https://file.aiquickdraw.com/mathbot/file/1729261997180h1r0d0pp.jpg

Let's go through the questions in your image one by one.

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### 17. Evaluate: \( x^3 - zy^2 \) if \( x = -2 \), \( z = 5 \), and \( y = -3 \)

Substitute the values:

\[
x^3 - zy^2 = (-2)^3 - 5(-3)^2
\]

\[
= -8 - 5(9) = -8 - 45 = -53
\]

The correct answer is **[A] -53**.

---

### 18. Simplify: \( x^3 y x y^2 x^3 z \)

Combine the like terms by adding the exponents of the same variables:

\[
x^3 \cdot x \cdot x^3 = x^{3+1+3} = x^7
\]
\[
y \cdot y^2 = y^{1+2} = y^3
\]
Thus, the expression simplifies to:

\[
x^7 y^3 z
\]

The correct answer is **[E] None of these** (as no given option matches).

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### 19. Solve: \( \frac{y}{2 \frac{1}{3}} = 15 \)

First, convert \( 2 \frac{1}{3} \) to an improper fraction:

\[
2 \frac{1}{3} = \frac{7}{3}
\]

Now, solve the equation:

\[
\frac{y}{\frac{7}{3}} = 15
\]

Multiply both sides by \( \frac{7}{3} \):

\[
y = 15 \times \frac{7}{3} = \frac{105}{3} = 35
\]

The correct answer is **[A] \( y = 35 \)**.

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### 20. Solve: \( s - 16 = -31 \)

Add 16 to both sides:

\[
s = -31 + 16 = -15
\]

The correct answer is **[E] None of these** (no option is exactly \( s = -15 \)).

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Would you like further details on any of these solutions? Here are five related questions:

1. How do you simplify expressions with multiple variables?
2. What is the general approach to evaluating an expression by substituting variables?
3. Can you explain how to solve linear equations step-by-step?
4. What is the difference between improper fractions and mixed numbers?
5. How can combining exponents of the same variable be applied in more complex problems?

**Tip**: When combining terms with the same base, remember to add exponents when multiplying and subtract them when dividing.

Evaluate the expressions, simplify terms, and solve equations as shown in the image.

Learn how to evaluate algebraic expressions by substituting values, simplify terms with exponents, and solve linear equations. Detailed step-by-step solutions for problems involving operations with variables, exponent rules, and conversion between mixed and improper fractions. Suitable for Grades 7-9.

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