Solve –2.8(z + 1) – (3.5z – 9) = –31.6 for z. a. –1.32 b. 0.94 c. 6 d. –7.72

1. 3. can also be expressed as (22/7)

2. -4.5

3. 3.6

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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