Melody

$$4x^3 + 16x^2 - 8x$$

This cannot be simplified.  

It can be factorised - but not simplified 

Thanks Titanium, I will fix it up :))

@@ End of Day Wrap  Sat 4/7/15   Sydney, Australia Time   11:57pm  ♪ ♫

Hi all,

Great answers today from TitaniumRome, Radix, CPhill, Fiora and Civoamzuk.  Thank you 

$$\\\frac{sin \angle POM_1}{1}=\frac{sin45}{\sqrt5}\\\\
\frac{sin \angle POM_1}{1}=\frac{1}{\sqrt2*\sqrt5}\\\\
\frac{sin \angle POM_1}{1}=\frac{1}{\sqrt{10}}\\\\
\angle POM_1=asin\left( \frac{1}{\sqrt{10}}\right)\\\\$$

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{1}}}{{\sqrt{{\mathtt{10}}}}}}\right)} = {\mathtt{18.434\: \!948\: \!822\: \!922^{\circ}}}$$

$$\\\angle NOM_1=30-18.434948822922=\;11.565051177078$$

$${\mathtt{30}}{\mathtt{\,-\,}}{\mathtt{18.434\: \!948\: \!822\: \!922}} = {\mathtt{11.565\: \!051\: \!177\: \!078}}$$

Now Find N

N is the intersection of 

$$y=(tan30)x = \frac{x}{\sqrt3} \qquad and \qquad y=-x+2\sqrt2$$

$$\underset{\,\,\,\,{\textcolor[rgb]{0.66,0.66,0.66}{\rightarrow {\mathtt{y, x}}}}}{{solve}}{\left(\begin{array}{l}{\mathtt{y}}={\frac{{\mathtt{x}}}{{\sqrt{{\mathtt{3}}}}}}\\
{\mathtt{y}}={\mathtt{\,-\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{2}}}}\end{array}\right)} \Rightarrow \left\{ \begin{array}{l}{\mathtt{y}} = {\sqrt{{\mathtt{2}}}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{2}}}}\\
{\mathtt{x}} = {\mathtt{3}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{2}}}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{2}}}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{y}} = {\mathtt{1.035\: \!276\: \!180\: \!410\: \!083}}\\
{\mathtt{x}} = {\mathtt{1.793\: \!150\: \!944\: \!336\: \!107}}\\
\end{array} \right\}$$

$$N(3\sqrt2-\sqrt6,\;\sqrt6-\sqrt2)$$

Distance ON

$${\sqrt{{\left({\mathtt{3}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{2}}}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{6}}}}\right)}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\left({\sqrt{{\mathtt{6}}}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{2}}}}\right)}^{{\mathtt{2}}}}} = {\mathtt{2.070\: \!552\: \!360\: \!820\: \!166}}$$

$$Area\;\triangle\;ONM_1= 0.464\;units^2 \qquad $correct to 3 decimal places$$$ 

$${\mathtt{0.5}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{5}}}}{\mathtt{\,\times\,}}{\mathtt{2.070\: \!552\: \!360\: \!820\: \!166}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{11.565\: \!051\: \!177\: \!078}}^\circ\right)} = {\mathtt{0.464\: \!101\: \!615\: \!138\: \!509\: \!6}}$$

$$Area\;\triangle\;ONM_1= 0.464\;units^2 \qquad $correct to 3 decimal places$$$ 

NOW If I haven't made any stupid errors (which I probably have) that should be correct :)

Thanks Radix,  here is another way to look at it :/

$$\\9.5\%*X=733.55\\\\
so\\\\
X=733.55\div 9.5\%$$

$${\frac{{\mathtt{733.55}}}{\left({\frac{{\mathtt{9.5}}}{{\mathtt{100}}}}\right)}} = {\mathtt{7\,721.578\: \!947\: \!368\: \!421\: \!052\: \!6}}$$

Doesn't make sense

1×√(1-(719.31÷89602783250817600)

$${\mathtt{1}}{\mathtt{\,\times\,}}{\sqrt{\left({\mathtt{1}}{\mathtt{\,-\,}}\left({\frac{{\mathtt{719.31}}}{{\mathtt{89\,602\,783\,250\,817\,600}}}}\right)\right)}} = {\mathtt{0.999\: \!999\: \!999\: \!999\: \!996}}$$

It worked fine    

For my college grades my second year was worth 30% and third year was worth 70%...

If I got 53.92 in second year and 58.92 in third year what's my overall percentage? 

I will assume that those marks are out of 100.

$${\frac{{\mathtt{53.92}}}{{\mathtt{100}}}}{\mathtt{\,\times\,}}{\mathtt{30}} = {\frac{{\mathtt{2\,022}}}{{\mathtt{125}}}} = {\mathtt{16.176}}$$

$${\frac{{\mathtt{58.92}}}{{\mathtt{100}}}}{\mathtt{\,\times\,}}{\mathtt{70}} = {\mathtt{41.244}}$$

$${\mathtt{16.176}}{\mathtt{\,\small\textbf+\,}}{\mathtt{41.244}} = {\frac{{\mathtt{2\,871}}}{{\mathtt{50}}}} = {\mathtt{57.42}}$$      percent