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Answer :
Sure! Let's solve this step by step. We need to isolate [tex]\( y^2 \)[/tex] in the equation:
[tex]\[ 4x^2 + 25y^2 = 100 \][/tex]
Here’s how you can do it:
1. Subtract [tex]\( 4x^2 \)[/tex] from both sides to get the terms with [tex]\( y^2 \)[/tex] by itself on one side of the equation:
[tex]\[ 25y^2 = 100 - 4x^2 \][/tex]
2. Divide every term by 25 to solve for [tex]\( y^2 \)[/tex]:
[tex]\[ y^2 = \frac{100 - 4x^2}{25} \][/tex]
3. Simplify the expression: Divide each term in the numerator separately by 25:
[tex]\[ y^2 = \frac{100}{25} - \frac{4x^2}{25} \][/tex]
[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]
Looking at the choices given, the correct answer is:
D. [tex]\( y^2 = 4 - \frac{4}{25} x^2 \)[/tex]
[tex]\[ 4x^2 + 25y^2 = 100 \][/tex]
Here’s how you can do it:
1. Subtract [tex]\( 4x^2 \)[/tex] from both sides to get the terms with [tex]\( y^2 \)[/tex] by itself on one side of the equation:
[tex]\[ 25y^2 = 100 - 4x^2 \][/tex]
2. Divide every term by 25 to solve for [tex]\( y^2 \)[/tex]:
[tex]\[ y^2 = \frac{100 - 4x^2}{25} \][/tex]
3. Simplify the expression: Divide each term in the numerator separately by 25:
[tex]\[ y^2 = \frac{100}{25} - \frac{4x^2}{25} \][/tex]
[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]
Looking at the choices given, the correct answer is:
D. [tex]\( y^2 = 4 - \frac{4}{25} x^2 \)[/tex]
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