To determine the system of inequality that has been graphed, we need to be very smart.
Observe that all the equations are the same.
Also note that all the lines are solid. This should tell you that the inequities should involve.
Therefore the answer is between option A and B.
So we choose a point in the solution region to discriminate between A and B.
Let us choose the origin since that is easy to evaluate.
We substitute into option A to get.
The above statements are false
We now substitute into option B
Both statements are true, therefore the correct answer is option B.
Answer:
2, 1, 1/2, 1/4
Step-by-step explanation:
2¹ = 2
2^0 = 1
2^-¹
= 1/2¹
= 1/2
2^-2
= 1/2²
= 1/2*2
= 1/4
To complete the table
2² 2¹ 2^0 2^-1 2^-2
4 2 1 1/2 1/4
Answer:
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Slope-intercept form:
y=mx+b
m=slope
b=y-intercept
Data of the first line:
m=-5
b=y-intercept=3 (y-intercept=it is the value of "y" when x=0)
y=-5x+3
A line perpendicular to the line y=mx+b will have the following slope:
m`=-1/m
Therefore: the line perpendicular to the line y=-5x+3 will have the following slope:
m´=-1/(-5)=1/5
Point-slope form of a line: we need a point (x₀,y₀) and the slope (m):
y-y₀=m(x-x₀)
We know, the slope (m=1/5) and we have a point (3,2) therefore:
y-y₀=m(x-x₀)
y-2=1/5(x-3) (point-slope form)
y-2=(1/5)x-3/5
y=(1/5)x-3/5+2
y=(1/5)x+7/5 (slope-intercept form)
Answer: the line perpendicular to the first line will be: y=(1/5)x+7/5
