Which of the following describes a situation in which the total distance a basketball player travels is 0 meter from his starting point? (5 points)
The player runs 9 meters forward and then runs 0 meters in the opposite direction.
The player runs 5 meters forward and then runs 6 meters in the opposite direction.
The player runs 6 meters forward and then runs 5 meters in the opposite direction.
The player runs 4 meters forward and then runs 4 meters in the opposite direction.
The player runs 4 meters forward and then runs 4 meters in the opposite direction.
Which of the following correctly uses absolute value to show the distance between −50 and 12? (5 points)
|−50 − 12| = |−62| = −62 units
|−50 + 12| = |−38| = 38 units
|−50 + 12| = |−38| = −38 units
|−50 − 12| = |−62| = 62 units
|−50 + 12| = |−38| = 38 units
Maya is showing her work in simplifying (5.2 − 4.5) − 5.5 + 4.8. Identify any error in her work or reasoning. (5 points)
Step 1: (5.2 − 4.5) − 5.5 + 4.8
Step 2: 5.2 + (− 4.5 − 5.5) + 4.8 (identity property)
Step 3: 5.2 − 10 + 4.8
Step 4: 5.2 + 4.8 − 10 (commutative property)
Step 5: 10 − 10 = 0
She wrote identity instead of commutative in Step 2.
She wrote commutative instead of distributive in Step 4.
She wrote identity instead of associative in Step 2.
She wrote commutative instead of associative in Step 4.
She wrote identity instead of associative in Step 2.
The situation in which the total distance a basketball player travels is 0 meters from his starting point is when the player runs 4 meters forward and then runs 4 meters in the opposite direction.
To determine the situation in which the total distance a basketball player travels is 0 meters from his starting point, we need to calculate the net displacement, which is the vector sum of all the distances and directions traveled.
Let's evaluate each situation:
1. The player runs 9 meters forward and then runs 0 meters in the opposite direction:
- The total displacement is 9 meters forward.
- Therefore, the total distance traveled is not 0 meters.
2. The player runs 5 meters forward and then runs 6 meters in the opposite direction:
- The total displacement is 5 meters forward - 6 meters backward = -1 meter.
- Therefore, the total distance traveled is not 0 meters.
3. The player runs 6 meters forward and then runs 5 meters in the opposite direction:
- The total displacement is 6 meters forward - 5 meters backward = 1 meter.
- Therefore, the total distance traveled is not 0 meters.
4. The player runs 4 meters forward and then runs 4 meters in the opposite direction:
- The total displacement is 4 meters forward - 4 meters backward = 0 meters.
- Therefore, the total distance traveled is 0 meters.
Based on the calculations, option 4, where the player runs 4 meters forward and then runs 4 meters in the opposite direction, describes a situation in which the total distance a basketball player travels is 0 meters from his starting point.