A committee consists of eight students and five faculty.
how many possible five-person subcommittees are there?
Answer: We have a total of 13 people from whom we have to choose 5-person subcommittee.
Therefore, the number of possible ways is:
ways
how many that contain exactly three students?
Answer: The number of ways that will contain exactly three students is:
ways
how many that contain at least three students
Answer: The number of ways that will contain at least three students is:
ways
we are given
distance=6.7 furlongs
(a) In rods
we know that
we can multiply both sides by 6.7
..............Answer
(b) In chains
we know that
we can multiply both sides by 6.7
..............Answer
Answer:
(3x + 11y)^2
Step-by-step explanation:
The polynomial is a perfect square trinomial, because:
1) √ [9x^2] = 3x
2) √121y^2] = 11y
3) 66xy = 2 *(3x)(11y)
Then it is factored as a square binomial, being the factored expression:
[ 3x + 11y]^2
Now you can verify working backwar, i.e expanding the parenthesis.
Remember that the expansion of a square binomial is:
- square of the first term => (3x)^2 = 9x^2
- double product of first term times second term =>2 (3x)(11y) = 66xy
- square of the second term => (11y)^2 = 121y^2
=> [3x + 11y]^2 = 9x^2 + 66xy + 121y^2, which is the original polynomial.
Complex roots occur as conjugates so the other root is 3 + 2i
so we have the factored form
(x - (3 - 2i)(x - (3 + 2i)
= (x - 3 + 2i)(x - 3 - 2i)
= x^2 -3x - 2ix - 3x + 9 + 6i + 2ix - 6i- 4i^2
= x^2 -6x + 9 + 4
= x^2 - 6x + 13 Answer