Find the area of the shaded regions.

Step-by-step explanation:

The area of the shaded region can be calculated as the area of the semicircle less the area of the right triangle.

The area of the right triangle can be calculated as:

Where LM and MN have the same length because the internal angles are L=45°, M=90°, and N=45°. So the area is:

The diameter of the circle can be calculated using the Pythagorean theorem as:

So, the radius is

Finally, the area of the semicircle is:

So, the area of the shaded region is:

c. prove the lengths are the same.

step-by-step explanation:

you need to prove the segments are congruent. congruent segments have the same length. find the lengths of the segments using the distance formula, and compare them.

answer: c. prove the lengths are the same.

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following