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Answers by Michael F.

The pattern you seem to be looking at is for every integer n, the number g you seek is such that n/g = n+g This gives g2+ng-n=0 or that g=(-n±√(n2+4n))/2 If you use the plus sign you get n= 1     g=0.618033989 n=2     ...

I assume that you mean log8x-log810=log84.  That is log8(x/10)=log84.  Raise 8 to the power of each of the equal sides and have x/10=4, or x=40.

Assuming that the area, length times width = x4+10x2+9=(x2+9)(x2+1) and assuming that one of these factors is the height and the other the width, and that the width is the larger number, then it is x2+9 which is, for any real number greater than x2+1

The sum of the angles of a triangle is 180 degrees. Draw triangle ABC.  Make BC horizontal, for convenience. Through point A draw a line parallel to the opposite side, namely BC. Mark a point L on this line to the left of A, and a point R on this line to the right of A. ∠LAB...

Adding acid? (answer)

.5×7 + x = the acid in the final soloution 7+x is the amount of the final solution (3.5+x)/(7+x)=.7 3.5+x=.7(7+x) 3.5+x=4.9+.7x .3x=1.4 x=14/3=4 2/3 gal Note:3 1/2 + 4 2/3 = 8  1/6  total acid after addition of acid 7+4...

x6-19x3-216=0 Let y=x3 and have y2-19y-216=0 which may be factored as (y-27)(y+8)=0 which gives that y=27, y=-8 and so that x=3 or x=-2