Question
Sarah's school is holding a read-a-thon challenge to encourage students to spend time reading. Sarah read for 6.5 hours last week. This week, she set a goal to either match or beat last week's time.
Let t represent the time, in hours, Sarah plans to read this week. 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 t represent the time, in hours, Sarah plans to read this week. 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 Sarah's goal for reading this week, we can represent the time she plans to read with the variable \( t \). Since Sarah wants to match or beat her reading time from last week, which was 6.5 hours, the appropriate inequality would be:
\[ t \geq 6.5 \]
This means that the time \( t \) that Sarah reads this week must be greater than or equal to 6.5 hours.
### Graphing the Inequality:
1. **Select the endpoint**: The endpoint will be at \( 6.5 \) on the number line, since she wants to read at least that much time.
2. **Closed Endpoint**: Since the inequality includes "equal to" (≥), we need a closed circle at \( 6.5 \).
3. **Ray**: Draw a ray to the right of \( 6.5 \) to indicate that \( t \) can be any value greater than 6.5 hours.
### Visualization:
- On a number line, mark the point \( 6.5 \).
- Draw a closed circle at \( 6.5 \) (indicating it is included).
- Draw a ray starting from \( 6.5 \) and going to the right, indicating all values greater than 6.5 hours.
### Summary:
The inequality that models Sarah's reading time is \( t \geq 6.5 \), and the graph of this inequality shows a closed circle at \( 6.5 \) with a ray extending to the right.
\[ t \geq 6.5 \]
This means that the time \( t \) that Sarah reads this week must be greater than or equal to 6.5 hours.
### Graphing the Inequality:
1. **Select the endpoint**: The endpoint will be at \( 6.5 \) on the number line, since she wants to read at least that much time.
2. **Closed Endpoint**: Since the inequality includes "equal to" (≥), we need a closed circle at \( 6.5 \).
3. **Ray**: Draw a ray to the right of \( 6.5 \) to indicate that \( t \) can be any value greater than 6.5 hours.
### Visualization:
- On a number line, mark the point \( 6.5 \).
- Draw a closed circle at \( 6.5 \) (indicating it is included).
- Draw a ray starting from \( 6.5 \) and going to the right, indicating all values greater than 6.5 hours.
### Summary:
The inequality that models Sarah's reading time is \( t \geq 6.5 \), and the graph of this inequality shows a closed circle at \( 6.5 \) with a ray extending to the right.