What is the intermediate step in the form (x+ a)^2 = b as a result of completing the square for the following equation? x^2 - 27x+ 65 = -13x

In trapezoid abcd, ac is a diagonal and ∠abc≅∠acd. find ac if the lengths of the bases bc and ad are 12m and 27m respectively.

How does the graph of g(x)=⌊x⌋−3 differ from the graph of f(x)=⌊x⌋? the graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted right 3 units. the graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted up 3 units. the graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted down 3 units. the graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted left 3 units.

The letters g e o r g i a are placed in a bag . if you picked a card and knew it was a vowel , what is the probability that it is an a ?