10 50 10
Why are the solutions to the proportions X - 20
and 50
20
the same?
X
because both result in the equation 20x=500, which simplifies to x = 25
because both result in the equation 20x = 500, which simplifies to X = 250
because both result in the equation 10x = 1,000, which simplifies to x = 10
obecause both result in the equation 10x = 1,000, which simplifies to x= 100

step-by-step explanation:

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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