Solve for x and y and explain

If a(0,0,0) and b(2,2,2) are points in coordinate space, how many paths are there from a to b that move from one lattice point to another in the positive x-,y- or z- direction?

Which is f(5) for the function –2x2 + 2x - 3?

Rhombus adef is inscribed into a triangle abc so that they share angle a and the vertex e lies on the side bc . what is the length of the side of the rhombus if ab=c, and ac=b.