3) -3(-5) = 2(4) -9 +15 = 8-9 +15= 14

3. Simplify:

C. (Correct Answer)

Explanation

You need to simplify each exponent, since you are dealing with a square root you need to rewrite the exponents as even exponents.

a³ = a²a

b⁷= b⁶b

Z³ =Z²Z

Now you can divide the exponents by two:

ab³Z and the rest has to be inside the square root √(abZ)

4. Multiply:

(3X -5)(2X+ 5)

5. Solve:

3(5X-1)<4(X-6)

Explanation

3(5X-1)<4(X-6)

15X-3 < 4X -24

15X-4X < -24 + 3

11X < -21

X< -21/11

6. Solve for X:

3(X-5)-4X = 6(X-10) -(X+ 5)

Explanation

3X -15 -4X= 6X -60 -X- 5

-X -15= 5X -65

-6X= -65 +15

-6X= -50

X= -50/-6 = 25/3

7. Translate the following sentence into an algebraic expression:

" The product of a number and six is three times the same number less than ten"

Explanation

The product means multiplication: 6 and X

is means equal sign =

three times the same number less than ten

10 -3X

8. Simplify: -3(p-5p²) + 3p²-6P

Explanation

-3p + 15p²+ 3p²-6p= 18p²-9p

9. Which of the following equations passes through point (-3,-16)

10. -------------------------------------------------

Top of Form

11. Bottom of Form

Explanation

Substituting the values in all the equations we get that the answer is

Y= 2X-10...