The problem asks us to evaluate the function $F(x) = x^2 + 3x - 9$ at $x = -2$ and $x = -5$, and then determine which of the given statements are true.

1. Problem Description

The problem asks us to evaluate the function $F(x) = x^2 + 3x - 9$ at $x = -2$ and $x = -5$, and then determine which of the given statements are true.

2. Solution Steps

First, evaluate $F(-2)$.

$F(-2) = (-2)^2 + 3(-2) - 9 = 4 - 6 - 9 = -11$.

So, $F(-2) = -11$.

Statement a) $F(-2) = -2F$ means $F(-2)$ is $-2$ times some value $F$, which is not related to the function $F(x)$ defined. Since we know $F(-2) = -11$, statement a) should be $F(-2) = -11$ which is not $-2F$ for any constant $F$.

Next, evaluate $F(-5)$.

$F(-5) = (-5)^2 + 3(-5) - 9 = 25 - 15 - 9 = 1$.

So, $F(-5) = 1$.

Let's examine the provided statements:

a) $F(-2) = -2F$. As stated above, we cannot say if this statement is true or false, because the variable $F$ on the right side is not defined, but the expression is clearly wrong.

b) $F(-5) = -11$. Since $F(-5) = 1$, this statement is false.

c) $F(-5) = -17$. Since $F(-5) = 1$, this statement is false.

d) $F(-5) = 1$. Since $F(-5) = 1$, this statement is true.

3. Final Answer

The true statement is d) $F(-5) = 1$.