Hello from MrBillDoesMath!
Answer: N = 143
Discussion:
This one took some trial and error! At first I listed all 2 digit primes, looked at the list, but didn't know how to proceed. So, I took the smallest 2 digit primes numbers: 11 and 13 and wondered if their product, 13*11 = 143, could be represented as the sum of 3 consecutive primes. I went back to my list of primes, added groups of three consecutive numbers that seemed to be in the right range to give the desired sum, and stumbled on 43, 47, and 53!
43 + 47 + 53 = 143 !
Therefore N = 143. It's the sum of 43, 47, and 53 as well as the product of 11 and 13.
Thank you,
MrB
Two lines are perpendicular if and only if the product of their slopes is - 1.
So, you just need to find the slope of each line and find out the product of their slopes.
I will do one example for you.
L1: y = 3x + 5
L2: y = - 3x + 14
L3: y = -x/3 + 14
The slope of a line is the coefficient of the x.
So the slopes are:
L1: slope 3
L2: slope -3
L3: slope -1/3
So now multiply the slopes of each pair of lines:
L1 and L2: 3 * (-3) = - 9 => No, they are not perpendicular
L2 and L3: (-3) * (-1/3) = 1 => No, they are not perpendicular
L1 and L3: (3) * (-1/3) = -1 => Yes, they are penpendicular.
Triangle WYZ and triangle TWY are congruent, therefore WZ = TW
WZ = TW
3x - 5 = 2x
3x - 2x = 5
x = 5
The value of x is 5
Answer:

Step-by-step explanation:
The given complex number is

The polar form of this complex number is;
, where


and

This implies that;
to the nearest degree.
Hence the polar form is

You want to get the x's on one side and all the other numbers on the other side of the equation.
2x-5x+6=0
2x-5x=-6
-3x=-6
x=2