Et $r = \zz[\sqrt{-n}]$ where $n$ is a squarefree integer $> 3$. prove that $2$, $\sqrt{-n}$, and $1 + \sqrt{-n}$ are all irreducible in $r$. \item prove that $r$ is not a ufd. [hint: show that either $\sqrt{-n}$ or $1+\sqrt{-n}$ is not prime.] \item find a non-principal ideal in r.

The table below represents the displacement of a fish from its reef as a function of time: time (hours) x displacement from reef (feet) y 0 4 1 64 2 124 3 184 4 244 part a: what is the y-intercept of the function, and what does this tell you about the fish? (4 points) part b: calculate the average rate of change of the function represented by the table between x = 1 to x = 3 hours, and tell what the average rate represents. (4 points) part c: what would be the domain of the function if the fish continued to swim at this rate until it traveled 724 feet from the reef? (2 points)

Find the vertex for the parabola given by the function ƒ(x) = −3x2 − 6x.

Acompany had forty one employees and ordered nine hundred eighty uniforms for them. if they wanted to give each employees the same number of uniforms, how many more uniforms should they order so they don't have any extra