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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 :

Let's solve the equation step-by-step to find the expression for [tex]\( y^2 \)[/tex].

We start with the given equation:

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

Step 1: Subtract [tex]\( 4x^2 \)[/tex] from both sides to start isolating the [tex]\( y^2 \)[/tex] term:

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

Step 2: Divide every term by 25 to solve for [tex]\( y^2 \)[/tex]:

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

Now, let's simplify the right side:

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

The fraction [tex]\(\frac{100}{25}\)[/tex] simplifies to 4. Hence,

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

Therefore, the correct answer is:

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

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