Question

question 10 of 10
what is the result of isolating ( y^2 ) in the equation below?
( 4x^2 + 25y^2 = 100 )

a. ( y^2 = 100 - \frac{4}{25}x^2 )
b. ( y^2 = 4 - \frac{4}{25}x^2 )
c. ( y^2 = 25 - \frac{4}{25}x^2 )
d. ( y^2 = 100 - 4x^2 )

Explanation:

Step1: Subtract \(4x^2\) from both sides

To isolate the term with \(y^2\), we start by subtracting \(4x^2\) from both sides of the equation \(4x^2 + 25y^2=100\). This gives us \(25y^2=100 - 4x^2\).

Step2: Divide both sides by 25

Next, we divide each side of the equation \(25y^2 = 100-4x^2\) by 25 to solve for \(y^2\). When we divide \(100\) by \(25\) we get \(4\), and when we divide \(- 4x^2\) by \(25\) we get \(-\frac{4}{25}x^2\). So, \(y^2=\frac{100 - 4x^2}{25}=\frac{100}{25}-\frac{4x^2}{25}=4-\frac{4}{25}x^2\).

Answer:

B. \(y^{2}=4-\frac{4}{25}x^{2}\)