Answer :

- First, evaluate $F(5)$ by substituting $x=5$ into $F(x)$, which gives $F(5) = 5^2 + 4(5) = 45$.
- Next, evaluate $G(6)$ by substituting $x=6$ into $G(x)$, which gives $G(6) = 2(6) + 2 = 14$.
- Finally, add the results: $F(5) + G(6) = 45 + 14 = 59$.
- Therefore, the final answer is $\boxed{59}$.

### Explanation
1. Understanding the problem
We are given two functions, $F(x) = x^2 + 4x$ and $G(x) = 2x + 2$. Our goal is to find the value of $F(5) + G(6)$.

2. Calculating F(5)
First, let's evaluate $F(5)$ by substituting $x = 5$ into the expression for $F(x)$: $$F(5) = (5)^2 + 4(5) = 25 + 20 = 45.$$

3. Calculating G(6)
Next, let's evaluate $G(6)$ by substituting $x = 6$ into the expression for $G(x)$: $$G(6) = 2(6) + 2 = 12 + 2 = 14.$$

4. Adding F(5) and G(6)
Finally, we add the results of $F(5)$ and $G(6)$ to obtain the final answer: $$F(5) + G(6) = 45 + 14 = 59.$$

5. Final Answer
Therefore, $F(5) + G(6) = 59$.

### Examples
Imagine you're calculating the total cost of materials for a project. $F(x)$ could represent the cost of the primary material based on its quantity $x$, and $G(x)$ could represent the cost of a secondary material. By finding $F(5) + G(6)$, you're determining the total cost when you need 5 units of the primary material and 6 units of the secondary material. This kind of calculation is useful in budgeting and resource management.

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Rewritten by : Barada