Answer is A. It is the center of the circle that can be inscribed in a given triangle
Explanation
The circumcenter is called ”the circumcenter” because it is the center of the circle that ”circumscribes” the triangle.
The answer would be <span>6.5.12
A triangle couldn't be made if the total sum of the two shortest side is less than the longest side. In this case, the two shortest side would be 5 and 6. The longest side would be 12.
If you try to add the two lowest side, the result would be 5+6=11. That means even if you make the triangle with 179.99 degrees that the 5 and 6 look like a straight line, the longest side it can achieve is 11.</span>
So this is essentially a proportion problem. They want you to be able to recognize a relationship between the two. The easiest way to go about this is to draw a picture (I have included one). What you want to do is notice that you are given both shadow lengths. This is essentially going to be your first step to creating the proportion.
Understanding that we know the shadow lengths, we can turn these into a fraction such as so:
4ft/20ft.
Now that we know that, we need to look at are unknown. Our unknown is the height of the utility pole. We can solve this by substituting for X since we know the utility worker is 5.5 ft tall.
Your fraction for that would look like:
5.5ft/X
Make sure to always make your top to top match, such as since I put the utility worker's shadow on top, I need to put his height on top.
Now we can solve.
4ft/20ft =5.5ft/X
We need to cross multiply to get an equation we can work with. If we cross multiply, Your equation will look like:
4x = 110ft
This is a simple one step equation. Divide both sides by 4 to get your answer.
x= 27.5ft.
This means your Utility pole's height is 27.5ft.
Answer:
13
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is

Here [ a, b ] = [2, 6 ]
f(b) = f(6) = 6² + 5(6) - 8 = 36 + 30 - 8 = 58
f(a) = f(2) = 2² + 5(2) - 8 = 4 + 10 - 8 = 6
Hence
average rate of change =
=
= 13