https://file.aiquickdraw.com/mathbot/file/1726941567008pbygkzne.jpg

Let's go over the questions from the image one by one:

### 29. Communicate and Justify
**Question:** Which track member’s long jump length would be represented by the point closest to, but not equal to, 0 on the number line?

**Explanation:**
The table shows the long jump lengths relative to the state qualifying distance:
- Theresa: -5.625 in.
- Ann: 2 in.
- Shirley: -3 in.
- Delia: 0 in.

When plotting these values on a number line, we can see that Ann's jump of **2 inches** is the closest value to 0, but it is not equal to 0. So, **Ann's long jump** would be represented by the point closest to 0 on the number line.

### 30. Delia’s relative long jump length was recorded as 0. What does this mean?
This means that Delia's jump was exactly the same as the state qualifying distance. She neither exceeded nor fell short of the required distance for qualification.

### 31. Check for Reasonableness
**Question:** Which track members did NOT qualify for the state championship? Construct an argument to explain how you know.

To qualify for the state championship, the athlete’s long jump must meet or exceed the state qualifying distance, which is represented by 0 inches. Looking at the table:
- **Theresa:** -5.625 in. (did not qualify, as she jumped short of the qualifying distance by 5.625 inches)
- **Ann:** 2 in. (qualified, as she exceeded the qualifying distance by 2 inches)
- **Shirley:** -3 in. (did not qualify, as she jumped short of the qualifying distance by 3 inches)
- **Delia:** 0 in. (qualified, as she matched the qualifying distance exactly)

So, **Theresa and Shirley did not qualify**, while **Ann and Delia qualified**.

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### Related Questions:
1. How would the number line look if all the jumps were plotted?
2. What is the average of all the long jumps listed in the table?
3. How much more or less did Theresa need to jump to meet the qualifying distance?
4. If Shirley improved her jump by 4 inches, would she qualify?
5. How would you graph these jumps visually to compare them?

**Tip:** When interpreting data on a number line, remember that values to the right of zero are positive (above the target), while values to the left are negative (below the target).

Which track member’s long jump length would be represented by the point closest to, but not equal to, 0 on the number line?

In this math problem, students learn how to interpret long jump distances relative to a state qualifying distance using a number line. This example involves comparing four jump lengths and identifying the one closest to zero.

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