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

Answer :

To solve the problem of isolating [tex]\( y^2 \)[/tex] in the equation [tex]\( 4x^2 + 25y^2 = 100 \)[/tex], let's go through the steps:

1. Start with the given equation:

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

2. Isolate the term with [tex]\( y^2 \)[/tex] on one side. To do this, subtract [tex]\( 4x^2 \)[/tex] from both sides of the equation:

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

3. Solve for [tex]\( y^2 \)[/tex]. Divide every term by 25 to isolate [tex]\( y^2 \)[/tex]:

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

4. Simplify the expression. Break down the fraction:

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

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

Based on the simplification, the result of isolating [tex]\( y^2 \)[/tex] is:

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

Therefore, the correct answer is:

C. [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