Practice worksheet for writing algebraic expressions and evaluating them, from Glencoe Algebra 1, Chapter 1.

Problem Analysis:

The image contains a worksheet titled "Variables and Expressions" from Glencoe Algebra 1. The tasks involve translating verbal expressions into algebraic expressions, evaluating numerical expressions, and writing verbal expressions for given algebraic expressions. Additionally, there are two application problems related to books and geometry.

Below, I will solve each part of the problem systematically.

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Part 1: Write an algebraic expression for each verbal expression

#### 1. The difference of 10 and \( u \)
- Verbal expression: "Difference" means subtraction.
- Algebraic expression: \( 10 - u \)

#### 2. The sum of 18 and a number
- Let the number be \( x \).
- Verbal expression: "Sum" means addition.
- Algebraic expression: \( 18 + x \)

#### 3. The product of 33 and \( j \)
- Verbal expression: "Product" means multiplication.
- Algebraic expression: \( 33j \)

#### 4. 74 increased by 3 times \( y \)
- Verbal expression: "Increased by" means addition, and "3 times \( y \)" means \( 3y \).
- Algebraic expression: \( 74 + 3y \)

#### 5. 15 decreased by twice a number
- Let the number be \( n \). "Twice a number" means \( 2n \).
- Verbal expression: "Decreased by" means subtraction.
- Algebraic expression: \( 15 - 2n \)

#### 6. 91 more than the square of a number
- Let the number be \( x \). "Square of a number" means \( x^2 \).
- Verbal expression: "More than" means addition.
- Algebraic expression: \( 91 + x^2 \)

#### 7. Three fourths the square of \( b \)
- "Three fourths" means \( \frac{3}{4} \), and "square of \( b \)" means \( b^2 \).
- Verbal expression: Multiplication.
- Algebraic expression: \( \frac{3}{4}b^2 \)

#### 8. Two fifths the cube of a number
- Let the number be \( x \). "Cube of a number" means \( x^3 \).
- Verbal expression: "Two fifths" means \( \frac{2}{5} \), and this is multiplied by \( x^3 \).
- Algebraic expression: \( \frac{2}{5}x^3 \)

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Part 2: Evaluate each expression

#### 9. \( 11^2 \)
- \( 11^2 = 11 \times 11 = 121 \)

#### 10. \( 8^3 \)
- \( 8^3 = 8 \times 8 \times 8 = 512 \)

#### 11. \( 5^4 \)
- \( 5^4 = 5 \times 5 \times 5 \times 5 = 625 \)

#### 12. \( 4^5 \)
- \( 4^5 = 4 \times 4 \times 4 \times 4 \times 4 = 1024 \)

#### 13. \( 9^3 \)
- \( 9^3 = 9 \times 9 \times 9 = 729 \)

#### 14. \( 6^4 \)
- \( 6^4 = 6 \times 6 \times 6 \times 6 = 1296 \)

#### 15. \( 10^5 \)
- \( 10^5 = 10 \times 10 \times 10 \times 10 \times 10 = 100,000 \)

#### 16. \( 12^3 \)
- \( 12^3 = 12 \times 12 \times 12 = 1728 \)

#### 17. \( 100^4 \)
- \( 100^4 = 100 \times 100 \times 100 \times 100 = 100,000,000 \)

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Part 3: Write a verbal expression for each algebraic expression

#### 18. \( 23f \)
- Verbal expression: "The product of 23 and \( f \)" or "23 times \( f \)"

#### 19. \( p^5 \)
- Verbal expression: "The fifth power of \( p \)" or "\( p \) raised to the fifth power"

#### 20. \( 5m^2 + 2 \)
- Verbal expression: "Five times the square of \( m \), plus 2"

#### 21. \( 4d^3 - 10 \)
- Verbal expression: "Four times the cube of \( d \), minus 10"

#### 22. \( x^3 \cdot y^4 \)
- Verbal expression: "The cube of \( x \) multiplied by the fourth power of \( y \)"

#### 23. \( b^2 - 3c^3 \)
- Verbal expression: "The square of \( b \), minus three times the cube of \( c \)"

#### 24. \( \frac{k^5}{6} \)
- Verbal expression: "The fifth power of \( k \), divided by 6"

#### 25. \( \frac{4n^2}{7} \)
- Verbal expression: "Four times the square of \( n \), divided by 7"

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Part 4: Application Problems

#### 26. Books
- A used bookstore sells excellent-condition paperbacks for \$2.50 and fair-condition paperbacks for \$0.50.
- Let \( e \) be the number of excellent-condition paperbacks and \( f \) be the number of fair-condition paperbacks.
- Cost of \( e \) excellent-condition paperbacks: \( 2.50e \)
- Cost of \( f \) fair-condition paperbacks: \( 0.50f \)
- Total cost: \( 2.50e + 0.50f \)

#### 27. Geometry
- The surface area of the side of a right cylinder is found by multiplying twice the number \( \pi \) by the radius \( r \) times the height \( h \).
- Given: Radius \( r \) and height \( h \).
- Surface area of the side: \( 2\pi r h \)

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Final Answers:

1. \( 10 - u \)
2. \( 18 + x \)
3. \( 33j \)
4. \( 74 + 3y \)
5. \( 15 - 2n \)
6. \( 91 + x^2 \)
7. \( \frac{3}{4}b^2 \)
8. \( \frac{2}{5}x^3 \)

9. \( 121 \)
10. \( 512 \)
11. \( 625 \)
12. \( 1024 \)
13. \( 729 \)
14. \( 1296 \)
15. \( 100,000 \)
16. \( 1728 \)
17. \( 100,000,000 \)

18. "The product of 23 and \( f \)"
19. "\( p \) raised to the fifth power"
20. "Five times the square of \( m \), plus 2"
21. "Four times the cube of \( d \), minus 10"
22. "The cube of \( x \) multiplied by the fourth power of \( y \)"
23. "The square of \( b \), minus three times the cube of \( c \)"
24. "The fifth power of \( k \), divided by 6"
25. "Four times the square of \( n \), divided by 7"

26. \( 2.50e + 0.50f \)
27. \( 2\pi r h \)

Boxed Final Answer:
\[
\boxed{2.50e + 0.50f \quad \text{and} \quad 2\pi r h}
\]