Question
The vertical number line below represents a diving board and a pool. The diving board is 10 feet high and the pool has a depth of 6 feet.
The vertical number line shows numbers from -6 to 10 in increments of 2 has point B at -5, point C is at 0 and point A is at 10.
Enrique stands on the diving board, which is at point A on the number line. He jumps off of the diving board and ends up at point B. After a few seconds, he swims to point C on the number line.
Determine whether each statement below is true or false. Select True or False for each statement.
Statement
True
False
The equation I 10 - (-5)I = 15
represents the difference between the highest point and the lowest point for Enrique.
Enrique is underwater at point B.
The change in elevation for Enrique from point B to point C is represented by the equation
(-5) - 0 = -5
Answers
GPT-4o mini
Let's evaluate each statement one by one:
1. **The equation |10 - (-5)| = 15 represents the difference between the highest point and the lowest point for Enrique.**
- The highest point (diving board) is at point A (10 feet) and the lowest point (where Enrique lands) is at point B (-5 feet). So, the difference is calculated as:
\[
|10 - (-5)| = |10 + 5| = |15| = 15
\]
- **This statement is True.**
2. **Enrique is underwater at point B.**
- Point B is at -5 feet, and since the surface of the water is at 0 feet, any depth below 0 feet is considered underwater. Therefore, Enrique is indeed underwater at -5 feet.
- **This statement is True.**
3. **The change in elevation for Enrique from point B to point C is represented by the equation (-5) - 0 = -5.**
- The change in elevation from point B (-5 feet) to point C (0 feet) is calculated as follows:
\[
0 - (-5) = 0 + 5 = 5
\]
- The equation given, \((-5) - 0 = -5\), is not correctly representing the change in elevation.
- **This statement is False.**
To summarize:
- The first statement is True.
- The second statement is True.
- The third statement is False.
1. **The equation |10 - (-5)| = 15 represents the difference between the highest point and the lowest point for Enrique.**
- The highest point (diving board) is at point A (10 feet) and the lowest point (where Enrique lands) is at point B (-5 feet). So, the difference is calculated as:
\[
|10 - (-5)| = |10 + 5| = |15| = 15
\]
- **This statement is True.**
2. **Enrique is underwater at point B.**
- Point B is at -5 feet, and since the surface of the water is at 0 feet, any depth below 0 feet is considered underwater. Therefore, Enrique is indeed underwater at -5 feet.
- **This statement is True.**
3. **The change in elevation for Enrique from point B to point C is represented by the equation (-5) - 0 = -5.**
- The change in elevation from point B (-5 feet) to point C (0 feet) is calculated as follows:
\[
0 - (-5) = 0 + 5 = 5
\]
- The equation given, \((-5) - 0 = -5\), is not correctly representing the change in elevation.
- **This statement is False.**
To summarize:
- The first statement is True.
- The second statement is True.
- The third statement is False.