Which equation can be solved to find one of the missing side lengths in the triangle?
1 answer:
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Answer:
The system of inequalities is -2x + y > 0 -x + y ≥ 0
Step-by-step explanation:
The form of the equation of a line is y = m x + b, where
- m is the slope
- b is the y-intercept
The line passes through the origin, then
- The value of b = 0
- The form of the equation is y = m x
Let us look at the graph to find the correct answer
∵ One of the lines are solid and the other is dashed
∵ The shaded area is over the two lines
∴ The signs of the two inequalities are ≥ and >
∵ The two lines pass through the origin
→ That means the y-intercepts are 0
∴ The form of the inequalities are y ≥ m x and y > m
There are only two answers that have these forms, so we must find the slope of each line
∵ m = , (x1, y1) and (x2, y2) are two points on the line
∵ The solid line passes through points (0, 0) and (2, 2)
∴ m =
=
= 1
→ Substitute it in the form of the equation
∴ y ≥ 1(x)
∴ y ≥ x
→ Subtract x from both sides
∴ -x + y ≥ 0
∵ The dashed line passes through points (0, 0) and (1, 2)
∴ m =
=
= 2
→ Substitute it in the form of the equation
∴ y > 2(x)
∴ y > 2x
→ Subtract 2x from both sides
∴ -2x + y > 0
The system of inequalities is -2x + y > 0 -x + y ≥ 0
Answer:
128 girls
Step-by-step explanation:
The ratio of boys to girls is 6 to 8. We need to find how many girls there are if there are 96 boys in the camp. One way to solve this is by using cross multiplication:
=
multiply the 6 by the x: 6x
multiply 8 by 96: 768
6x = 768
divide both sides of the equation by 6 to isolate the x:
6x/6 = 768/6
x = 128
When there are 96 boys in camp, there will be 128 girls.