OK you must establish a relation of the two first quantities, it means 1/4 lime : 3/4 oil, then with 1 cup oil it will be x quantity of lime
1/4 cup lime____3/4 cup oil
x_________1 cup oil x = 1*1/4÷3/4 , x= 1/3 lime juice
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!
3 + 0.45*M<=8,40. Notice the equal, because you may use all the money. Then, rearranging: M<=(8.40-3)/0.45= 12, so M<=12. Now, obviously time is positive, so you may end saying 0<=M<=12, with M=0 meaning no call! :)
<span>1. Martina is given to be 14 years older than Joey who is x years old. Hence, the age of Martina can be expressed as,
x + 14
2. If Joey's current age is x then in 5 years he will become x+5 years old.
3. Martina's age will be her current age added with 5 making it, x+14+5 or x + 19.
4. The equation that would best represent the given scenario in this item is:
x + 19 = 3(x + 5)
5. From the given above, the value of x is equal to 2. This is Joey's current age.
6. The current age of Martina is x + 14 which is equal to 16.</span>
Answer:
a. m<B = 100°
b. m<L = 55°
c. Scale factor = 9/11
Step-by-step explanation:
a) Similar triangles have their three corresponding angles congruent to each other, while the ratio of their corresponding sides are proportional to each other.
Since ∆ABC ~ ∆GLJ, therefore,
<A = <G,
<B = <J
<C = <L
m<J = 100° (given)
Therefore,
m<B = m<J = 100°
m<B = 100°
b) m<A = m<G
m<A = 25° (given)
Therefore,
m<A = m<G = 25°
m<G = 25°
m<L = 180° - (m<J + m<G)
Substitute
m<L = 180° - (100° + 25°)
m<L = 55°
c) scale factor of smaller triangle to the larger = side length of smaller triangle / corresponding side length of bigger triangle
Scale factor = AB/GJ
Substitute
Scale factor = 18/22
Simplify
Scale factor = 9/11
