Given the following two equations determine if they are parallel, perpendicular, or neither. 3x + 6y = 30
4y + 2x = 9

Please show work!

Parallel

Step-by-step explanation:

What you want to do first is to put both equations into the slope intercept form: y=mx+b.

In the first equation, you move the to the right side of the equal sign by subtracting on both sides:

Then you want to divide both sides by 6 to isolate y:

Next for the second equation, you do similar steps. You subtract from both sides:

Then you want to divide both sides by '4' to isolate y:

Now to check if the two equations are parallel, perpendicular, or neither, you compare the slopes 'm' which is the coefficient next 'x'. If two equations have the same slope, then they are parallel. If the slopes multiplied equal -1, then they are perpendicular. If the slopes are not the same or if the product of the slopes is not -1, then it is neither.

In the case of this problem, the slopes are the same, so the equations are parallel:

Of course, with a triangle with a 90° angle, a right triangle, you can simply use pythagoras theorem  (a2+b2=c2)  then SOH-CAH-TOA to solve for the angle  (θ=Cos−1(adjacenthypotenuse)) .

But what if it isn't a right triangle? The cosine rule works for all triangles, even if they don't have a 90° angle.

a2=b2+c2−2(b)(c)Cos(A)  

Where a is the missing side, and A is the angle opposite to side a.

With this rule, we can find a missing angle or a missing side to any type of triangle, assuming you have the needed variables.

Explanation: