Draw the image of the following segment after a dilation centered at the origin with a scale factor of 2/3

Step-by-step explanation:

Let the ends of the given segment are A and B.

Coordinates of A → (8, 6)

Coordinates of B → (12, 12)

If a point (x, y) is dilated by a scale factor 'k' about the origin, rule to be followed,

(x, y) → (kx, ky)

If k =

(x, y) →

By this rule coordinates of the image points of A and B will be,

A(8, 6) →

           → A'(5.3, 4)

B(12, 12) →

             → B'(8, 8)

Now we can get the image of segment AB after dilation by a scale factor of .

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.