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Item 23 of 27
Let the function
h be defined as
h(x)=c*2^(x-c)+k, where
c and
k are constants. If
h(c)=20, which of the following equations correctly expresses
c in terms of
k?

Let the function $h$ be defined as $h(x)=c \cdot 2^{x-c}+k$ , where $c$ and $k$ are constants. If $h(c)=20$ , which of the following equations correctly expresses $c$ in terms of $k ?$

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Write a quadratic function from its x-intercepts and another point

Full solution

Q. Let the function

h

be defined as

h(x)=c \cdot 2^{x-c}+k

, where

c

and

k

are constants. If

h(c)=20

, which of the following equations correctly expresses

c

in terms of

k ?

Substitute $x$ with $c$ : We are given the function $h(x) = c \cdot 2^{(x-c)} + k$ and the condition $h(c) = 20$ . We need to find the value of $c$ in terms of $k$ . First, let's substitute $x$ with $c$ in the function $h(x)$ to apply the given condition $h(c) = 20$ . $c$ $0$
Simplify using exponents: Now, let's simplify the equation using the property of exponents that any number to the power of $0$ is $1$ .
$h(c) = c \cdot 2^0 + k$
$h(c) = c \cdot 1 + k$
$h(c) = c + k$
Substitute $h(c)$ with $20$ : We know that $h(c) = 20$ , so we can substitute $20$ for $h(c)$ in the equation. $\newline$ $20 = c + k$
Isolate $c$ in equation: To express $c$ in terms of $k$ , we need to isolate $c$ on one side of the equation. We do this by subtracting $k$ from both sides of the equation. $\newline$ $20 - k = c + k - k$ $\newline$ $20 - k = c$
Final expression for $c$ : We have now expressed $c$ in terms of $k$ . The equation is: $\newline$ $c = 20 - k$ $\newline$ This is the final answer.

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