Question
Cody and his friend Scott made a banner to carry during the Memorial Day parade. They need to buy a pole from which to hang their 54-inch-long banner. The pole needs to be longer than the banner so that they can each hold one end.
Let p represent how long, in inches, the pole 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 p represent how long, in inches, the pole 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 the situation described in the story, we need to express the relationship between the length of the pole \( p \) and the length of the banner, which is 54 inches. Since the pole needs to be longer than the banner, the inequality can be written as:
\[
p > 54
\]
### Graphing the Inequality:
1. **Draw a number line**: First, draw a horizontal line and mark appropriate values for the pole length, including at least the value 54.
2. **Plot the point**: Mark the point at 54 on the number line.
3. **Select the open endpoint**: Since the inequality is \( p > 54 \), we'll use an open circle at 54, indicating that 54 is not included in the solution set.
4. **Draw the ray**: From 54, draw a ray extending to the right to indicate that \( p \) can take any value greater than 54. You can place an arrow at the end of the ray to indicate it continues indefinitely.
### Summary:
The inequality that models the situation is \( p > 54 \), and the graph will have an open circle at 54 and a ray extending to the right. Would you like any more help with this problem or anything else?
\[
p > 54
\]
### Graphing the Inequality:
1. **Draw a number line**: First, draw a horizontal line and mark appropriate values for the pole length, including at least the value 54.
2. **Plot the point**: Mark the point at 54 on the number line.
3. **Select the open endpoint**: Since the inequality is \( p > 54 \), we'll use an open circle at 54, indicating that 54 is not included in the solution set.
4. **Draw the ray**: From 54, draw a ray extending to the right to indicate that \( p \) can take any value greater than 54. You can place an arrow at the end of the ray to indicate it continues indefinitely.
### Summary:
The inequality that models the situation is \( p > 54 \), and the graph will have an open circle at 54 and a ray extending to the right. Would you like any more help with this problem or anything else?