Evaluate Expressions worksheet with algebraic problems for various variables.

To solve the problem, we need to evaluate each expression by substituting the given values for the variables. Let's go through each section step by step.

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Section 1: Evaluate the following expressions for \( x = 4 \)

1. \( x + 16 \)
\[
x + 16 = 4 + 16 = 20
\]

2. \( 2x - 20 \)
\[
2x - 20 = 2(4) - 20 = 8 - 20 = -12
\]

3. \( 10 + x^2 \)
\[
10 + x^2 = 10 + 4^2 = 10 + 16 = 26
\]

4. \( -x - 12 \)
\[
-x - 12 = -(4) - 12 = -4 - 12 = -16
\]

5. \( x - 2x \)
\[
x - 2x = 4 - 2(4) = 4 - 8 = -4
\]

6. \( x^3 - 20 \)
\[
x^3 - 20 = 4^3 - 20 = 64 - 20 = 44
\]

---

Section 2: Evaluate the following expressions for \( h = 3 \)

1. \( 3h + 9 \)
\[
3h + 9 = 3(3) + 9 = 9 + 9 = 18
\]

2. \( 19 + h^2 \)
\[
19 + h^2 = 19 + 3^2 = 19 + 9 = 28
\]

3. \( h + 14 \)
\[
h + 14 = 3 + 14 = 17
\]

4. \( -2h + 14 \)
\[
-2h + 14 = -2(3) + 14 = -6 + 14 = 8
\]

5. \( 2h + 15 \)
\[
2h + 15 = 2(3) + 15 = 6 + 15 = 21
\]

6. \( h^0 + 12 \)
\[
h^0 + 12 = 3^0 + 12 = 1 + 12 = 13
\]

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Section 3: Evaluate the following expressions for \( y = 10 \)

1. \( 4y - 8 \)
\[
4y - 8 = 4(10) - 8 = 40 - 8 = 32
\]

2. \( 22 - y^2 \)
\[
22 - y^2 = 22 - 10^2 = 22 - 100 = -78
\]

3. \( y + 10 \)
\[
y + 10 = 10 + 10 = 20
\]

4. \( -y + 25 \)
\[
-y + 25 = -(10) + 25 = -10 + 25 = 15
\]

5. \( y - 15 \)
\[
y - 15 = 10 - 15 = -5
\]

6. \( y^2 - 12 \)
\[
y^2 - 12 = 10^2 - 12 = 100 - 12 = 88
\]

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Section 4: Evaluate the following expressions for \( t = -5 \)

1. \( 2t + 6 \)
\[
2t + 6 = 2(-5) + 6 = -10 + 6 = -4
\]

2. \( 22 + t^2 \)
\[
22 + t^2 = 22 + (-5)^2 = 22 + 25 = 47
\]

3. \( t - 10 \)
\[
t - 10 = -5 - 10 = -15
\]

4. \( -4t + 18 \)
\[
-4t + 18 = -4(-5) + 18 = 20 + 18 = 38
\]

5. \( 2t - 10 \)
\[
2t - 10 = 2(-5) - 10 = -10 - 10 = -20
\]

6. \( t^3 + 75 \)
\[
t^3 + 75 = (-5)^3 + 75 = -125 + 75 = -50
\]

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Section 5: Evaluate the following expressions for \( v = 0.5 \)

1. \( v^1 + 4 \)
\[
v^1 + 4 = 0.5^1 + 4 = 0.5 + 4 = 4.5
\]

2. \( 3v + 6 \)
\[
3v + 6 = 3(0.5) + 6 = 1.5 + 6 = 7.5
\]

3. \( 12 + v^0 \)
\[
12 + v^0 = 12 + 0.5^0 = 12 + 1 = 13
\]

4. \( v + 17 \)
\[
v + 17 = 0.5 + 17 = 17.5
\]

5. \( -2v + 10 \)
\[
-2v + 10 = -2(0.5) + 10 = -1 + 10 = 9
\]

6. \( v + 5 \)
\[
v + 5 = 0.5 + 5 = 5.5
\]

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Final Answer

\[
\boxed{
\begin{array}{lll}
x + 16 = 20 & 2x - 20 = -12 & 10 + x^2 = 26 \\
-x - 12 = -16 & x - 2x = -4 & x^3 - 20 = 44 \\
3h + 9 = 18 & 19 + h^2 = 28 & h + 14 = 17 \\
-2h + 14 = 8 & 2h + 15 = 21 & h^0 + 12 = 13 \\
4y - 8 = 32 & 22 - y^2 = -78 & y + 10 = 20 \\
-y + 25 = 15 & y - 15 = -5 & y^2 - 12 = 88 \\
2t + 6 = -4 & 22 + t^2 = 47 & t - 10 = -15 \\
-4t + 18 = 38 & 2t - 10 = -20 & t^3 + 75 = -50 \\
v^1 + 4 = 4.5 & 3v + 6 = 7.5 & 12 + v^0 = 13 \\
v + 17 = 17.5 & -2v + 10 = 9 & v + 5 = 5.5 \\
\end{array}
}
\]