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

Answer :

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

We start with the given equation:
[tex]\[ 4x^2 + 25y^2 = 100 \][/tex]

1. Move [tex]\( 4x^2 \)[/tex] to the right side of the equation:

Subtract [tex]\( 4x^2 \)[/tex] from both sides:
[tex]\[ 25y^2 = 100 - 4x^2 \][/tex]

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

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

3. Simplify the fractions:

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

So the equation becomes:
[tex]\[ y^2 = 4 - \frac{4}{25}x^2 \][/tex]

The isolated form of [tex]\( y^2 \)[/tex] is:
[tex]\[ y^2 = 4 - \frac{4}{25}x^2 \][/tex]

This matches option C.

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