There are 6 brown, 5 blue, and 2 orange marbles in a hat. what is the probability of picking two orange marbles in a row without returning the marbles back to the hat? (write your answer as a fraction.)

Lets look at the information we have-

6 brown marbles
5 blue marbles 
2 orange marbles. 

Question:- 
What is the probability of picking two orange marbles in a row without returning the marbles back to the hat?
Solve:-

First add all the marbles:-

6 + 5 + 2 = 13

13 marbles in total. 

Now lets write the 1st probability:- 

2 orange
13 together


2nd probability:- 

13 - 1 = 12

1 orange (left)
12 total (without putting back)


Hope i helped ya!! xD

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x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

(x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81