Question
Devin wants to be a superhero for Halloween and is making his own costume. He doesn't want to trip over his cape, so Devin plans to make it at most 46.75 inches long.
Let 𝓁 represent the length, in inches, that Devin's cape might be. Which inequality models the story?
Graph the inequality that models the story.
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.
Let 𝓁 represent the length, in inches, that Devin's cape might be. Which inequality models the story?
Graph the inequality that models the story.
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.
Answers
GPT-4o mini
To model Devin's cape length using an inequality, we can express the constraints on the length \( \ell \) as follows:
\[
\ell \leq 46.75
\]
This inequality states that the length \( \ell \) of the cape can be any value that is less than or equal to 46.75 inches.
### Graphing the Inequality
1. **Identify the endpoint:** The endpoint for this inequality would be at 46.75 on the number line.
2. **Determine whether the endpoint is included:** Since the inequality is \( \ell \leq 46.75 \), this means that 46.75 is included in the solution set. So, you would use a closed circle on the 46.75 mark.
3. **Shading the region:** You will shade to the left of the closed circle because \( \ell \) can take any value up to and including 46.75 inches.
Here's how to graph it:
1. Draw a number line.
2. Locate the point 46.75 on the number line.
3. Place a closed circle on 46.75 to indicate that this value is included in the solution.
4. Shade the region to the left of 46.75 to represent all values less than or equal to 46.75.
### Summary
- The inequality is \( \ell \leq 46.75 \).
- The graph includes a closed circle at 46.75 and a shaded line extending to the left.
\[
\ell \leq 46.75
\]
This inequality states that the length \( \ell \) of the cape can be any value that is less than or equal to 46.75 inches.
### Graphing the Inequality
1. **Identify the endpoint:** The endpoint for this inequality would be at 46.75 on the number line.
2. **Determine whether the endpoint is included:** Since the inequality is \( \ell \leq 46.75 \), this means that 46.75 is included in the solution set. So, you would use a closed circle on the 46.75 mark.
3. **Shading the region:** You will shade to the left of the closed circle because \( \ell \) can take any value up to and including 46.75 inches.
Here's how to graph it:
1. Draw a number line.
2. Locate the point 46.75 on the number line.
3. Place a closed circle on 46.75 to indicate that this value is included in the solution.
4. Shade the region to the left of 46.75 to represent all values less than or equal to 46.75.
### Summary
- The inequality is \( \ell \leq 46.75 \).
- The graph includes a closed circle at 46.75 and a shaded line extending to the left.