Question
Arianna has been growing her hair out for years to donate to a wig charity. Today, she plans to cut off at least 9 inches for the donation.
Let 𝓁 represent the length, in inches, of the hair Arianna might cut off. 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, of the hair Arianna might cut off. 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 the story of Arianna cutting her hair, we can create an inequality based on the information provided. She plans to cut off at least 9 inches of hair, which means she could cut off any amount of hair greater than or equal to 9 inches.
We can express this situation with the following inequality:
\[ \ell \geq 9 \]
Where:
- \( \ell \) represents the length of hair (in inches) that Arianna might cut off.
### Graphing the Inequality
1. **Drawing the Ray:**
- Start by plotting a point on the number line at \( \ell = 9 \).
2. **Closed or Open Endpoint:**
- Since the inequality includes "at least", the endpoint at \( \ell = 9 \) should be **closed** (indicating that 9 inches is included in the possible lengths that can be cut off).
3. **Direction of the Ray:**
- Since Arianna can cut off lengths greater than 9 inches, draw a ray extending to the right from the closed endpoint at \( 9 \).
### Finished Graph
- The graph will have a closed circle at \( 9 \) (indicating that 9 is included), and a ray extending to the right towards positive infinity, representing all values greater than 9.
If you're visualizing this on the number line:
- Draw a vertical line and place a closed circle on the 9.
- Draw a continuous line to the right from that point, continuing indefinitely.
This represents the inequality \( \ell \geq 9 \).
We can express this situation with the following inequality:
\[ \ell \geq 9 \]
Where:
- \( \ell \) represents the length of hair (in inches) that Arianna might cut off.
### Graphing the Inequality
1. **Drawing the Ray:**
- Start by plotting a point on the number line at \( \ell = 9 \).
2. **Closed or Open Endpoint:**
- Since the inequality includes "at least", the endpoint at \( \ell = 9 \) should be **closed** (indicating that 9 inches is included in the possible lengths that can be cut off).
3. **Direction of the Ray:**
- Since Arianna can cut off lengths greater than 9 inches, draw a ray extending to the right from the closed endpoint at \( 9 \).
### Finished Graph
- The graph will have a closed circle at \( 9 \) (indicating that 9 is included), and a ray extending to the right towards positive infinity, representing all values greater than 9.
If you're visualizing this on the number line:
- Draw a vertical line and place a closed circle on the 9.
- Draw a continuous line to the right from that point, continuing indefinitely.
This represents the inequality \( \ell \geq 9 \).