If y varies inversely as x, and y=10 when x=4, what is the value of y when x=8 ? A quad y=2.5 B y=5 C y=40 D quad y=(1)/(5)

Given Inverse Variation: Given that y varies inversely as x. This means y = k / x where k is a constant. Find Constant k: We know y = 10 when x = 4. Substitute these values to find k. 10 = k / 4. Write Variation Equation: Solve for k: Multiply both sides by 4 to isolate k. 10 * 4 = k. k = 40. Find y for x=8: Now, use the found value of k to write the inverse variation equation. y = 40 / x. To find y when x = 8, substitute 8 for x in the equation. y = 40 / 8. y = 5.

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If
y varies inversely as
x, and
y=10 when
x=4, what is the value of
y when
x=8 ?
A
quad y=2.5
B
y=5
C
y=40
D
quad y=(1)/(5)

If $y$ varies inversely as $x$ , and $y=10$ when $x=4$ , what is the value of $y$ when $x=8$ ? $\newline$ A) $y=2.5$ $\newline$ B) $y=5$ $\newline$ C) $y=40$ $\newline$ D) $y=\frac{1}{5}$

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Math Problems

Algebra 1

Write and solve inverse variation equations

Full solution

Q. If

y

varies inversely as

x

, and

y=10

when

x=4

, what is the value of

y

when

x=8

\newline

y=2.5

\newline

y=5

\newline

y=40

\newline

y=\frac{1}{5}

Given Inverse Variation: Given that $y$ varies inversely as $x$ . This means $y = \frac{k}{x}$ where $k$ is a constant.
Find Constant $k$ : We know $y = 10$ when $x = 4$ . Substitute these values to find $k$ . $10 = \frac{k}{4}$ .
Write Variation Equation: Solve for $k$ : Multiply both sides by $4$ to isolate $k$ . $10 \times 4 = k$ . $k = 40$ .
Find $y$ for $x=8$ : Now, use the found value of $k$ to write the inverse variation equation. $y = \frac{40}{x}$ .
Find $y$ for $x=8$ : Now, use the found value of $k$ to write the inverse variation equation. $y = \frac{40}{x}$ . To find $y$ when $x = 8$ , substitute $8$ for $x$ in the equation. $y = \frac{40}{8}$ . $y = 5$ .