We appreciate your visit to Suppose tex y tex varies directly as tex x tex If tex y 7 tex when tex x 28 tex what is the value of. 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!
Answer :
Sure! Let's solve the problem step-by-step.
We are told that [tex]\( y \)[/tex] varies directly as [tex]\( x \)[/tex]. This means there is a constant [tex]\( k \)[/tex] such that [tex]\( y = kx \)[/tex].
1. Find the constant of variation [tex]\( k \)[/tex]:
We know from the problem that when [tex]\( y = 7 \)[/tex], [tex]\( x = 28 \)[/tex]. Using the direct variation equation [tex]\( y = kx \)[/tex], we can substitute the known values:
[tex]\[
7 = k \times 28
\][/tex]
Solving for [tex]\( k \)[/tex], we divide both sides by 28:
[tex]\[
k = \frac{7}{28} = \frac{1}{4} = 0.25
\][/tex]
2. Use [tex]\( k \)[/tex] to find [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex]:
Now that we know [tex]\( k = 0.25 \)[/tex], we use the direct variation equation to find [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex]:
[tex]\[
3 = 0.25 \times x
\][/tex]
Solving for [tex]\( x \)[/tex], divide both sides by 0.25:
[tex]\[
x = \frac{3}{0.25} = 12
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex] is [tex]\(\boxed{12}\)[/tex]. So, the correct answer is option C.
We are told that [tex]\( y \)[/tex] varies directly as [tex]\( x \)[/tex]. This means there is a constant [tex]\( k \)[/tex] such that [tex]\( y = kx \)[/tex].
1. Find the constant of variation [tex]\( k \)[/tex]:
We know from the problem that when [tex]\( y = 7 \)[/tex], [tex]\( x = 28 \)[/tex]. Using the direct variation equation [tex]\( y = kx \)[/tex], we can substitute the known values:
[tex]\[
7 = k \times 28
\][/tex]
Solving for [tex]\( k \)[/tex], we divide both sides by 28:
[tex]\[
k = \frac{7}{28} = \frac{1}{4} = 0.25
\][/tex]
2. Use [tex]\( k \)[/tex] to find [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex]:
Now that we know [tex]\( k = 0.25 \)[/tex], we use the direct variation equation to find [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex]:
[tex]\[
3 = 0.25 \times x
\][/tex]
Solving for [tex]\( x \)[/tex], divide both sides by 0.25:
[tex]\[
x = \frac{3}{0.25} = 12
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 3 \)[/tex] is [tex]\(\boxed{12}\)[/tex]. So, the correct answer is option C.
Thanks for taking the time to read Suppose tex y tex varies directly as tex x tex If tex y 7 tex when tex x 28 tex what is the value of. 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!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
