meredith48034
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Suppose y varies inversely with x, and y = 18 when x = 12. What is the value of x when y = 24? NO LINKS OR ANSWERING YOU DON'T KNOW?

a. 24
b. 9
c. 12
d. 18​

Sagot :

xKelvin

Answer:

B. 9

Step-by-step explanation:

We are given that y varies inversely with x. Recall that inverse variation has the form:

[tex]\displaystyle y=\frac{k}{x}[/tex]

Where k is the constant of variation.

We are given that y = 18 when x = 12. Hence:

[tex]\displaystyle (18)=\frac{k}{(12)}[/tex]

Solve for k. Multiply both sides by 12:

[tex]k=12(18)=216[/tex]

Thus, our equation is:

[tex]\displaystyle y=\frac{216}{x}[/tex]

We want to find x when y = 24. Substitute:

[tex]\displaystyle \frac{24}{1}=\frac{216}{x}[/tex]

Cross-multiply:

[tex]24x=216[/tex]

Divide both sides by 24. Hence:

[tex]x=9[/tex]

Our answer is B.

Answer:

B

Step-by-step explanation:

Given that y varies inversely with x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

To find k use the condition y = 18 when x = 12 , then

18 = [tex]\frac{k}{12}[/tex] ( multiply both sides by 12 )

216 = k

y = [tex]\frac{216}{x}[/tex] ← equation of variation

When y = 24 , then

24 = [tex]\frac{216}{x}[/tex] ( multiply both sides by x )

24x = 216 ( divide both sides by 24 )

x = 9

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