You want to end up with 
. Expand this using the angle sum identity for sine:
We want this to line up with 
. Right away, we know 
.
We also need to have
Recall that 
for all 
; this means
Then
So we end up with
12. I’m sorry I’m horrible at word problems
13. C
14. C
FOIL
First = 6x(2x) = 12x
Outside = 6x(-3) = -18x
Inside = -5(2x) = -10x
Last = -5(-3) = 15
12x - 18x - 10x + 15
12x - 28 + 15
-16x + 15
Hope this helps =)
0+x*7=14
X=2 is the correct answer
To solve this problem, we make use of the formula of
combination.
nCr = n! / r! (n – r)!
where n is the total number of subject teachers and r is
the number of subjects r = 1
For the English class n = 3
3C1 = 3! / 1! (3 – 1)! = 3
For the Algebra class n = 4
4C1 = 4! / 1! (4 – 1)! = 4
For the Biology class n = 2
2C1 = 2! / 1! (2 – 1)! = 2
The total number of different schedules would be the
product of the three combinations:
total combinations possible = 3 * 4 * 2
total combinations possible = 24
