Respuesta :
When the inequality sign is </> (less than/greater than), the dot is an open circle.
When the inequality sign is ≤/≥ (less than or equal to/greater than or equal to), the dot is a closed circle.
y = number that is a solution/makes the inequality true
y ≤ 8 (y is any number less than or equal to 8)
#1: y = 0 is part of the solution set.
Yes because if you substitute/plug in 0 into "y" in the inequality, since y = 0:
0 ≤ 8 0 is less than 8.
#2: y = 8 is part of the solution set.
Yes because if you plug it into the inequality:
8 ≤ 8 8 is equal to 8
#3: y = 10 is part of the solution set.
No because if you plug it into the inequality:
10 ≤ 8 10 is not less than or equal to 8
#4: There is an open circle on the graph at 8.
No because the inequality sign is ≤, so there should be a closed circle on 8.
#5: There is a closed circle on the graph at 8.
Yes because the inequality sign is ≤
#6: The arrow on the graph points left.
Yes because if the arrow is pointing left then the numbers are decreasing, and y is any number less than or equal to 8.
#7: The arrow on the graph points right.
No because if the arrow is point right then the numbers are increasing, but y is not a number greater than 8.
Your answer is the 1st, 2nd, 5th, and 6th option
To solve the problem first we need to understand the Inequality Signs.
Inequality Sign
In an inequality sign there is a dot(circle) present, but whether the circle is open or closed depends, upon the inequality sign.
If the inequality sign is less than(<) or greater than(>), the dot is an open circle.
whereas, if the inequality sign is less than or equal to (≤) and greater than or equal to(≥), the dot is a closed circle.
The correct options are A, B, E, and F.
Explanation
Given statements to us,
A.) y = 0 is part of the solution set.
B.) y = 8 is part of the solution set.
C.) y = 10 is part of the solution set.
D.) There is an open circle on the graph at 8.
E.) There is a closed circle on the graph at 8.
F.) The arrow on the graph points left.
G.) The arrow on the graph points right.
Solutions
We know that the number line is always decreasing number or negative towards the left while positive towards the right.
Therefore, y≤8 means, y is true for any value less than and equal to 8, which will give a closed circle on the graph, and the arrow will be pointing toward the left.
Now looking at the options we have,
A.) y = 0 is part of the solution set.
The statement is true as the y value is less than 8.
B.) y = 8 is part of the solution set.
The statement is true as the y value is equal to 8.
C.) y = 10 is part of the solution set.
The statement is false as the y value is greater than 8.
D.) There is an open circle on the graph at 8.
The statement is false as the inequality sign given is less than or equal to (≤).
E.) There is a closed circle on the graph at 8.
The statement is true as the inequality sign given is less than or equal to (≤).
F.) The arrow on the graph points left.
The statement is true as the value of y is always on the decreasing side, the number line is always decreasing the number or negative towards the left while positive towards the right.
G.) The arrow on the graph points right.
The statement is false as the value of y is always on the decreasing side, the number line is always decreasing the number or negative towards the left while positive towards the right.
Hence, the correct options are A, B, E, and F.
Learn more about Inequality Sign:
https://brainly.com/question/19491153
