Answer:
Step-by-step explanation:
The equation of a linear function in a slope-intercept form is written as
where
m is the slope of the line
q is the y-intercept
We proceed as follows. First of all, we find the y-intercept, which is the value of y at which the line touches the y-axis.
From the graph, we see that this occurs at y = 4, therefore the y-intercept is
Now we have to find the slope. We do that by choosing two points along the line, with coordinates 
and 
and by using the equation
Here we take the two points:
(0,4)
(-8,0)
So the slope is
Therefore, the equation of the line is
Answer:
72 feet from the shorter pole
Step-by-step explanation:
The anchor point that minimizes the total wire length is one that divides the distance between the poles in the same proportion as the pole heights. That is, the two created triangles will be similar.
The shorter pole height as a fraction of the total pole height is ...
18/(18+24) = 3/7
so the anchor distance from the shorter pole as a fraction of the total distance between poles will be the same:
d/168 = 3/7
d = 168·(3/7) = 72
The wire should be anchored 72 feet from the 18 ft pole.
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<em>Comment on the problem</em>
This is equivalent to asking, "where do I place a mirror on the ground so I can see the top of the other pole by looking in the mirror from the top of one pole?" Such a question is answered by reflecting one pole across the plane of the ground and drawing a straight line from its image location to the top of the other pole. Where the line intersects the plane of the ground is where the mirror (or anchor point) should be placed. The "similar triangle" description above is essentially the same approach.
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Alternatively, you can write an equation for the length (L) of the wire as a function of the location of the anchor point:
L = √(18²+x²) + √(24² +(168-x)²)
and then differentiate with respect to x and find the value that makes the derivative zero. That seems much more complicated and error-prone, but it gives the same answer.
Answer:
18
Step-by-step explanation:
8 3/4 + 9 2/8
We can simplify 2/8 by dividing the top and bottom by 2
8 3/4 + 9 1/4
Add the whole numbers
8+9 = 17
3/4 + 1/4 = 4/4 = 1
Add this to the whole numbers
17+1 = 18
Answer:
Step-by-step explanation:
50*20%=10
10 players are left-handed.
Answer:
x = -3
Step-by-step explanation:
The vertex lies on the axis of symmetry, whose x-coordinate is halfway between -9 and 3: x = -3
