Janelle saved up 265$ then she bought a sweater for d dollars. how much money does janelle have left? write your answer as an expression.

Let J(d) represent the amount of money Janelle has left.  Then:

J(d) = $265 - d, where d is the price paid for that sweater.

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

thus, the first answer choice, y = sec x, is the correct one