Question
Which statements are true about y≤8
and its graph? Check the four that apply.(4 points)
Responses
y=0
is part of the solution set.
y is equal to 0 is part of the solution set.
y=10
is part of the solution set.
y is equal to 10 is part of the solution set.
y=8
is part of the solution set.
y is equal to 8 is part of the solution set.
There is an open circle on the graph at 8.
There is an open circle on the graph at 8.
There is a closed circle on the graph at 8.
There is a closed circle on the graph at 8.
The arrow on the graph points left.
The arrow on the graph points left.
The arrow on the graph points right.
and its graph? Check the four that apply.(4 points)
Responses
y=0
is part of the solution set.
y is equal to 0 is part of the solution set.
y=10
is part of the solution set.
y is equal to 10 is part of the solution set.
y=8
is part of the solution set.
y is equal to 8 is part of the solution set.
There is an open circle on the graph at 8.
There is an open circle on the graph at 8.
There is a closed circle on the graph at 8.
There is a closed circle on the graph at 8.
The arrow on the graph points left.
The arrow on the graph points left.
The arrow on the graph points right.
Answers
Answered by
GPT-4o mini
Let's analyze the inequality \( y \leq 8 \) and determine which of the provided statements are true.
1. **y = 0 is part of the solution set.**
- **True.** Since \( 0 \leq 8 \), this statement is true.
2. **y is equal to 0 is part of the solution set.**
- **True.** This is essentially the same statement as the first one, confirming that \( 0 \leq 8 \).
3. **y = 10 is part of the solution set.**
- **False.** Since \( 10 \) is not less than or equal to \( 8 \), this statement is false.
4. **y is equal to 10 is part of the solution set.**
- **False.** This is the same as the previous statement; thus, it is false.
5. **y = 8 is part of the solution set.**
- **True.** Since \( 8 \leq 8 \), this statement is true.
6. **y is equal to 8 is part of the solution set.**
- **True.** This is the same as the previous statement, confirming that \( 8 \leq 8 \).
7. **There is an open circle on the graph at 8.**
- **False.** Because \( y \leq 8 \) includes the point where \( y = 8 \), there will be a closed circle at this point.
8. **There is a closed circle on the graph at 8.**
- **True.** Since the inequality includes \( y = 8 \), there will be a closed circle at \( 8 \).
9. **The arrow on the graph points left.**
- **False.** This is not applicable because the graph is vertical along the \( y \)-axis and does not have arrows that indicate left or right.
10. **The arrow on the graph points right.**
- **False.** Similar to the previous point, this statement is not applicable either.
### Summary of True Statements:
- \( y = 0 \) is part of the solution set.
- \( y \) is equal to 0 is part of the solution set.
- \( y = 8 \) is part of the solution set.
- \( y \) is equal to 8 is part of the solution set.
- There is a closed circle on the graph at 8.
Therefore, the true statements are:
1. y = 0 is part of the solution set.
2. y is equal to 0 is part of the solution set.
3. y = 8 is part of the solution set.
4. y is equal to 8 is part of the solution set.
5. There is a closed circle on the graph at 8.
1. **y = 0 is part of the solution set.**
- **True.** Since \( 0 \leq 8 \), this statement is true.
2. **y is equal to 0 is part of the solution set.**
- **True.** This is essentially the same statement as the first one, confirming that \( 0 \leq 8 \).
3. **y = 10 is part of the solution set.**
- **False.** Since \( 10 \) is not less than or equal to \( 8 \), this statement is false.
4. **y is equal to 10 is part of the solution set.**
- **False.** This is the same as the previous statement; thus, it is false.
5. **y = 8 is part of the solution set.**
- **True.** Since \( 8 \leq 8 \), this statement is true.
6. **y is equal to 8 is part of the solution set.**
- **True.** This is the same as the previous statement, confirming that \( 8 \leq 8 \).
7. **There is an open circle on the graph at 8.**
- **False.** Because \( y \leq 8 \) includes the point where \( y = 8 \), there will be a closed circle at this point.
8. **There is a closed circle on the graph at 8.**
- **True.** Since the inequality includes \( y = 8 \), there will be a closed circle at \( 8 \).
9. **The arrow on the graph points left.**
- **False.** This is not applicable because the graph is vertical along the \( y \)-axis and does not have arrows that indicate left or right.
10. **The arrow on the graph points right.**
- **False.** Similar to the previous point, this statement is not applicable either.
### Summary of True Statements:
- \( y = 0 \) is part of the solution set.
- \( y \) is equal to 0 is part of the solution set.
- \( y = 8 \) is part of the solution set.
- \( y \) is equal to 8 is part of the solution set.
- There is a closed circle on the graph at 8.
Therefore, the true statements are:
1. y = 0 is part of the solution set.
2. y is equal to 0 is part of the solution set.
3. y = 8 is part of the solution set.
4. y is equal to 8 is part of the solution set.
5. There is a closed circle on the graph at 8.