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Which equation describes this relationship? Remember to include $k$ , the constant of variation. $\newline$ $z$ varies inversely with $x$ and $y$ $\newline$ Choices: $\newline$ (A) $z = \frac{k}{xy}$ $\newline$ (B) $z = \frac{kx}{y}$ $\newline$ (C) $z = kxy$ $\newline$ (D) $z = \frac{ky}{x}$

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Write joint and combined variation equations II

Full solution

Q. Which equation describes this relationship? Remember to include

k

, the constant of variation.

\newline

z

varies inversely with

x

and

y

\newline

Choices:

\newline

(A)

z = \frac{k}{xy}

\newline

(B)

z = \frac{kx}{y}

\newline

(C)

z = kxy

\newline

(D)

z = \frac{ky}{x}

Identify equation form: Since $z$ varies inversely with both $x$ and $y$ , the equation should have $z$ on one side and the product of $x$ and $y$ in the denominator on the other side.
Determine correct equation form: The correct form for an equation where $z$ varies inversely with $x$ and $y$ is $z = \frac{k}{xy}$ , where $k$ is the constant of variation.
Match equation form with choices: Looking at the choices, $(A)z = \frac{k}{xy}$ matches the form we need for an inverse variation with both $x$ and $y$ .

More problems from Write joint and combined variation equations II

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Question

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\_\_\_\_

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Question

z

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\newline

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Question

Which equation describes this relationship? Remember to include

k

, the constant of variation.

a

varies directly with

b

and inversely with

c

d

\newline

\newline

\[[A]a = \frac{kb}{cd}\]

\newline

\[[B]a = \frac{kbd}{c}\]

\newline

\[[C]a = \frac{k}{bcd}\]

\newline

\[[D]a = \frac{kd}{bc}\]

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Question

z

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\newline

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\newline

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\newline

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Question

Square VWXY is dilated by a scale factor of

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\newline

In the equation shown,

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\newline

1

\newline

3

\newline

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6

\newline

7

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