Let's evaluate each expression step by step for the given values of the variables.
### Problem 31
Evaluate the expression [tex]\(4t + 7\)[/tex] for [tex]\(t = 7\)[/tex]:
1. Substitute [tex]\(t = 7\)[/tex] into the expression: [tex]\(4(7) + 7\)[/tex].
2. Calculate [tex]\(4 \times 7 = 28\)[/tex].
3. Add 7 to the result: [tex]\(28 + 7 = 35\)[/tex].
So, the value of [tex]\(4t + 7\)[/tex] when [tex]\(t = 7\)[/tex] is 35.
### Problem 32
Evaluate the expression [tex]\(5w - 7\)[/tex] for [tex]\(w = -4\)[/tex]:
1. Substitute [tex]\(w = -4\)[/tex] into the expression: [tex]\(5(-4) - 7\)[/tex].
2. Calculate [tex]\(5 \times (-4) = -20\)[/tex].
3. Subtract 7 from the result: [tex]\(-20 - 7 = -27\)[/tex].
So, the value of [tex]\(5w - 7\)[/tex] when [tex]\(w = -4\)[/tex] is -27.
### Problem 33
Evaluate the expression [tex]\(\frac{g}{3} + (-2)\)[/tex] for [tex]\(g = 9\)[/tex]:
1. Substitute [tex]\(g = 9\)[/tex] into the expression: [tex]\(\frac{9}{3} + (-2)\)[/tex].
2. Calculate [tex]\(\frac{9}{3} = 3\)[/tex].
3. Add [tex]\(-2\)[/tex] to the result: [tex]\(3 + (-2) = 1\)[/tex].
So, the value of [tex]\(\frac{g}{3} + (-2)\)[/tex] when [tex]\(g = 9\)[/tex] is 1.
### Problem 34
Evaluate the expression [tex]\((h + 9)(h - 9)\)[/tex] for [tex]\(h = 11\)[/tex]:
1. Substitute [tex]\(h = 11\)[/tex] into the expression: [tex]\((11 + 9)(11 - 9)\)[/tex].
2. Calculate the sum inside the parentheses: [tex]\(h + 9 = 11 + 9 = 20\)[/tex].
3. Calculate the difference inside the parentheses: [tex]\(h - 9 = 11 - 9 = 2\)[/tex].
4. Multiply the results: [tex]\(20 \times 2 = 40\)[/tex].
So, the value of [tex]\((h + 9)(h - 9)\)[/tex] when [tex]\(h = 11\)[/tex] is 40.
In summary, the evaluated values are:
- [tex]\(31. \; 4t + 7\; \text{for}\; t = 7\)[/tex] is 35.
- [tex]\(32. \; 5w - 7\; \text{for}\; w = -4\)[/tex] is -27.
- [tex]\(33. \; \frac{g}{3} + (-2)\; \text{for}\; g = 9\)[/tex] is 1.
- [tex]\(34. \; (h + 9)(h - 9)\; \text{for}\; h = 11\)[/tex] is 40.
