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vesna_86 [32]
3 years ago
9

Please help thank you!

Mathematics
1 answer:
kirill [66]3 years ago
3 0
Question 1:

Look at the image. 

First, we graph the points on a grid.

Then, we find the perpendicular bisectors and find where they intersect.

They intersect on the circumcenter of the triangle.

The circumcenter is (5,3)

Question 2:

The answer is III only because the perpendicular bisector for the longest side will always have to point outside the triangle in order to intersect with the other two perpendicular bisectors.

Question 3:

The answer is a perpendicular bisector because it is a perpendicular line that bisects a side of the triangles, which is the exact definition of a perpendicular bisector.

Have an awesome day! :)

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Part A:

The average rate of change refers to a function's slope. Thus, we are going to need to use the slope formula, which is:

m = \dfrac{y_2 - y_1}{x_2 - x_1}

  • (x_1, y_1) and (x_2, y_2) are points on the function

You can see that we are given the x-values for our interval, but we are not given the y-values, which means that we will need to find them ourselves. Remember that the y-values of functions refers to the outputs of the function, so to find the y-values simply use your given x-value in the function and observe the result:

h(0) = 3(5)^0 = 3 \cdot 1 = 3

h(1) = 3(5)^1 = 3 \cdot 5 = 15

h(2) = 3(5)^2 = 3 \cdot 25 = 75

h(3) = 3(5)^3 = 3 \cdot 125 = 375


Now, let's find the slopes for each of the sections of the function:

<u>Section A</u>

m = \dfrac{15 - 3}{1 - 0} = \boxed{12}

<u>Section B</u>

m = \dfrac{375 - 75}{3 - 2} = \boxed{300}


Part B:

In this case, we can find how many times greater the rate of change in Section B is by dividing the slopes together.

\dfrac{m_B}{m_A} = \dfrac{300}{12} = 25


It is 25 times greater. This is because 3(5)^x is an exponential growth function, which grows faster and faster as the x-values get higher and higher. This is unlike a linear function which grows or declines at a constant rate.

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