Answer:
Option A) m∠RNS=27°
Step-by-step explanation:
We know that
∠UNR = 180°. This tells us that the Sum of the enclosed angles should equal 180°, by trigonometry. So the enclosed angles are:
∠RNS = ![(3x+6)^{o}](https://tex.z-dn.net/?f=%283x%2B6%29%5E%7Bo%7D)
∠SNT= ![(13x+3)^{o}](https://tex.z-dn.net/?f=%2813x%2B3%29%5E%7Bo%7D)
∠TNU= ![(10x-11)^{o}](https://tex.z-dn.net/?f=%2810x-11%29%5E%7Bo%7D)
Now let us add all the angles and solve for the value of
as follow:
![m_{RSN}+m_{SNT}+m_{TNU}=m_{UNR}\\\\(3x+6)+(13x+3)+(10x-11)=180\\\\3x+13x+10x+6+3-11=180\\\\26x-2=180\\\\26x=180+2\\\\26x=182\\\\](https://tex.z-dn.net/?f=m_%7BRSN%7D%2Bm_%7BSNT%7D%2Bm_%7BTNU%7D%3Dm_%7BUNR%7D%5C%5C%5C%5C%283x%2B6%29%2B%2813x%2B3%29%2B%2810x-11%29%3D180%5C%5C%5C%5C3x%2B13x%2B10x%2B6%2B3-11%3D180%5C%5C%5C%5C26x-2%3D180%5C%5C%5C%5C26x%3D180%2B2%5C%5C%5C%5C26x%3D182%5C%5C%5C%5C)
![x=\frac{182}{26} \\\\x=7](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B182%7D%7B26%7D%20%5C%5C%5C%5Cx%3D7)
Now lets plug in the value into the expression for angle
∠RNS to find the angle as:
![RNS = (3x+6)^{o}\\\\RNS=(3(7)+6)^{o}\\\\RNS=(21+6)^{o}\\\\RNS=27^{o}](https://tex.z-dn.net/?f=RNS%20%3D%20%283x%2B6%29%5E%7Bo%7D%5C%5C%5C%5CRNS%3D%283%287%29%2B6%29%5E%7Bo%7D%5C%5C%5C%5CRNS%3D%2821%2B6%29%5E%7Bo%7D%5C%5C%5C%5CRNS%3D27%5E%7Bo%7D)
Thus Option A. is the correct answer.
Answer:
![8.49\ units](https://tex.z-dn.net/?f=8.49%5C%20units)
Step-by-step explanation:
we know that
The Pythagorean Theorem states that in a right triangle
![c^2=a^2+b^2](https://tex.z-dn.net/?f=c%5E2%3Da%5E2%2Bb%5E2)
where
c is the greater side (the hypotenuse)
a and b are the legs
In this problem
Let
c=AB ---> distance from point A to point B
a ---> the difference of the x-coordinates both points
b ---> the difference of the y-coordinates both points
so
![a=1-(-5)=6\ units\\b=6-0=6\ units](https://tex.z-dn.net/?f=a%3D1-%28-5%29%3D6%5C%20units%5C%5Cb%3D6-0%3D6%5C%20units)
substitute
![AB^2=6^2+6^2](https://tex.z-dn.net/?f=AB%5E2%3D6%5E2%2B6%5E2)
![AB^2=72](https://tex.z-dn.net/?f=AB%5E2%3D72)
![AB=\sqrt{72}\ units](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B72%7D%5C%20units)
![AB=8.49\ units](https://tex.z-dn.net/?f=AB%3D8.49%5C%20units)
The simplified expression is 6+3i
Answer:
n=o
Step-by-step explanation:
Answer:
it would be
Step-by-step explanation:
I do not think you need an explanation but if so just comment