When the value of yberries directly with x when y equals 75 x equals 1/2 what is the value of y when x is 2 and 1/4

337.5

Step-by-step explanation:

direct variation means y=kx (inverse variation is yx=k or y=k/x)

so we are given that:

75=k/2, so k=150 which means:

y=150x  now

y(2.25)=150(2.25)=337.5

Hope this helps

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