Answer:
q=(40-7)/3 or simplified q=11
Step-by-step explanation:
So we know that the perimeter is 40 inches and one of the sides is 7 so logically we do 40-7 to get the length of the three remaining sides combined. Then to find the length q, we have to divide that answer by 3 because the three sides have the same length or (40-7)/3, which simplified is 11, so the length of the side is 11 inches and the expression is q=(40-7)/3.
The formula of the length of the segment AB:

We have:

Substitute:

Answer:
B) 10.
Problem 2
Part (a)
The 3D shape formed when rotating around the y axis forms a pencil tip
The shape formed when rotating around the x axis is a truncated cone turned on its side.
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Part (b)
Check out the two diagrams below.
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Problem 3
Answer: Choice A and Choice C
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Explanation:
Think of stacks of coins. Let's say we had 2 stacks of 10 quarters each. The quarters are identical, so they must produce identical volumes. Those sub-volumes then add up to the same volume for each stack. Now imagine one stack is perfectly aligned and the other stack is a bit crooked. Has the volume changed for the crooked stack? No, it hasn't. We're still dealing with the same amount of coins and they yield the same volume.
For more information, check out Cavalieri's Principle.
With all that in mind, this leads us to choice C. If the bases are the same, and so are the heights, then we must be dealing with the same volumes.
On the other hand, if one base is wider (while the heights are still equal) then the wider based block is going to have more volume. This leads us to choice A.
For this case we have the following expression:

Since the denominator is equal, then we can add the numerator.
We have then:

Adding similar terms we have:

Rewriting we have:

Doing common factor in the numerator we have:

Factoring the denominator we have:

Canceling similar terms we have:
Answer:
The simplest form of the expression has 7 in the numerator and m+4 in the denominator.