High School

We appreciate your visit to 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. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

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

Answer :

Let's solve the equation [tex]\(4x^2 + 25y^2 = 100\)[/tex] to isolate [tex]\(y^2\)[/tex].

1. Start with the original equation:
[tex]\[
4x^2 + 25y^2 = 100
\][/tex]

2. Subtract [tex]\(4x^2\)[/tex] from both sides to move it to the other side of the equation:
[tex]\[
25y^2 = 100 - 4x^2
\][/tex]

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

4. Simplify by dividing each component inside the fraction by 25:
[tex]\[
y^2 = \frac{100}{25} - \frac{4x^2}{25}
\][/tex]

5. Simplify the division:
[tex]\[
y^2 = 4 - \frac{4}{25}x^2
\][/tex]

This matches option B:
[tex]\[
y^2 = 4 - \frac{4}{25}x^2
\][/tex]

So, the correct answer is B. [tex]\(y^2 = 4 - \frac{4}{25} x^2\)[/tex].

Thanks for taking the time to read 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. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada

Other Questions