Question
Which statements are true about y≤8
and its graph? Check the four that apply.(4 points)
Responses
y=8
is part of the solution set.
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.
The arrow on the graph points right.
y=0
is part of the solution set.
y is equal to 0 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.
y=10
is part of the solution set.
pick four
and its graph? Check the four that apply.(4 points)
Responses
y=8
is part of the solution set.
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.
The arrow on the graph points right.
y=0
is part of the solution set.
y is equal to 0 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.
y=10
is part of the solution set.
pick four
Answers
Answered by
GPT-4o mini
Let's analyze the inequality \( y \leq 8 \) and its graph:
1. **\( y = 8 \) is part of the solution set.** - **True**. The inequality includes values less than or equal to 8, so \( y = 8 \) is included in the solution set.
2. **There is a closed circle on the graph at 8.** - **True**. Since the inequality is less than or equal to (≤), the endpoint at \( y = 8 \) is included in the graph, which means there is a closed circle at that point.
3. **The arrow on the graph points left.** - **False**. The arrow actually points downward, indicating that \( y \) can take values less than 8.
4. **The arrow on the graph points right.** - **False**. As stated above, the graph does not point to the right; it points downwards.
5. **\( y = 0 \) is part of the solution set.** - **True**. Since 0 is less than 8, it is included in the solution set.
6. **There is an open circle on the graph at 8.** - **False**. An open circle would imply that \( y = 8 \) is not included in the solution set, which is not true here.
7. **\( y = 10 \) is part of the solution set.** - **False**. Since 10 is greater than 8, it is not included in the solution set.
Based on this analysis, the four true statements are:
1. \( y = 8 \) is part of the solution set.
2. There is a closed circle on the graph at 8.
3. \( y = 0 \) is part of the solution set.
4. The arrow on the graph points downwards (not listed, but must be understood).
Since only four options were requested and I indicated more than four, the correct selections based on the original list would be:
1. \( y = 8 \) is part of the solution set.
2. There is a closed circle on the graph at 8.
3. \( y = 0 \) is part of the solution set.
4. The arrow on the graph does not point left or right; it points downward.
However, as no option mentions the downward arrow directly, you may clarify that by indicating the arrow points down, which is relevant but not listed. The three above states are valid true statements from your options.
1. **\( y = 8 \) is part of the solution set.** - **True**. The inequality includes values less than or equal to 8, so \( y = 8 \) is included in the solution set.
2. **There is a closed circle on the graph at 8.** - **True**. Since the inequality is less than or equal to (≤), the endpoint at \( y = 8 \) is included in the graph, which means there is a closed circle at that point.
3. **The arrow on the graph points left.** - **False**. The arrow actually points downward, indicating that \( y \) can take values less than 8.
4. **The arrow on the graph points right.** - **False**. As stated above, the graph does not point to the right; it points downwards.
5. **\( y = 0 \) is part of the solution set.** - **True**. Since 0 is less than 8, it is included in the solution set.
6. **There is an open circle on the graph at 8.** - **False**. An open circle would imply that \( y = 8 \) is not included in the solution set, which is not true here.
7. **\( y = 10 \) is part of the solution set.** - **False**. Since 10 is greater than 8, it is not included in the solution set.
Based on this analysis, the four true statements are:
1. \( y = 8 \) is part of the solution set.
2. There is a closed circle on the graph at 8.
3. \( y = 0 \) is part of the solution set.
4. The arrow on the graph points downwards (not listed, but must be understood).
Since only four options were requested and I indicated more than four, the correct selections based on the original list would be:
1. \( y = 8 \) is part of the solution set.
2. There is a closed circle on the graph at 8.
3. \( y = 0 \) is part of the solution set.
4. The arrow on the graph does not point left or right; it points downward.
However, as no option mentions the downward arrow directly, you may clarify that by indicating the arrow points down, which is relevant but not listed. The three above states are valid true statements from your options.