Becky wants to fence in a rectangular play area for her dog. If she was 82 feet of fencing and wants the length of the play area to be 9 feet longer than its width then what should the dimensions of the play area be?

Answer:

The point A′ of the image coincides with point D of the preimage. The point B′ of the image coincides with point E of the preimage.

Step-by-step explanation:

It is given that regular octagon ABCDEFGH rotates 135º clockwise about its center to form octagon A′B′C′D′E′F′G′H′.

It means the central angle divided in 8 equal parts. The central angle between two consecutive vertices is

The regular octagon ABCDEFGH rotates 135º clockwise.

Therefore the point A′ of the image coincides with point D of the preimage. The point B′ of the image coincides with point E of the preimage.

Answer:

Point A' will coincide D and B' will coincide with E.

Step-by-step explanation:

In the figure attached we have regular octagon ABCDEFGH. It's a regular octagon means all it's sides are equal and central angle of one sector out of 8 sectors formed will be =

Now this octagon is rotated about it's center to form new octagon A'B'C'D'E'F'G'H'

Since angle of rotation is 135° clockwise which means octagon is rotated by 45×3 = 3×(central angle of one sector)

After rotation clockwise new image will coincide like this

A = F'

B = G'

C = H'

D = A'

E =  B'

F = C'

G = D'

H = E'

Now we can easily tell that point A' will coincide with the point D of preimage. Similarly point B' of the image will coincide with the point E.

Answer:

C

Step-by-step explanation:

You can start by "filling up" all of the bigger boxes. 75*14=1050 cupcakes, which when subtracted from the total initial amount leaves 400 cupcakes for the smaller boxes. The smallest multiple of 13 smaller than 400 is 390, which is 10 smaller than 400. Therefore, there will be 10 cupcakes left over, or answer choice C. Hope this helps!