amazingxin777

hint:  this question involves the law of sines!! I'm pretty sure- (if you haven't gotten this far yet... i don't recommend myself for this question). The law of sines states:

\(\frac{\text{sin} A}{a}=\frac{\text{sin}B}{b}= \frac{\text{sin}C}{c}\) where A, B, and C are the sides of the triangle, and a, b, and c are the opposite angles, respectively. 

Draw a rectangle surrounding the triangle. You should get a 5x3 rectangle. Minus the extra triangles within the rectangle: 4, 5/2, 3/2. 15-8=7. The answer is \(\boxed7\)

Plug x in:

\((\sqrt{2+\sqrt{2}})^4+\frac{4}{(\sqrt{2+\sqrt{2}})^4}\) 

Simplify:

\(6+4\sqrt2+\frac{4}{6+4\sqrt{2}}\)

The fraction's numerator and denominator can both be divided by 2:

\(6+4\sqrt2+\frac{2}{3+2\sqrt2}\)

I am not sure if this is the simplest form - someone please double check~!!!

If we simplify that expression we get: \(\frac{y+6}{(y-1)(y-4)}\). The expression is undefined when the denominator is equal to 0 which is when y=1 or 4. So the sum of 1 and 4 is \(\boxed{5}\). 

2) The discrimant is \(b^2-4ac\) so it would be \(4-160\Rightarrow -156\)

what's an elaborate number?

Guest provided the correct answer but I expanded on it: 

The formula for a cone's  volume is  \(V=\frac{1}{3}hπr²\) where h is the height and r is the radius. So let's plug what we know into that equation. The slant height is 13 and the radius is 5. If we use the Pythagorean theorem (\(a^2+b^2=c^2\)- where a, b, and c are the sides of a triangle), you find out that the third side of the triangle (or the height) is 12. So the radius is 5 and the height is 12 \(\Rightarrow \frac {1}{3}\times12\times\pi\times25 \Rightarrow 100\pi\) which is \(100\pi \space or \space \boxed{c}\).

I'm pretty sure this is off-topic. 

Angle bisector means it halves the angle. So that means \(ABE=EBC\)\(\Rightarrow2x+20=4x-6\Rightarrow2x=26\Rightarrow x=13\). Plug that into \(2x+20\) to find ABE. \(2\times13+20\Rightarrow46\) and the answer is \(\boxed{46}\)

Heron's formula is \(\sqrt{s(s-a)(s-b)(s-c)}=area\) where s is the semi-perimeter (in less fancy words \(\frac{area}{2}\)) and a, b, c are the sides of the triangle. I'm pretty sure the guest did something wrong in the calculations there and that is why he/she was wrong