Aregular pentagon shares a common center with a regular hexagon. if lm || ab, across how many lines of reflection can the combined figure be reflected to map onto itself?

This problem is very difficult to imagine without the figure. However I dug up on other sources and I think I found the correct figure to work with (see the attached pic).

We can see that in the figure, the hexagon is inscribing the pentagon. What is meant here to be lines of reflection simply means lines of symmetry. If we take on the hexagon alone, there are a lot of lines of symmetry. We can create the line intersecting E & B and the figure would still be symmetrical on both sides or D & A, F & C and etc. So there are a lot for hexagon alone.

However in this case, our lines of symmetry is made limited by the presence of the pentagon. If we slice the pentagon into two, the only line of symmetry we could create would be the line intersecting O and the median of LM. Other lines would not create a symmetrical half.

Therefore the line of reflection is only 1.

The answer is 1

Step-by-step explanation:

This was correct on edmentum

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

the 4th choice is the correct one

step-by-step explanation: