Answer:
![PX=4\\PY=4\sqrt{3}](https://tex.z-dn.net/?f=PX%3D4%5C%5CPY%3D4%5Csqrt%7B3%7D)
Step-by-step explanation:
Let ![\angle PYZ=Q](https://tex.z-dn.net/?f=%5Cangle%20PYZ%3DQ)
![\Rightarrow \angle XYP=90-\angle PYZ\\\angle XYP=90-\theta](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cangle%20XYP%3D90-%5Cangle%20PYZ%5C%5C%5Cangle%20XYP%3D90-%5Ctheta)
In the ![\Delta PYZ](https://tex.z-dn.net/?f=%5CDelta%20PYZ)
![\tan\theta =\frac{opposite}{adjacent}=\frac{PZ}{PY}......(1)](https://tex.z-dn.net/?f=%5Ctan%5Ctheta%20%3D%5Cfrac%7Bopposite%7D%7Badjacent%7D%3D%5Cfrac%7BPZ%7D%7BPY%7D......%281%29)
In the ![\Delta YPX](https://tex.z-dn.net/?f=%5CDelta%20YPX)
![\tan(90-\theta)=\frac{opposite}{adjacent}=\frac{PX}{PY}](https://tex.z-dn.net/?f=%5Ctan%2890-%5Ctheta%29%3D%5Cfrac%7Bopposite%7D%7Badjacent%7D%3D%5Cfrac%7BPX%7D%7BPY%7D)
![\cot=\frac{PX}{PY}....(2)](https://tex.z-dn.net/?f=%5Ccot%3D%5Cfrac%7BPX%7D%7BPY%7D....%282%29)
eqn(1)
eqn(2)
![\tan\times\cot\theta=\frac{PZ}{PY}\times\frac{PX}{PY}\\\\1=\frac{PZ\times PX}{PY^2}\ \ (as\ tan\theta\ =\frac{1}{\cot\theta})\\\\PY^2=PZ\times PX\\PY^2=12PX.......(3)](https://tex.z-dn.net/?f=%5Ctan%5Ctimes%5Ccot%5Ctheta%3D%5Cfrac%7BPZ%7D%7BPY%7D%5Ctimes%5Cfrac%7BPX%7D%7BPY%7D%5C%5C%5C%5C1%3D%5Cfrac%7BPZ%5Ctimes%20PX%7D%7BPY%5E2%7D%5C%20%5C%20%28as%5C%20tan%5Ctheta%5C%20%3D%5Cfrac%7B1%7D%7B%5Ccot%5Ctheta%7D%29%5C%5C%5C%5CPY%5E2%3DPZ%5Ctimes%20PX%5C%5CPY%5E2%3D12PX.......%283%29)
Now in ![\Delta XYP](https://tex.z-dn.net/?f=%5CDelta%20XYP)
use Pythagorean theorem
![XY^2=PY^2+PX^2\\8^2=PY^2+PX^2\ \ (as\ XY\ =8)\\PX^2+PY^2=64\\\\PY^2=12PX\ \ (eqn(3)\\\\\Rightarrow PX^2+12PX=64\\\\PX^2+12PX-64=0\\\\PX^2+16-4PX-64=0\\\\(PX+16)(PX-4)=0\\\\PX=4,\ -16](https://tex.z-dn.net/?f=XY%5E2%3DPY%5E2%2BPX%5E2%5C%5C8%5E2%3DPY%5E2%2BPX%5E2%5C%20%5C%20%28as%5C%20XY%5C%20%3D8%29%5C%5CPX%5E2%2BPY%5E2%3D64%5C%5C%5C%5CPY%5E2%3D12PX%5C%20%5C%20%28eqn%283%29%5C%5C%5C%5C%5CRightarrow%20PX%5E2%2B12PX%3D64%5C%5C%5C%5CPX%5E2%2B12PX-64%3D0%5C%5C%5C%5CPX%5E2%2B16-4PX-64%3D0%5C%5C%5C%5C%28PX%2B16%29%28PX-4%29%3D0%5C%5C%5C%5CPX%3D4%2C%5C%20-16)
Length can not be negative
Hence ![PX=4](https://tex.z-dn.net/?f=PX%3D4)
![PY^2=12PX=12\times4=48\\\\PY=\sqrt{48}=4\sqrt{3}](https://tex.z-dn.net/?f=PY%5E2%3D12PX%3D12%5Ctimes4%3D48%5C%5C%5C%5CPY%3D%5Csqrt%7B48%7D%3D4%5Csqrt%7B3%7D)
Hence
Answer:
x = 59°
y = 130°
Step-by-step explanation:
Find x:
Recall: the measure of an inscribed angle = ½(measure of intercepted arc), based in the inscribed angles theorem
Therefore,
x = ½(118°)
x = 59°
Find y:
y = 2(180 - (56 + x)) => inscribed angles theorem
Plug in the value of x
y = 2(180 - (56 + 59))
y = 2(180 - 115)
y = 2(65)
y = 130°
Answer:
a=0
sbsuqvhqua2hw7avwbs7zbehsbz zhs
9/20
explanation:
7/10 - 1/4
14/20 - 5/20
14-5/20
9/20
Answer:
The answer would be B.
Step-by-step explanation:
The X-intercept is simply the point in which the line crosses the x axis, and the point where it crosses or touches is 0, 0