Imagine you saved $4000 to spend winter break visiting your relatives in new york. it costs $1200 for the plane ticket and $300 per night for the hotel. think of the function that demonstrates the cost (c) based on the number of nights (n) you spend. what is the rate of change?

answer: 298143

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4