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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 :

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

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

1. Start by moving [tex]\( 4x^2 \)[/tex] to the other side of the equation. You can do this by subtracting [tex]\( 4x^2 \)[/tex] from both sides:

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

2. Now, to isolate [tex]\( y^2 \)[/tex], divide everything by 25:

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

3. This can be simplified by splitting the fraction:

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

4. Simplifying each term gives:

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

So the result of isolating [tex]\( y^2 \)[/tex] is:

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

The correct answer is:

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

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