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

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

C. [tex]$y^2 = 100 - \frac{4}{25}x^2$[/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], we can follow these steps:

1. Start with the given equation:
[tex]\[
4x^2 + 25y^2 = 100
\][/tex]

2. Move [tex]\( 4x^2 \)[/tex] to the right side by subtracting it from both sides of the equation:
[tex]\[
25y^2 = 100 - 4x^2
\][/tex]

3. Divide both sides by 25 to solve for [tex]\( y^2 \)[/tex]:
[tex]\[
y^2 = \frac{100 - 4x^2}{25}
\][/tex]

4. Simplify the expression:
[tex]\[
y^2 = \frac{100}{25} - \frac{4x^2}{25}
\][/tex]

5. Calculate the division:
[tex]\[
y^2 = 4 - \frac{4}{25}x^2
\][/tex]

So, the correct answer is:

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

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