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Let's solve each question on this worksheet.

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### 1. Coin Machine Inequality
The machine only accepts dimes and quarters, with:
- Dime worth: $0.10
- Quarter worth: $0.25
- Maximum capacity: $50.00

Let $ x $ be the number of dimes and $ y $ be the number of quarters. The inequality representing the maximum amount is:
\[
0.10x + 0.25y \leq 50.00
\]
Thus, the correct answer is **A**.

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### 2. Soil Remaining with Succulents
The table shows the amount of soil remaining as succulents are planted. This forms a linear relationship, as each additional succulent reduces soil by a constant amount.

To find the function $ f(x) $:
1. The soil starts at 12 ounces when $ x = 0 $.
2. With each additional succulent, the soil decreases by approximately 0.6 ounces.

So, the equation is:
\[
f(x) = -0.6x + 12
\]
Thus, the correct answer is **A**.

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### 3. Expression Interpretation
The expression given is $ 30 + 7.59x $, where:
- 30 represents a fixed amount, perhaps the cost of the drill.
- $ 7.59 $ is multiplied by $ x $, indicating it's the cost per box of screws.

Therefore, $ 7.59 $ represents **the cost per box of screws**.

So, the correct answer is **A**.

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### 4. Y-Intercept Interpretation
The function $ f(x) = -1.50x + 25 $ represents the remaining amount of money after purchasing tickets at a fair.
- The y-intercept occurs when $ x = 0 $, which is $ f(0) = 25 $.
- This represents the initial amount of money before buying any tickets.

Thus, the y-intercept represents **the amount of money, in dollars, the student has when 0 tickets have been purchased**.

So, the correct answer is **B**.

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### 5. Graph Interpretation
Without the full graph displayed here, it's difficult to solve specifically, but the question would likely involve interpreting the slope, y-intercept, or trend of the function based on the graph. 

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Would you like further details on any of these answers?

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**Related Questions:**
1. How would the inequality change if quarters were worth $0.30?
2. If the price of each ticket in question 4 increased, how would that affect the function's slope?
3. What would be the effect on the function in question 2 if each succulent reduced soil by 1 ounce?
4. For question 3, what would the fixed cost represent if $ 30 $ were changed?
5. How does the y-intercept help us understand initial values in linear functions?

**Tip:** Always check the units and context of each term in expressions to interpret functions accurately.

Solve the math worksheet questions involving inequalities, functions, and interpreting expressions.

Learn how to solve problems involving linear inequalities, functions, and expressions with detailed explanations and step-by-step solutions. Covers key concepts in Algebra I, including interpreting graphs and finding function models based on real-world scenarios. Suitable for Grades 9-10.

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