A company buys a machine for $225,000 that depreciates at a rate of 30% per year.

Step-by-step explanation:

In this problem we are expected to model the depreciated value of the machine after some years of purchase (n years)

initial value of the machine is $225,000

after a year it reduces by 30%

Therefore the new value is now 70% of the initial value

= $157,500

After another year it reduces by 30%

Hence the new value is

= $110250

that after n years the value will be

MN=8

Step-by-step explanation:

since AM/AC = AN/AB = 2/5,

then ∆ABC similar to ∆ANM.

since ∆ABC ~ ∆ANM,

then MN || BC.

by similarity

MN = BC•2/5 = 8