Question
The Bay Grove local news channel is predicting a heat wave in the area next week. The temperature is predicted to be as high as 105 degrees Fahrenheit.
Let t represent the temperature, in degrees Fahrenheit, during the heat wave. 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 temperature, in degrees Fahrenheit, during the heat wave. 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 heat wave described in your story, we want to express that the temperature \( t \) is expected to reach as high as 105 degrees Fahrenheit. This means that the temperature can be any value that is below or equal to 105 degrees.
Thus, we can represent this situation with the following inequality:
\[ t \leq 105 \]
This inequality states that the temperature \( t \) is less than or equal to 105 degrees Fahrenheit.
### Graphing the Inequality
1. **Plot the endpoint**: First, plot the point at 105 on the temperature axis. Since the temperature can be exactly 105 degrees, you will use a closed circle at this point.
2. **Select the arrow**: Since the inequality indicates that the temperature can be anything less than or equal to 105, you will draw a ray extending to the left from the point at 105.
### Visual Representation:
- The graph will have:
- A closed circle at \( t = 105 \).
- A ray extending leftwards from that point indicating that \( t \) could be any value less than \( 105 \).
This graph visually communicates that all temperatures less than or equal to 105 degrees Fahrenheit are included in the solution to the inequality.
Feel free to let me know if you need any additional help with the graphing process!
Thus, we can represent this situation with the following inequality:
\[ t \leq 105 \]
This inequality states that the temperature \( t \) is less than or equal to 105 degrees Fahrenheit.
### Graphing the Inequality
1. **Plot the endpoint**: First, plot the point at 105 on the temperature axis. Since the temperature can be exactly 105 degrees, you will use a closed circle at this point.
2. **Select the arrow**: Since the inequality indicates that the temperature can be anything less than or equal to 105, you will draw a ray extending to the left from the point at 105.
### Visual Representation:
- The graph will have:
- A closed circle at \( t = 105 \).
- A ray extending leftwards from that point indicating that \( t \) could be any value less than \( 105 \).
This graph visually communicates that all temperatures less than or equal to 105 degrees Fahrenheit are included in the solution to the inequality.
Feel free to let me know if you need any additional help with the graphing process!