At lunchtime of the students at a school buy juice. Of those students, - buy orange juice. What fraction of the students buy orange juice? Write your answer in simplest form. 4​

this shows a reflection over the x-axis and is translated one unit down and 6 units to the right (x + 6, y - 1)

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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