The student council has decided to have a raffle at the carnival. they came up with a table to show the relationship between the number of tickets bought and the number of raffle entries. explain why it could be for the student council to determine an equation to represent this data.

so they know if they need to sell more tickets

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225

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