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!
I just took the quiz so the answer's are...
The bowling alley charges $2 to rent shoes. Tom is going to rent shoes at the bowling alley. Therefore, Tom expects to spend $2 to rent shoes at the bowling alley.
Opposite sides of a rectangle are parallel. Side ABSide AB and side CDside CD are opposite sides of a rectangle. Therefore, side ABside AB and side CDside CD are parallel.
All four sides of a rhombus are the same length. Quadrilateral ABCDQuadrilateral ABCD is a rhombus. Therefore, all four sides of quadrilateral ABCDquadrilateral ABCD are the same length.
Answer:
A
Step-by-step explanation:
For test A, the unit rate is 30 words per minute divided by 4 minutes, or 7.5 words per minute.
Unit rate = 78 words/15 minutes = 5.2 words per minute for test B.
The unit rate for test C is 99 words/22 minutes, or 4.5 words per minute.
Answer:
Roughly
1143$ annually
But if you want exact then its
1142.857143$
Step-by-step explanation:
Answer:
1/92^7
this is correct answer of this question
hope it helps
