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 $x^2 + y^2 = N.$

Students buying lunch at rockwell elementary school yesterday chose either burritos or pizza. 185 students chose burritos and 252 chose pizza. 1. estimate the number of students who brought lunch by rounding each number to the nearest hundred. 2. estimate how many students bought lunch by rounding each number to the nearest ten. 3. find the total number of students who brought lunch. which of your estimates is closer to the actual total? explain. 4. draw a figure on a sheet of paper. estimate how many pennies will fit inside the figure. check your prediction using pennies.

Matteo makes raspberry punch. the table shows how many parts ginger ale and raspberry juice to use for a batch. raspberry punch parts ginger ale 2 parts raspberry juice 3 matteo decides to add one part of raspberry juice. what is the new ratio of ginger ale to raspberry juice?

Check all that apply. f is a function. f is a one-to-one function. c is a function. c is a one-to-one function.