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

Answer :

Let's solve the equation step-by-step to isolate [tex]\( y^2 \)[/tex] in the given equation:

The original equation is:
[tex]\[ 4x^2 + 25y^2 = 100 \][/tex]

1. Subtract [tex]\( 4x^2 \)[/tex] from both sides:

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

2. Divide both sides by 25 to solve for [tex]\( y^2 \)[/tex]:

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

3. Simplify the expression:

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

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

So, the correct expression for [tex]\( y^2 \)[/tex] is:
[tex]\[ y^2 = 4 - \frac{4}{25}x^2 \][/tex]

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

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