ΔRST, U lies on TS with TU:US = 2:3. M is the midpoint of RU. TM intersects RS at V. Find RV:RS.

  2 : 7

Step-by-step explanation:

Draw a line parallel to RS through U. Label its intersection with TM as point X. This will create triangle UMX congruent to triangle RMV by the ASA postulate. (Vertical angles at M are congruent; MR = MU by definition: and angles VRM and XUM are alternate interior angles at a transversal of parallel lines.) Then UX = RV by CPCTC.

The line UX has also created similar triangles TUX and TSV. Their scale factor is TU : TS = 2 : (2+3) = 2 : 5. The sides UX : SV have the same scale factor, 2 : 5.

From above, we know that UX = RV, which tells us the scale factor of RV : SV is 2 : 5. Thus ...

  RV:RS = RV:(RV+SV) = 2:(2+5)

  RV:RS = 2:7

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Comment on the solution

I had to draw the attached figure to see what the ratio was. Then I had to figure out a way to show why. The congruent angles at M and the equal sides RM and UM offered a clue as to how to do it.

i think the answer is fried chicken ; >

step-by-step explanation:

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.