Alright. One way you can do this is to list multiples of each denominator:
1/4:
4, 8, 12, 16, 20, 24, 28, 32, 36...... and so on
3/7:
7, 14, 21, 28, 35, 42, 49, 57, 63......
1/11;
11, 22, 33, 44, 55, 66, 77, 88......
Keep going until you see the least common denominator!
Now an easier way to do this is by multiplying all of the numbers in the denominator then get the factors:
4*7*11 = 308
And since those are not divisible by a whole number (besides 4 but 308 won't be divisible by 2*7*11)
Therefore 308 is the least common denominator.
This is a doozy so pay attention. First thing you have to recognize is that is a trig identity, the sum identity for cosine to be exact. That formula is
.
So that means you need to find the cosine of alpha and the sin of beta. We are given the sin of alpha being 4/5 in the first quadrant. If you set up the sin ratio which is side opposite over hypotenuse of a right triangle, you put the 4 on the side opposite the reference angle, alpha, and the hypotenuse of 5 on the terminal ray and then you have to find the missing side of the right triangle you created. Using Pythagorean's theorem, you find that the missing side, which is the adjacent side to alpha, is 3. Now you can find the cosine of alpha as well, since cosine is the side adjacent, 3, over the hypotenuse, 5. So far wwe have
and
for that first angle. Now moving on to the second angle. The cosine of beta is side adjacent, 5, over the hypotenuse, 13, and we are missing the side opposite the reference angle beta. Using Pythagorean's theorem again to find the side opposite, we have that that side measures 12. Now we can find the sine of beta using that opposite side, 12, over the hypotenuse, 13. What we have now is
and
. According to the identity, we have to multiply those ratios now:
.
When you do that you get
.
Of course in order to subtract those 2 fractions you need a common denominator which is 65 so
which gives you a final answer of 
which is the first choice given above. There you go!
Answer:
-2
Step-by-step explanation:
as x goes up 1 y goes down 2
slope is change in y over change in x
-2/1=-2
hey its -100 percent. the negative to show decrease.
First you have all ten books, but then every time after, you loose one because you can't put the same book in the group twice.
10 * 9 * 8 * 7 = 5040 groups
