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Travka [436]
2 years ago
15

Is this a function yes / no

Mathematics
1 answer:
Doss [256]2 years ago
3 0

Answer:

yes

Step-by-step explanation:

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Question is 15 points
mihalych1998 [28]

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

cos(\alpha +\beta )=cos\alpha cos\beta -sin\alpha sin\beta.

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

sin\alpha =\frac{4}{5} and

cos\alpha =\frac{3}{5} 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

cos\beta =\frac{5}{13} and

sin\beta =\frac{12}{13}. According to the identity, we have to multiply those ratios now:

(\frac{3}{5}*\frac{5}{13})-(\frac{4}{5}*\frac{12}{13}).

When you do that you get

\frac{3}{13}-\frac{48}{65}.

Of course in order to subtract those 2 fractions you need a common denominator which is 65 so

\frac{15}{65}-\frac{48}{65} which gives you a final answer of -\frac{33}{65} which is the first choice given above. There you go!

4 0
2 years ago
What is the simplified value of the expression below?<br><br> Negative 2.6 + 5.8
Katen [24]
8.4 )::::: I think sorry
5 0
2 years ago
Read 2 more answers
What is the difference between axiom and postulate theorem
nydimaria [60]

Answer:

Axioms or postulates are universal truths. They cannot be proved. Theorem are statements which can be proved.

6 0
2 years ago
F almonds sell for $1.20 per pound, and walnuts sell for $.75 per pound, how many pounds of each must be used to make 45 pounds
lukranit [14]

Answer:

Option A.) 20 pounds of walnuts and 25 pounds of almonds is correct.

Step-by-step explanation:

i) let x be the the number of pounds of almonds

ii) let y be the number of pounds of walnuts

iii) therefore x + y = 45 pounds of the mixture

iv) 1.2x + 0.75y = 1.00 \times 45 = 45

v) Multipling equation in iv) by 4 we get

  4.8x + 3y = 180

vi) multiplying equation in iii) by 3 we get

     3x + 3y = 135

vii) subtracting equation vi) from equation v)  we get 1.8x = 45

ix) therefore we get x = 45/1.8 = 25 pounds of almonds

x) therefore 25 + y = 45  .... substituting value of x from ix) in iii) we get

   therefore y = 20 pounds of walnuts

Therefore option A.) 20 pounds of walnuts and 25 pounds of almonds is correct.

7 0
2 years ago
19. Calculate the size of the angle marked x in the diagram.
algol [13]

Answer:

151°

Step-by-step explanation:

126°+221°+95°+57°+70+x=720° ( sum of interior angles of hexagon)

x + 569° =720°

x = 720°- 569°

=151°

7 0
2 years ago
Read 2 more answers
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