A + b
= -10 + 4
= 4 - 10
= -6
Answer:
The answer to your question is: x = 2
Step-by-step explanation:
Data
LM = 6x
MN = 10x + 4
LN = 20x - 4
x = ?
Process
LM + MN = LN
Then
6x + 10x + 4 = 20x - 4
Solve for x 16x + 4 = 20x -4
16x - 20x = -4 - 4
-4x = -8
x = -8/-4
x = 2
6(2) + 10(2) + 4 = 20(2) - 4
12 + 20 + 4 = 40 -4
36 = 36
X^3 - 6x^2 + 11x - 6 = 0
f(1) = 1^3 - 6(1)^2 + 11(1) - 6 = 1 - 6 + 11 - 6 = 0
This means that x - 1 is a factor of x^3 - 6x^2 + 11x - 6 = 0
x^2 - 5x + 6
___________________
x - 1 | x^3 - 6x^2 + 11x - 6
- | x^3 - x^2
|______________
| -5x^2 + 11x - 6
- | -5x^2 + 5x
|_____________________
| 6x - 6
- | 6x - 6
x^3 - 6x^2 + 11x - 6 = (x - 1)(x^2 - 5x + 6) = (x - 1)(x - 2)(x - 3)
Therefore, solutions to x^3 - 6x^2 + 11x - 6 are 1, 2 and 3.
Note the answer must be positive because if sin>0, then csc > 0.
There are two ways to do this problem.
1) Use a trig identity:

Sub in value for cot

2) Use a right triangle and SOH CAH TOA
cot = 1/tan = adjacent/opposite = -21/20
Therefore adjacent side = 21, opposite side = 20
Use pythagorean thm to find hypotenuse:

csc = 1/sin = hypotenuse/opposite = 29/20
Hope this helps.