Answer:
Option 2 - ![x=\frac{7\pm3\sqrt{3}i}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B7%5Cpm3%5Csqrt%7B3%7Di%7D%7B2%7D)
Step-by-step explanation:
Given : Equation ![(x-5)^2+3(x-5)+9=0](https://tex.z-dn.net/?f=%28x-5%29%5E2%2B3%28x-5%29%2B9%3D0)
To find : What is the solution of the equation ?
Solution :
Using substitution method,
Let y=x-5
![y^2+3y+9=0](https://tex.z-dn.net/?f=y%5E2%2B3y%2B9%3D0)
Using quadratic formula, ![x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Here, a=1, b=3 and c=9
![y=\frac{-3\pm\sqrt{3^2-4(1)(9)}}{2(1)}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-3%5Cpm%5Csqrt%7B3%5E2-4%281%29%289%29%7D%7D%7B2%281%29%7D)
![y=\frac{-3\pm\sqrt{-27}}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-3%5Cpm%5Csqrt%7B-27%7D%7D%7B2%7D)
![y=\frac{-3\pm3\sqrt{3}i}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-3%5Cpm3%5Csqrt%7B3%7Di%7D%7B2%7D)
Substitute back,
![x=\frac{-3\pm3\sqrt{3}i}{2}+5](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-3%5Cpm3%5Csqrt%7B3%7Di%7D%7B2%7D%2B5)
![x=\frac{-3\pm3\sqrt{3}i+10}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-3%5Cpm3%5Csqrt%7B3%7Di%2B10%7D%7B2%7D)
![x=\frac{7\pm3\sqrt{3}i}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B7%5Cpm3%5Csqrt%7B3%7Di%7D%7B2%7D)
Therefore, option 2 is correct.
Answer:
q=45
Step-by-step explanation:
To do this we have to isolate q.
q is being divided by 3, so to reverse that we have to multiply it by 3.
However, in an equation, what you do to one side, you must do to the other. This is so the equation stays equal.
15=q/3
That said, what we can do is multiply the entire equation by 3.
45=q
So the solution to the equation is 45.
Triangle ABC has angles 130, 15 and 35
Triangle DEF has angles 35, 15, and 130
4) The triangles have 3 pairs of congruent angles.
Answer:
3 +3×2=12cm
Step-by-step explanation:
Add all the Side Perimeter = L+W ×2