Math Problem Statement

Find h(4) for h(n) = -2n + 4 and find h(-2) for h(t) = -2 * 5 - t - 1

Solution

Let's solve the two problems shown in the image.

Problem 3:

The function given is h(n)=2n+4h(n) = -2n + 4. We need to find h(4)h(4).

Solution: Substitute n=4n = 4 into the function:

h(4)=2(4)+4=8+4=4h(4) = -2(4) + 4 = -8 + 4 = -4

So, h(4)=4h(4) = -4.

Problem 4:

The function given is h(t)=25t1h(t) = -2 \cdot 5 - t - 1. We need to find h(2)h(-2).

Solution: First, simplify the function. It looks like there may be some confusion with the expression, but assuming it is:

h(t)=2×5t1h(t) = -2 \times 5 - t - 1

Simplifying further:

h(t)=10t1=t11h(t) = -10 - t - 1 = -t - 11

Now substitute t=2t = -2 into the function:

h(2)=(2)11=211=9h(-2) = -(-2) - 11 = 2 - 11 = -9

So, h(2)=9h(-2) = -9.

Would you like any more details, or do you have any questions? Here are some related questions you might find interesting:

  1. What would h(n)h(n) be if n=3n = -3 in problem 3?
  2. Can you rewrite the function in problem 4 in a different form?
  3. What is the general method for evaluating a function at a specific value?
  4. How would the results change if the coefficient of tt in problem 4 were positive?
  5. How can you check your answers to these types of problems?

Tip: Always double-check the original function to ensure you're simplifying it correctly before substituting values.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Functions

Formulas

h(n) = -2n + 4
h(t) = -10 - t - 1

Theorems

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Suitable Grade Level

Grades 7-9