A civics teacher asked her students to indicate whether they believed each of two headlines. One headline was false and the other was true, but the students did not know this. The probability that a student selected at random believed the true headline was 90\%90%90, percent and the probability that the student believed the false headline was 82\%82%82, percent. She found that 75\%75%75, percent of the students believed both headlines

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step-by-step explanation:

sdfghjkl; vbnm,

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