$${\mathtt{\,-\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{50}}{\mathtt{\,-\,}}{\mathtt{2}} \Rightarrow {\mathtt{x}} = -{\mathtt{4}}$$
Pick an interior point of the polygon. Connect the point to each of the vertices. This gives you n triangles, whose angle sum is 180° * n. You don't have to count the 360° at hte center.
So the sum of the polygon's angles is 180° * n - 360° = 180° * (n - 2).
$${\sqrt{{\mathtt{225}}}} = {\mathtt{15}}$$
$${\sqrt{{\mathtt{123\,456\,789\,789\,786\,456.003}}}} = {\mathtt{351\,364\,183.988\: \!332\: \!049\: \!237\: \!642\: \!1}}$$
$${\left|-{\mathtt{6}}\right|}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{\left|{\mathtt{4}}\right|}{\mathtt{\,\small\textbf+\,}}{\left|-{\mathtt{5}}\right|}{\mathtt{\,-\,}}{\mathtt{0}}{\mathtt{\,\times\,}}{\mathtt{6}} = {\mathtt{23}}$$
$${{\mathtt{\pi}}}^{{\mathtt{2}}} = {\mathtt{9.869\: \!604\: \!401\: \!089\: \!358\: \!6}}$$
$${\mathtt{90}}{\mathtt{\,\small\textbf+\,}}\left({\mathtt{90}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{6}} = {\mathtt{186}}$$
density = mass / volume , therefore volume = mass / density
75 / 7.14 = 10.5042017 milliliters = 10.5042017 cm^3
The black rose carpet cheaper.
In this case the 4m wide is just enough (3.85 + 0.15 = 4) and you have to cut to the length of 2.35 + 0.15 = 2.50m. 2.5 * 4 = 10 m^2. The cost is 10 * 8 = £80.
In the second case you have to buy carpet with 4m length. After you bought it you have to cut the width to 2.50m. Hence you have to buy 3 * 4 = 12 m^2 carpet which costs 12 * 7 = £84
In conclusion the first choice is cheaper by £4.
$${{\mathtt{5}}}^{-{\mathtt{2}}} = {\frac{{\mathtt{1}}}{{\mathtt{25}}}} = {\mathtt{0.04}}$$
$$199! = \Gamma(200)$$
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