Let's solve Kylie's equation step-by-step to find the diameter of the circle.
The given equation is:
[tex]\[ 4(d - 4) = 7^2 \][/tex]
First, we start by simplifying the right-hand side of the equation. We know that:
[tex]\[ 7^2 = 49 \][/tex]
So, the equation now becomes:
[tex]\[ 4(d - 4) = 49 \][/tex]
Next, we need to solve for [tex]\(d\)[/tex]. To do this, we first divide both sides of the equation by 4:
[tex]\[ d - 4 = \frac{49}{4} \][/tex]
Simplifying the right-hand side:
[tex]\[ \frac{49}{4} = 12.25 \][/tex]
Now our equation is:
[tex]\[ d - 4 = 12.25 \][/tex]
To isolate [tex]\(d\)[/tex], we add 4 to both sides of the equation:
[tex]\[ d = 12.25 + 4 \][/tex]
Adding these gives us:
[tex]\[ d = 16.25 \][/tex]
Therefore, the diameter of the circle is:
[tex]\[ \boxed{16.25 \text{ in.}} \][/tex]
It appears there may have been an error in the list of options provided, as none of them match the calculated diameter of 16.25 inches. However, based on our solution, 16.25 inches is indeed the correct diameter of the circle.
