Step-by-step explanation:

As we know that,

So,


Answer:
See below.
Step-by-step explanation:
The converse of the Pythagorean Theorem tells us that if the sum of the square of the two shorter lengths is equivalent to the square of the longest length, then the triangle is indeed a right triangle.
We have the side lengths (x²-1), (2x), and (x²+1).
We can see that our hypotenuse will be (x²+1), since it will always yield the largest value for x.
So, we can use the Pythagorean Theorem:

Substitute (x²-1) and (2x) for a and b, and substitute (x²+1) for c:

Square each expression:

Combine like terms:

Add:

We can see that the resulting equations are equivalent, proving that the triangle is indeed a right triangle.
And we're done!
Answer:
Each friend will get more than 4 whole bagels.
Step-by-step explanation:
First off, although the question asks for 13 bagels divided between 3 friends, let's use a number that results in a whole number when divided by 3, but is close to 13.
This number can be 12.
12 divided by 3 is 4, so each friend gets 4 bagels if there are a total of 12 bagels.
However, there are more than 12 bagels so we know that each of the the 3 friends will get more than 4 bagels each.