Prove that there exists a positive integer $N$ such that there are at least 2005 ordered pairs $(x, y),$ of non-negative integers $x$ and $y,$ satisfying $x^2 + y^2 = N.$

Which statement accurately explains whether a reflection over the y-axis and a 270° counterclockwise rotation would map figure acb onto itself? a coordinate plane with figure acb with point a at 1, 1, c at 3, 4 and b at 5, 1 yes, a″c″b″ is located at a″(1, 1), c″(4, 3), and b″(1, 5) yes, a″c″b′ is located at a″(1, 1), c″(3, 4), and b″(5, 1) no, a″c″b″ is located at a″(1, 1), c″(4, 3), and b″(1, 5) no, a″c″b″ is located at a″(1, 1), c″(3, 4), and b″(5, 1)

If 2(a^2+b^2)=(a+b)^2 then, > a+b=0, > ab=0, > a=b, > 2a=b

The graph of y x3 is translated so that the point (1. 1) is moved to (1, 4). what is the equation of the new graph?