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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 = 100 - \frac{4}{25} x^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 :

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]

Step 1: Move the term involving [tex]\( x^2 \)[/tex] to the right side of the equation.
[tex]\[ 25y^2 = 100 - 4x^2 \][/tex]

Step 2: Divide every term in the equation by 25 to solve for [tex]\( y^2 \)[/tex].
[tex]\[ y^2 = \frac{100 - 4x^2}{25} \][/tex]

Now, let's simplify the expression on the right:
[tex]\[ y^2 = \frac{100}{25} - \frac{4x^2}{25} \][/tex]

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

The correct answer is:
C. [tex]\( y^2 = 4 - \frac{4}{25}x^2 \)[/tex]

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