<u>Answer:</u>
Angle A = 39°
<u>Step-by-step explanation:</u>
We are given that there is a triangle ABC where a = 9, c = 5 and angle B = 120° and we are to find the measure of angle A.
But first we need to find the side b using the law of cosine:
![b^2 = a^2 + c^2- 2a*c*cos(120)](https://tex.z-dn.net/?f=b%5E2%20%3D%20a%5E2%20%2B%20c%5E2-%202a%2Ac%2Acos%28120%29)
![b^2 = 81 + 25 - 2*9*5*(-0.5)](https://tex.z-dn.net/?f=b%5E2%20%3D%2081%20%2B%2025%20-%202%2A9%2A5%2A%28-0.5%29)
![b=\sqrt{151}](https://tex.z-dn.net/?f=b%3D%5Csqrt%7B151%7D)
Now finding angle A using law of cosine:
![cos(A) = \frac{b^2+c^2-a^2}{2b*c}](https://tex.z-dn.net/?f=cos%28A%29%20%3D%20%5Cfrac%7Bb%5E2%2Bc%5E2-a%5E2%7D%7B2b%2Ac%7D)
![cos(A) = \frac{151+25-81}{2*12.29*5}](https://tex.z-dn.net/?f=cos%28A%29%20%3D%20%5Cfrac%7B151%2B25-81%7D%7B2%2A12.29%2A5%7D)
![cos A=0.7730](https://tex.z-dn.net/?f=cos%20A%3D0.7730)
![A=39.38](https://tex.z-dn.net/?f=A%3D39.38)
Therefore, the measure of angle A = 39°.
The given details are illustrations of addition and subtractions of fractions. The scuba driver is at an elevation of
ft below the sea level.
Given that:
--- the first dive
---- the additional dive
From the question, we understand that the diver starts at the sea level.
This is represented with 0ft.
So, the diver's elevation (d) is calculated as follows:
--- we use subtraction because the diver is below the sea level
So, we have:
![d = 0 - 1\frac 23 - 3\frac 25](https://tex.z-dn.net/?f=d%20%3D%200%20-%201%5Cfrac%2023%20-%203%5Cfrac%2025)
![d = - 1\frac 23 - 3\frac 25](https://tex.z-dn.net/?f=d%20%3D%20-%201%5Cfrac%2023%20-%203%5Cfrac%2025)
Convert fractions
![d = - \frac 53 - \frac{17}5](https://tex.z-dn.net/?f=d%20%3D%20-%20%5Cfrac%2053%20-%20%5Cfrac%7B17%7D5)
Take LCM
![d = \frac{-5 \times 5 - 17 \times 3}{15}](https://tex.z-dn.net/?f=d%20%3D%20%5Cfrac%7B-5%20%5Ctimes%205%20-%2017%20%5Ctimes%203%7D%7B15%7D)
![d = \frac{-76}{15}](https://tex.z-dn.net/?f=d%20%3D%20%5Cfrac%7B-76%7D%7B15%7D)
Reduce fraction
![d = -5\frac{1}{15}](https://tex.z-dn.net/?f=d%20%3D%20-5%5Cfrac%7B1%7D%7B15%7D)
The above value means that the diver's elevation is at
ft below the sea level.
Read more about fractions at:
brainly.com/question/18134643
Answer:
I thinks they take 5 hours to meet each other
The correct answer is a = 12
Answer:
![y=10000(1.015)^{12t}](https://tex.z-dn.net/?f=y%3D10000%281.015%29%5E%7B12t%7D)
option-B......Answer
Step-by-step explanation:
We are given
amount taken for loan =$10000
so, P=10000
annual interest rate =18%
r=0.18
now, we can use formula
![y=P(1+\frac{r}{n} )^{nt}](https://tex.z-dn.net/?f=y%3DP%281%2B%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bnt%7D)
Since, it is compounded monthly
so, n=12
we can plug values
![y=10000(1+\frac{0.18}{12} )^{12t}](https://tex.z-dn.net/?f=y%3D10000%281%2B%5Cfrac%7B0.18%7D%7B12%7D%20%29%5E%7B12t%7D)
![y=10000(1.015)^{12t}](https://tex.z-dn.net/?f=y%3D10000%281.015%29%5E%7B12t%7D)