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?