thedudemanguyperson

Opposite sides of a parallelogram are equal. So $3x+20=5x-12$. Now continue.

Let the point be $(x,0)$. Use the distance formula to calculate the distances between this point and $A$ and this point and $B$. Equate the two, and solve for $x$.

Hint: Use Shoelace Theorem

Hint: By Angle Theorem: $7x+15=141$.

Very very interesting problem.

I can do this with the Lagrange Interpolation Formula. I will write up a solution very soon.

Hint: Rewrite as $(x(x(x*x^{1/2})^{1/3})^{1/3})^{1/3}$ and use $x^a*x^b=x^{a+b}$ as well as $(x^a)^{b}=x^{ab}$.

Hint: We know that $\angle BAC=\frac12\cdot 118$. Then use that the sum of the angles in a triangle are $180$ and apply the inscribed angle theorem once more to finish. (I'll leave it to you to figure out where)

Hint: They have the same base radius $r$ and height $h$. The volume of a cone is $\frac{\pi r^2 h}{3}$, which is given as $5$, and we want $\pi r^2 h$ (volume of a cylinder).

Hint: Substitute $y=-x-8$ and put into the equation so you get a quadratic. In a quadratic equation, the equation has only one solution if the discriminant is $0$. In $ax^2+bx+c$, the discriminant is $b^2-4ac$. From here you should be able to solve for k. Good luck! 

The question asked for a reference triangle.

Remember that sin is opposite over hypotenuse, meaning that the side opposite to angle with measure $x$ is $8$ and the hypotenuse is $17$. Use the Pythagorean theorem to find the other side. Then, use that $\cot(x)=\frac{\cos(x)}{\sin(x)}$, recalling that $\cos=\frac{\text{adjacent}}{\text{hypotenuse}}$.

(Remember: Soh Cah Toa!)