To solve $h(5) + g(9)$, we'll evaluate each function individually at the given values:

Step 1: Evaluate $h(5)$

Given:

$h(x) = |15 - 9x|$

Substituting $x = 5$:

$h(5) = |15 - 9(5)|$

$h(5) = |15 - 45|$

$h(5) = |-30|$

$h(5) = 30$

Step 2: Evaluate $g(9)$

Given:

$g(x) = x^2 - 7x$

Substituting $x = 9$:

$g(9) = 9^2 - 7(9)$

$g(9) = 81 - 63$

$g(9) = 18$

Step 3: Add $h(5)$ and $g(9)$

$h(5) + g(9) = 30 + 18$

$h(5) + g(9) = 48$

Final Answer:

$\boxed{48}$

Would you like more details or have any questions?

Here are some related questions you might consider:

1. How would you evaluate $h(-2) + g(3)$?
2. What is the result of $f(4) + g(-1)$?
3. How does the absolute value function affect the evaluation of $h(x)$?
4. What is the significance of the parameters in each function?
5. How would the result change if the function $h(x)$ were modified?

Tip: Absolute values always produce non-negative results, regardless of whether the input expression is positive or negative!