Question

Translate the following statement into an equation: "The quotient of 5 plus a number w and negative 5 is 36."

A) 5w - 5 = 36
B) 5/w - 5 = 36
C) 5(w + 5) = 36
D) 5(w - 5) = 36

If the monthly charge for premium cable is $90 and is $20 more than the cost of standard cable, what is the cost of standard cable?
A) x - 20 = 90
B) x + 20 = 90
C) x - 90 = 20
D) x + 90 = 20

The area of a rectangle is 1/2 square inch, and the length of the rectangle is 3/8 inch. What is the width of the rectangle?
A) 2w = 3/8
B) 2w = 1/2
C) 2/w = 3/8
D) 2/w = 1/2

The perimeter of a square is 26.46 inches. What is the side length of the square?
A) 4s = 26.46
B) s^2 = 26.46
C) 2s = 26.46
D) s = 26.46

Answer 1

The first statement translates to (5 + w) / (-5) = 36, making the correct option B. The cost of standard cable, given that premium is $20 more and costs $90, is found with the equation, option B, x + 20 = 90. To find the width of a rectangle with an area of 1/2 square inch and length 3/8 inch, use the equation width = 1/(2 × (3/8)), which is option A, and the side length of a square with a 26.46-inch perimeter is found using the equation 4s = 26.46, option A.

Step-by-step explanation:

The first question asks us to translate a statement into an equation. The correct translation for "The quotient of 5 plus a number w and negative 5 is 36" is option B: (5 + w) / (-5) = 36.

For the second question related to cable charges, we understand that If the monthly charge for premium cable is $90 and is $20 more than the cost of standard cable, we can set up the equation: standard cable cost x + 20 = 90, which represents option B.

In the third problem, we are asked to find the width of a rectangle when given the area and the length. If the area is 1/2 square inch and the length is 3/8 inch, we can set up the equation length × width = area, or (3/8) × width = 1/2. Solving for width provides us the correct answer A: width = 1/(2 × (3/8)).

The final question concerns the side length of a square, where the perimeter is given as 26.46 inches. Since the perimeter of a square is 4 times the side length, we can set up the equation 4 × side length = 26.46, resulting in option A: 4s = 26.46.