Question

a town is expanding the size of a square athletic field. the equation shown determines the building cost, y, in dollars, for every foot, x, added to the width of the athletic field.
y = (110.25)x²
which equation shows an equivalent equation rearranged to determine x in terms of y?
responses
answer
x = 10.5√y
x = 110.25/√y
x = √y/10.5
x = 110.25√y

Explanation:

Step1: Start with the given equation

We have the equation \( y = (110.25)x^2 \). Our goal is to solve for \( x \) in terms of \( y \).

Step2: Isolate \( x^2 \)

Divide both sides of the equation by \( 110.25 \) to get \( x^2 \) by itself. So, \( \frac{y}{110.25}=x^2 \).

Step3: Take the square root of both sides

Since \( x \) represents a length (feet added to the width), we take the positive square root. Recall that \( 110.25 = 10.5^2 \), so \( \sqrt{110.25}=10.5 \). Taking the square root of both sides: \( x=\sqrt{\frac{y}{110.25}}=\frac{\sqrt{y}}{\sqrt{110.25}}=\frac{\sqrt{y}}{10.5} \).

Answer:

\( x = \frac{\sqrt{y}}{10.5} \) (the third option among the given choices, which is \( x=\frac{\sqrt{y}}{10.5} \))