-6x + y = 11 add 6x to both sides
y = 11 + 6x
hope that helps, God bless!
Answer:
x = 5 (see below)
Step-by-step explanation:
Combine like terms by subtracting on both sides:
25 + 8x = 5 + 12x
20 = 4x
Then divide:
20 = 4x
5 = x
Move the variable to the left side of the equation:
x = 5
Let length of shortest side be x
then length of each congruent sides = x + 1
perimeter of the triangle = x + x+1 +x + 1 = 3x + 2
perimeter of the square = 4(x-2) = 4x - 8
So we have
4x - 8 = 3x + 2
x = 10
the shortest side is 10 units long.
Answer:
or ![P(x\le 4\ or x> 10) = 0.5714](https://tex.z-dn.net/?f=P%28x%5Cle%204%5C%20or%20x%3E%2010%29%20%3D%200.5714)
Step-by-step explanation:
Given
![x = \{1,2,3,4,5,6,7,8,9,10,11,12,13,14\}](https://tex.z-dn.net/?f=x%20%3D%20%5C%7B1%2C2%2C3%2C4%2C5%2C6%2C7%2C8%2C9%2C10%2C11%2C12%2C13%2C14%5C%7D)
Required
Determine ![P(x\le 4\ or x> 10)](https://tex.z-dn.net/?f=P%28x%5Cle%204%5C%20or%20x%3E%2010%29)
Because the events are independent, the probability can be solved using:
![P(A\ or\ B) = P(A) + P(B)](https://tex.z-dn.net/?f=P%28A%5C%20or%5C%20B%29%20%3D%20P%28A%29%20%2B%20P%28B%29)
So, we have:
![P(x\le 4\ or x> 10) = P(x \le 4) + P(x > 10)](https://tex.z-dn.net/?f=P%28x%5Cle%204%5C%20or%20x%3E%2010%29%20%3D%20P%28x%20%5Cle%204%29%20%2B%20P%28x%20%3E%2010%29)
When
, we have: ![x = \{1,2,3,4\}](https://tex.z-dn.net/?f=x%20%3D%20%5C%7B1%2C2%2C3%2C4%5C%7D)
So:
![P(x \le 4) = \frac{4}{14}](https://tex.z-dn.net/?f=P%28x%20%5Cle%204%29%20%3D%20%5Cfrac%7B4%7D%7B14%7D)
Also:
When
, we have: ![x = \{11,12,13,14\}](https://tex.z-dn.net/?f=x%20%3D%20%5C%7B11%2C12%2C13%2C14%5C%7D)
So:
![P(x>10) =\frac{4}{14}](https://tex.z-dn.net/?f=P%28x%3E10%29%20%3D%5Cfrac%7B4%7D%7B14%7D)
becomes
![P(x\le 4\ or x> 10) = \frac{4}{14} + \frac{4}{14}](https://tex.z-dn.net/?f=P%28x%5Cle%204%5C%20or%20x%3E%2010%29%20%3D%20%5Cfrac%7B4%7D%7B14%7D%20%2B%20%5Cfrac%7B4%7D%7B14%7D)
![P(x\le 4\ or x> 10) = \frac{4+4}{14}](https://tex.z-dn.net/?f=P%28x%5Cle%204%5C%20or%20x%3E%2010%29%20%3D%20%5Cfrac%7B4%2B4%7D%7B14%7D)
![P(x\le 4\ or x> 10) = \frac{8}{14}](https://tex.z-dn.net/?f=P%28x%5Cle%204%5C%20or%20x%3E%2010%29%20%3D%20%5Cfrac%7B8%7D%7B14%7D)
![P(x\le 4\ or x> 10) = \frac{4}{7}](https://tex.z-dn.net/?f=P%28x%5Cle%204%5C%20or%20x%3E%2010%29%20%3D%20%5Cfrac%7B4%7D%7B7%7D)
![P(x\le 4\ or x> 10) = 0.5714](https://tex.z-dn.net/?f=P%28x%5Cle%204%5C%20or%20x%3E%2010%29%20%3D%200.5714)