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

Answer :

Sure! Let's solve the problem step by step to isolate [tex]\( y^2 \)[/tex] in the equation [tex]\( 4x^2 + 25y^2 = 100 \)[/tex].

1. Start with the given equation:

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

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

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

3. Isolate [tex]\( y^2 \)[/tex] by dividing every term by 25:

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

Simplifying the right side of the equation, we perform the division:

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

This simplifies to:

[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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