$|7-|-3||$

$|\sqrt{2}-100|$

Evaluate ${\displaystyle \frac{x-3y}{2}}+xy$ for $x=5$ and $y=-3.$

Determine the domain of the variable x in the expression ${\displaystyle \frac{2x}{(x-3)(x+9)}}$ and write it in interval notation.

${\left({\displaystyle \frac{-3x^{2}y}{x}}\right)}^3$

$\sqrt[3]{-8x^6}$

$\sqrt{75x}-\sqrt{27x}$

$-{16}^{-3/2}$

${\left({\displaystyle \frac{x^{-2}{y}^4}{25x^3{y}^3}}\right)}^{-1/2}$

Rationalize the denominator of the expression ${\displaystyle \frac{5}{1-\sqrt{3}}}.$

$4(x^2-3x+2)+3(5x^2-2x+1)$

$(x-2)(5x-1)$

${(x^2+3y^2)}^2$

A circular rug has a border of uniform width. The distance from the center of the rug to the inner and outer edges of the border are 5 feet and x feet, respectively. Write a completely factored polynomial that gives the area of the border.

$x^2-5x+6$

$9x^2+12x+4$

$8x^3-27$

${\displaystyle \frac{6-3x}{x^2-4}}-{\displaystyle \frac{12}{2x+4}}$

${\displaystyle {\displaystyle \frac{{\displaystyle {\displaystyle \frac{1}{x^2}}}}{9-{\displaystyle {\displaystyle \frac{1}{x^2}}}}}}$

Find the length of the hypotenuse of a right triangle with legs a and b of lengths 35 and 12, respectively.