Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

The table represents a bicycle rental cost in dollars as a function of time in hours.

| Time (hours) | Cost (\[tex]$) |
|--------------|-----------|
| 0 | 0 |
| 2 | 10 |
| 4 | 20 |
| 6 | 30 |
| 8 | 40 |

Which explains whether or not the function represents a direct variation?

A. This function represents a direct variation because it passes through the origin and has a constant rate of change of $[/tex]5 per hour.
B. This function represents a direct variation because it has a positive, constant rate of change of [tex]$10 per hour.
C. This function does not represent a direct variation because it does not represent the cost for 1 hour.
D. This function does not represent a direct variation because the function rule for the cost is to add $[/tex]10, not multiply by a constant.

Sagot :

GinnyAnswer
Let's determine whether the given data represents a direct variation by examining its properties.

First, recall that a function represents a direct variation if:
1. The graph passes through the origin (0, 0).
2. The function has a constant rate of change (slope).

Here are the given data points:
- Time (hours): 0, 2, 4, 6, 8
- Cost (dollars): 0, 10, 20, 30, 40

### Step-by-Step Analysis

1. Passes through the origin:
- We check the point (0, 0) in the table:
- Time = 0 hours, Cost = \[tex]$0 - Since the function passes through the origin (0, 0), this condition is satisfied. 2. Constant rate of change: - Calculate the rate of change between consecutive data points: \[ \text{Rate of Change} = \frac{\text{Change in Cost}}{\text{Change in Time}} \] - Between (0, 0) and (2, 10): \[ \frac{10 - 0}{2 - 0} = \frac{10}{2} = 5 \] - Between (2, 10) and (4, 20): \[ \frac{20 - 10}{4 - 2} = \frac{10}{2} = 5 \] - Between (4, 20) and (6, 30): \[ \frac{30 - 20}{6 - 4} = \frac{10}{2} = 5 \] - Between (6, 30) and (8, 40): \[ \frac{40 - 30}{8 - 6} = \frac{10}{2} = 5 \] - The rate of change is constant and equals \$[/tex]5 per hour.

Since the function passes through the origin and has a constant rate of change of \[tex]$5 per hour, it satisfies the conditions of a direct variation. ### Conclusion The correct explanation is: This function represents a direct variation because it passes through the origin and has a constant rate of change of \$[/tex]5 per hour.
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.