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The height of a hill, [tex]h(x)[/tex], in a painting can be written as a function of [tex]x[/tex], the distance from the left side of the painting. Both [tex]h(x)[/tex] and [tex]x[/tex] are measured in inches.

[tex]h(x) = -\frac{1}{5}(x)(x-13)[/tex]

What is the height of the hill in the painting 3 inches from the left side of the picture?

A. 6 inches
B. 13 inches
C. 30 inches
D. 150 inches



Answer :

GinnyAnswer
Certainly! Let's find the height of the hill in the painting when we are 3 inches away from the left side of the painting.

The height of the hill is given by the function:
[tex]\[ h(x) = -\frac{1}{5} x (x - 13) \][/tex]

We need to find [tex]\( h(3) \)[/tex]. Plugging [tex]\( x = 3 \)[/tex] into the function:

[tex]\[ h(3) = -\frac{1}{5} \cdot 3 \cdot (3 - 13) \][/tex]

Let's break it down step-by-step:

1. Calculate [tex]\( 3 - 13 \)[/tex]:
[tex]\[ 3 - 13 = -10 \][/tex]

2. Multiply the result by 3:
[tex]\[ 3 \cdot (-10) = -30 \][/tex]

3. Now, multiply by [tex]\( -\frac{1}{5} \)[/tex]:
[tex]\[ -\frac{1}{5} \cdot (-30) \][/tex]

Multiplying these results:
[tex]\[ -\frac{1}{5} \cdot (-30) = 6 \][/tex]

Therefore, the height of the hill 3 inches from the left side of the painting is [tex]\( 6 \)[/tex] inches.

So, the correct answer is:

[tex]\[ \text{6 inches} \][/tex]

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