To solve the given problems, we need to substitute the provided values of the variables into each algebraic expression and simplify step by step. Let's go through each problem:
---
Problem 1: \( a^2 - 15 \) at \( a = 5 \)
1. Substitute \( a = 5 \) into the expression:
\[
a^2 - 15 = 5^2 - 15
\]
2. Calculate \( 5^2 \):
\[
5^2 = 25
\]
3. Subtract 15 from 25:
\[
25 - 15 = 10
\]
Answer:
\[
\boxed{10}
\]
---
Problem 2: \( x(x + 12) \) at \( x = 4 \)
1. Substitute \( x = 4 \) into the expression:
\[
x(x + 12) = 4(4 + 12)
\]
2. Simplify inside the parentheses:
\[
4 + 12 = 16
\]
3. Multiply:
\[
4 \cdot 16 = 64
\]
Answer:
\[
\boxed{64}
\]
---
Problem 3: \( \frac{d}{2} - 1 \) at \( d = 16 \)
1. Substitute \( d = 16 \) into the expression:
\[
\frac{d}{2} - 1 = \frac{16}{2} - 1
\]
2. Divide 16 by 2:
\[
\frac{16}{2} = 8
\]
3. Subtract 1:
\[
8 - 1 = 7
\]
Answer:
\[
\boxed{7}
\]
---
Problem 4: \( 9 - b \) at \( b = 2 \)
1. Substitute \( b = 2 \) into the expression:
\[
9 - b = 9 - 2
\]
2. Subtract:
\[
9 - 2 = 7
\]
Answer:
\[
\boxed{7}
\]
---
Problem 5: \( 13 - v \) at \( v = 2 \)
1. Substitute \( v = 2 \) into the expression:
\[
13 - v = 13 - 2
\]
2. Subtract:
\[
13 - 2 = 11
\]
Answer:
\[
\boxed{11}
\]
---
Problem 6: \( \frac{x}{2} + 6 \) at \( x = 1 \)
1. Substitute \( x = 1 \) into the expression:
\[
\frac{x}{2} + 6 = \frac{1}{2} + 6
\]
2. Add the fractions:
\[
\frac{1}{2} + 6 = \frac{1}{2} + \frac{12}{2} = \frac{13}{2}
\]
Answer:
\[
\boxed{\frac{13}{2}}
\]
---
Problem 7: \( (y + 2)^2 \) at \( y = 4 \)
1. Substitute \( y = 4 \) into the expression:
\[
(y + 2)^2 = (4 + 2)^2
\]
2. Simplify inside the parentheses:
\[
4 + 2 = 6
\]
3. Square 6:
\[
6^2 = 36
\]
Answer:
\[
\boxed{36}
\]
---
Problem 8: \( 5(x + 9) \) at \( x = -14 \)
1. Substitute \( x = -14 \) into the expression:
\[
5(x + 9) = 5(-14 + 9)
\]
2. Simplify inside the parentheses:
\[
-14 + 9 = -5
\]
3. Multiply:
\[
5 \cdot (-5) = -25
\]
Answer:
\[
\boxed{-25}
\]
---
Problem 9: \( \frac{9}{z} - 1 \) at \( z = 9 \)
1. Substitute \( z = 9 \) into the expression:
\[
\frac{9}{z} - 1 = \frac{9}{9} - 1
\]
2. Simplify the fraction:
\[
\frac{9}{9} = 1
\]
3. Subtract:
\[
1 - 1 = 0
\]
Answer:
\[
\boxed{0}
\]
---
Problem 10: \( \frac{25}{r - 4} \) at \( r = 9 \)
1. Substitute \( r = 9 \) into the expression:
\[
\frac{25}{r - 4} = \frac{25}{9 - 4}
\]
2. Simplify the denominator:
\[
9 - 4 = 5
\]
3. Divide:
\[
\frac{25}{5} = 5
\]
Answer:
\[
\boxed{5}
\]
---
Final Answers:
\[
\boxed{10, 64, 7, 7, 11, \frac{13}{2}, 36, -25, 0, 5}
\]
Parent Tip: Review the logic above to help your child master the concept of evaluating expressions worksheet.
