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Answer :
Let's solve the equation to isolate [tex]\( y^2 \)[/tex] step by step.
Given equation:
[tex]\[ 4x^2 + 25y^2 = 100 \][/tex]
1. First, we want to move the term with [tex]\( x^2 \)[/tex] to the right side of the equation. We do this by subtracting [tex]\( 4x^2 \)[/tex] from both sides:
[tex]\[ 25y^2 = 100 - 4x^2 \][/tex]
2. To isolate [tex]\( y^2 \)[/tex], divide every term in the equation by 25:
[tex]\[ y^2 = \frac{100 - 4x^2}{25} \][/tex]
3. Now, simplify the right side of the equation:
- Divide [tex]\( 100 \)[/tex] by 25:
[tex]\[ \frac{100}{25} = 4 \][/tex]
- Divide [tex]\( 4x^2 \)[/tex] by 25:
[tex]\[ \frac{4x^2}{25} = \frac{4}{25}x^2 \][/tex]
4. Rewrite the simplified equation:
[tex]\[ y^2 = 4 - \frac{4}{25}x^2 \][/tex]
So, the correct answer is:
D. [tex]\( y^2 = 4 - \frac{4}{25} x^2 \)[/tex]
Given equation:
[tex]\[ 4x^2 + 25y^2 = 100 \][/tex]
1. First, we want to move the term with [tex]\( x^2 \)[/tex] to the right side of the equation. We do this by subtracting [tex]\( 4x^2 \)[/tex] from both sides:
[tex]\[ 25y^2 = 100 - 4x^2 \][/tex]
2. To isolate [tex]\( y^2 \)[/tex], divide every term in the equation by 25:
[tex]\[ y^2 = \frac{100 - 4x^2}{25} \][/tex]
3. Now, simplify the right side of the equation:
- Divide [tex]\( 100 \)[/tex] by 25:
[tex]\[ \frac{100}{25} = 4 \][/tex]
- Divide [tex]\( 4x^2 \)[/tex] by 25:
[tex]\[ \frac{4x^2}{25} = \frac{4}{25}x^2 \][/tex]
4. Rewrite the simplified equation:
[tex]\[ y^2 = 4 - \frac{4}{25}x^2 \][/tex]
So, the correct answer is:
D. [tex]\( y^2 = 4 - \frac{4}{25} x^2 \)[/tex]
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