use f(x)=-3/2+11, g(x)=x^2-7x, and h(x)= |15-9x| to evaluate the function.  h(5)+g(9)

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!

Use f(x)=-3/2+11, g(x)=x^2-7x, and h(x)= |15-9x| to evaluate the function. h(5)+g(9)

Learn how to evaluate the functions h(x) = |15 - 9x| and g(x) = x^2 - 7x at specific values. This step-by-step guide breaks down how to solve h(5) and g(9), covering absolute value and quadratic function concepts. Suitable for students in Grades 9-11.

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