Julia drew a triangle with side lengths of 3 inches 5 inches and 3 inches which type of triangle did julia draw
2 answers:
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In this problem, we need to plug in the given x values for 
and find a and b.
When we plug in 1, we get:
Simplify:
We got our first statement about the values of the variables. If we find one more we can find those 2 variables.
We have another given root: 4.
Plug it in:
Now we have our second one. We can combine them:
I use elimination method which is easier here.
Multiply the top equation by -1:
Add them up:
Simplify:
Now we have a, we can plug in one of those equations to find b:
So, the answers are
and 
.
When we plug in 1, we get:
Simplify:
We got our first statement about the values of the variables. If we find one more we can find those 2 variables.
We have another given root: 4.
Plug it in:
Now we have our second one. We can combine them:
I use elimination method which is easier here.
Multiply the top equation by -1:
Add them up:
Simplify:
Now we have a, we can plug in one of those equations to find b:
So, the answers are
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:
and
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:
Now, let's find the slopes for each of the sections of the function:
<u>Section A</u>
<u>Section B</u>
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.
It is 25 times greater. This is because 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.