Answer :
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]
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]
