The correct answer is 3.
The formula for the law of sines is the following:
P/sin P = Q/sin Q = R/sin R
So, if you break these up into two different equations, you will have:
P/sin P = Q/sin Q and P/sin P = R/sin R
To solve, get P alone on one side of the equation by multiplying the other side by sin P:
P = Q sin P/sin Q and P = R sin P/sin R
When you look at the answers, you'll see that the second equation is an option.
ANSWER
![x = \frac{5}{4} - \frac{ \sqrt{ 17} }{4}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B5%7D%7B4%7D%20%20%20-%20%20%5Cfrac%7B%20%20%5Csqrt%7B%2017%7D%20%7D%7B4%7D%20)
or
![x = \frac{5}{4} + \frac{ \sqrt{ 17} }{4}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B5%7D%7B4%7D%20%20%2B%20%20%5Cfrac%7B%20%20%5Csqrt%7B%2017%7D%20%7D%7B4%7D%20)
EXPLANATION
The given equation is:
![2 {x}^{2} - 5x + 1= 0](https://tex.z-dn.net/?f=2%20%7Bx%7D%5E%7B2%7D%20-%205x%20%2B%201%3D%200)
Comparing this to
![a {x}^{2} + bx + c = 0](https://tex.z-dn.net/?f=a%20%7Bx%7D%5E%7B2%7D%20%20%2B%20bx%20%2B%20c%20%3D%200)
we have a=2, b=-5, c=1
The quadratic formula is given by
![x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B%20-%20b%20%5Cpm%20%5Csqrt%7B%20%7Bb%7D%5E%7B2%7D%20%20-%204ac%7D%20%7D%7B2a%7D%20)
We substitute the values to get,
![x = \frac{ - - 5 \pm \sqrt{ {( - 5)}^{2} - 4(1)(2)} }{2(2)}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B%20-%20%20-%205%20%5Cpm%20%5Csqrt%7B%20%7B%28%20-%205%29%7D%5E%7B2%7D%20%20-%204%281%29%282%29%7D%20%7D%7B2%282%29%7D%20)
![x = \frac{ 5 \pm \sqrt{ 17} }{4}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B%205%20%5Cpm%20%5Csqrt%7B%2017%7D%20%7D%7B4%7D%20)
![x = \frac{5}{4} - \frac{ \sqrt{ 17} }{4}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B5%7D%7B4%7D%20%20%20-%20%20%5Cfrac%7B%20%20%5Csqrt%7B%2017%7D%20%7D%7B4%7D%20)
or
![x = \frac{5}{4} + \frac{ \sqrt{ 17} }{4}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B5%7D%7B4%7D%20%20%20%2B%20%20%5Cfrac%7B%20%20%5Csqrt%7B%2017%7D%20%7D%7B4%7D%20)
Answer:
b i think (im not really sure
Step-by-step explanation: