invizzble

1) Calculate the brackets: -25-7a = -7a -21

2) isolate the a: -4 = 14a

3)Answer: a = -4/14 (-> a = -2/7)

atan(rise/run)

1) Bring it all to one side: 6x² - 11x = 0

2) Isolate one of the x's: x*(6x-11)=0

3)To become zero one of the factors must be zero: x = 0 or 6x-11 = 0

4)Solve: x = 0 or x = 11/6

If you'd have to calculate it you would wanna calculate the derivative and see where that equals 0. 

(To calculate the derivative of an absolute value function you have to split it into two for when 2sin(2x - pi/3) - 5 > 0 and 2sin(2x - pi/3) - 5 < 0 (and add a minus before this one))

if you simply need those values, just plot it and you'll get minimum 6, maximum 10

It's the standard unit of meausurement for angles where the complete circle is 2pi rad. This makes dealing with goniometrics h**l of a lot easier!

https://en.wikipedia.org/wiki/Radian

First approuch (Theoritical approuch)

Well we have the law of cosine that states: a² = b²+c² - 2bc*cos(A) (where A is the angle across the side a) 

We can manipulate this formula to the form of \(A = acos(\frac{(a²-b²-c²)}{-2bc}{})\)

So if we fill in our formula we'll get: \(A = acos(\frac{10²-4²-5²)}{-2*4*5}{})\)

We'd get \(A = acos(-1.475)\), which has no solution

Second approuch (Visual approuch)

You could look at the function \(f(x) = \sqrt{4² + 5² - 2*4*5*cos(x)}\)(where f(x) would be your third side and x would be the angle between the 4- and 5 side)

If you look at the plot of this function you'll see that it never reaches f(x) = 10

Third approuch (intuitional approuch)

A triangle has  three sides connected to eachother on their ends -> The sum of two sides must be bigger than or equal to the third side, else there would be no way to connect them to the ends of that side. 4+5 = 9 -> 9 < 10 thus the triangle would be impossible. 

Hope this helped!