DewdropDancer

Kyle is definitely wrong, 31/97 cannot be a perfect number, so Kyle must have rounded the number.

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Correct Guest...!

$1.5z=6$

$1.5z\cdot \:10=6\cdot \:10$

$15z=60$

$\frac{15z}{15}=\frac{60}{15}$

$z=4$

Oh, I'm sorry, I must have messed up on a part.

Well done CubeyThePenguin...!

$(3x - 5) + (x + 1) = 180$

$3x-5+x+1=180$

$3x+x-5+1=180$

$4x-5+1=180$

$4x-4=180$

$4x-4+4=180+4$

$4x=184$

$\frac{4x}{4}=\frac{184}{4}$

$x=46$

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

The factors of 28 are: 1, 2, 4, 7, 14, 28

Then the greatest common factor is 4.

(This way probably won't work on big numbers, so you should use EP's way.)

$-7\left(1+5m\right)-29<300+7m$

$-35m-36<300+7m$

$-35m-36+36<300+7m+36$

$-35m<7m+336$

$-35m-7m<7m+336-7m$

$-42m<336$

$\left(-42m\right)\left(-1\right)>336\left(-1\right)$

$42m>-336$

$\frac{42m}{42}>\frac{-336}{42}$

 $m>-8$

$Sin(330)$

$=\cos \left(90^{\circ \:}-330^{\circ \:}\right)$

$=\cos \left(-240^{\circ \:}\right)$

$=\cos \left(240^{\circ \:}\right)$

$=-\frac{1}{2}$

Correct thedudemanguyperson...!

$\frac{1}{\sqrt{2}+\frac{1}{\sqrt{8}+\sqrt{200}+\frac{1}{\sqrt{18}}}}$

                                        $​​​​\frac{1}{\sqrt{8}+\sqrt{200}+\frac{1}{\sqrt{18}}}=\frac{3\sqrt{2}}{73}$

$=\frac{1}{\sqrt{2}+\frac{3\sqrt{2}}{73}}$

                                        $\sqrt{2}+\frac{3\sqrt{2}}{73}:{\frac{76\sqrt{2}}{73}}$                  

$=\frac{1}{\frac{76\sqrt{2}}{73}}$

                                      $\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{1}{\frac{b}{c}}=\frac{c}{b}$

$=\frac{73}{76\sqrt{2}}$

                                      $Rationalize \frac{73}{76\sqrt{2}}:\frac{73\sqrt{2}}{152}$

$=\frac{73\sqrt{2}}{152}$

Oh, both of these answers or just mine?