800 - 50 = 750
750 ÷ 5 =150
150 small vehicles were washed
The area of a polygon is given by the formula Area = ap/2 where a is the length of the apothem and p is the perimeter. The apothem is a line from the center of the polygon perpendicular to a side.
Depending on the formula you know, you can find the length of a side in 1 of 2 ways.
The first way uses a triangle. Using the radius of the polygon you can create 8 congruent triangles. The center angle will be 360 / 8 = 45 and two side lengths of 20. You can find the length of the base using the law of cosines.
c^2 = 20^2 + 20^2 - 2(20)(20)(cos 45)
c^2 = 400 + 400 - 800(cos 45)
c^2 = 800 - 800(cos 45)
c = sqrt(800 - 800(cos 45)
c = 15.31
The second way is to use this formula:
r = s / (2 sin(180 / n))
20 = s / (2 sin(180/8)
(20)(2)sin(22.5) = s
(40)sin(22.5) = s
s = 15.31
We need to calculate the perimeter. As there are 8 sides (8)(15.31) = 122.48
Now we need to calculate the apothem using
a = S / (2 tan (180 / n)
a = 15.31 / (2 tan (180 / 8))
a = 18.48
Now solve for the area
Area = ap/2
Area = (18.48)(122.48)/2
Area = 1131.72
perimeter = 122.48
area = 1131.72
86% written as a fraction is 43/50
The first thing we notice is that the function is reflected. So we can start by reflecting it with respect to the x-axis.
We do this by adding a negative sign in the function:
Now, we have the function reflected, but in the wrong position. We can track its position by the vertex. It was originally at (0,0) and remains at (0,0) after the reflection.
But the final function have its vertex at (-5,0), so we have to translate the function 5 units to the left. we do this by adding 5 to the x in the function:
Now, to check if there isn't any dilatation, we can check on other point in the graph to see if it checks out.
In the blue graph, we see the point (-3,-4), so let's input x = -3 and see if it checks out:
We got y = -4, so it checks out.
Thus, the answer is:
