Sure, let's evaluate each expression step-by-step:
### Part a:
Evaluate the expression [tex]\(-7x^3 + 3x^2 + 11x - 9\)[/tex] for [tex]\(x = -2\)[/tex].
1. Substitute [tex]\(x = -2\)[/tex] into the expression:
[tex]\[-7(-2)^3 + 3(-2)^2 + 11(-2) - 9\][/tex]
2. Next, calculate each term:
[tex]\((-2)^3 = -8\)[/tex]
[tex]\[-7 \cdot (-8) = 56\][/tex]
[tex]\((-2)^2 = 4\)[/tex]
[tex]\[3 \cdot 4 = 12\][/tex]
[tex]\[11 \cdot (-2) = -22\][/tex]
3. Combine these results:
[tex]\[56 + 12 - 22 - 9\][/tex]
4. Simplify:
[tex]\[56 + 12 = 68\][/tex]
[tex]\[68 - 22 = 46\][/tex]
[tex]\[46 - 9 = 37\][/tex]
So, the result for part a is [tex]\(\boxed{37}\)[/tex].
### Part t:
Evaluate the expression [tex]\(4y^2 - 3y + 8\)[/tex] for [tex]\(y = -3\)[/tex].
1. Substitute [tex]\(y = -3\)[/tex] into the expression:
[tex]\[4(-3)^2 - 3(-3) + 8\][/tex]
2. Next, calculate each term:
[tex]\((-3)^2 = 9\)[/tex]
[tex]\[4 \cdot 9 = 36\][/tex]
[tex]\[-3 \cdot (-3) = 9\][/tex]
3. Combine these results:
[tex]\[36 + 9 + 8\][/tex]
4. Simplify:
[tex]\[36 + 9 = 45\][/tex]
[tex]\[45 + 8 = 53\][/tex]
So, the result for part t is [tex]\(\boxed{53}\)[/tex].
### Part c:
Evaluate the expression [tex]\(14x^2y + 3xy^2 + 2xy - 5\)[/tex] for [tex]\(x = 1\)[/tex] and [tex]\(y = 2\)[/tex].
1. Substitute [tex]\(x = 1\)[/tex] and [tex]\(y = 2\)[/tex] into the expression:
[tex]\[14(1)^2(2) + 3(1)(2)^2 + 2(1)(2) - 5\][/tex]
2. Next, calculate each term:
[tex]\((1)^2 = 1\)[/tex]
[tex]\[14 \cdot 1 \cdot 2 = 28\][/tex]
[tex]\[(2)^2 = 4\][/tex]
[tex]\[3 \cdot 1 \cdot 4 = 12\][/tex]
[tex]\[2 \cdot 1 \cdot 2 = 4\][/tex]
3. Combine these results:
[tex]\[28 + 12 + 4 - 5\][/tex]
4. Simplify:
[tex]\[28 + 12 = 40\][/tex]
[tex]\[40 + 4 = 44\][/tex]
[tex]\[44 - 5 = 39\][/tex]
So, the result for part c is [tex]\(\boxed{39}\)[/tex].
In summary, the results are:
- Part a: [tex]\(\boxed{37}\)[/tex]
- Part t: [tex]\(\boxed{53}\)[/tex]
- Part c: [tex]\(\boxed{39}\)[/tex]
