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What is the result of isolating [tex]$y^2$[/tex] in the equation below?

[tex]4x^2 + 25y^2 = 100[/tex]

A. [tex]y^2 = 100 - \frac{4}{25}x^2[/tex]

B. [tex]y^2 = 100 - 4x^2[/tex]

C. [tex]y^2 = 25 - \frac{4}{25}x^2[/tex]

D. [tex]y^2 = 4 - \frac{4}{25}x^2[/tex]

Answer :

To isolate [tex]\( y^2 \)[/tex] in the equation [tex]\( 4x^2 + 25y^2 = 100 \)[/tex], follow these steps:

1. Rearrange the equation: Start by moving the term that contains [tex]\( x^2 \)[/tex] to the other side of the equation. This can be done by subtracting [tex]\( 4x^2 \)[/tex] from both sides:

[tex]\[
25y^2 = 100 - 4x^2
\][/tex]

2. Solve for [tex]\( y^2 \)[/tex]: To get [tex]\( y^2 \)[/tex] by itself, divide each term in the equation by 25:

[tex]\[
y^2 = \frac{100}{25} - \frac{4x^2}{25}
\][/tex]

3. Simplify: Perform the division for each term:

[tex]\[
y^2 = 4 - \frac{4}{25}x^2
\][/tex]

Therefore, the correct answer is D. [tex]\( y^2 = 4 - \frac{4}{25}x^2 \)[/tex].

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