Answer:
M and N
Step-by-step explanation:
Given:
The equation is:
![\left(3+4\sqrt{3}\right)\left(2-a\sqrt{3}\right)=-18+2\sqrt{3}](https://tex.z-dn.net/?f=%5Cleft%283%2B4%5Csqrt%7B3%7D%5Cright%29%5Cleft%282-a%5Csqrt%7B3%7D%5Cright%29%3D-18%2B2%5Csqrt%7B3%7D)
To find:
The value of a.
Solution:
We have,
![\left(3+4\sqrt{3}\right)\left(2-a\sqrt{3}\right)=-18+2\sqrt{3}](https://tex.z-dn.net/?f=%5Cleft%283%2B4%5Csqrt%7B3%7D%5Cright%29%5Cleft%282-a%5Csqrt%7B3%7D%5Cright%29%3D-18%2B2%5Csqrt%7B3%7D)
On simplification, we get
![(3)(2)+(4\sqrt{3})(2)+(3)(-a\sqrt{3})+(4\sqrt{3})(-a\sqrt{3})=-18+2\sqrt{3}](https://tex.z-dn.net/?f=%283%29%282%29%2B%284%5Csqrt%7B3%7D%29%282%29%2B%283%29%28-a%5Csqrt%7B3%7D%29%2B%284%5Csqrt%7B3%7D%29%28-a%5Csqrt%7B3%7D%29%3D-18%2B2%5Csqrt%7B3%7D)
![6+8\sqrt{3}-3a\sqrt{3}-4a(3)=-18+2\sqrt{3}](https://tex.z-dn.net/?f=6%2B8%5Csqrt%7B3%7D-3a%5Csqrt%7B3%7D-4a%283%29%3D-18%2B2%5Csqrt%7B3%7D)
![6+8\sqrt{3}-3a\sqrt{3}-12a=-18+2\sqrt{3}](https://tex.z-dn.net/?f=6%2B8%5Csqrt%7B3%7D-3a%5Csqrt%7B3%7D-12a%3D-18%2B2%5Csqrt%7B3%7D)
![(6-12a)+(8-3a)\sqrt{3}=-18+2\sqrt{3}](https://tex.z-dn.net/?f=%286-12a%29%2B%288-3a%29%5Csqrt%7B3%7D%3D-18%2B2%5Csqrt%7B3%7D)
On comparing both sides, we get
![6-12a=-18](https://tex.z-dn.net/?f=6-12a%3D-18)
![-12a=-18-6](https://tex.z-dn.net/?f=-12a%3D-18-6)
![a=\dfrac{-24}{-12}](https://tex.z-dn.net/?f=a%3D%5Cdfrac%7B-24%7D%7B-12%7D)
![a=2](https://tex.z-dn.net/?f=a%3D2)
And,
![8-3a=2](https://tex.z-dn.net/?f=8-3a%3D2)
![-3a=2-8](https://tex.z-dn.net/?f=-3a%3D2-8)
![a=\dfrac{-6}{-3}](https://tex.z-dn.net/?f=a%3D%5Cdfrac%7B-6%7D%7B-3%7D)
![a=2](https://tex.z-dn.net/?f=a%3D2)
Therefore, the value of a is 2.
We have that AB || DC.
By a similar argument used to prove that AEB ≅ CED,we can show that (AED) ≅ CEB by (SAS) . So, ∠CAD ≅ ∠ (ACB) by CPCTC. Therefore, AD || BC by the converse of the (
ALTERNATE INTERIOR ANGLES) theorem. Since both pair of opposite sides are parallel, quadrilateral ABCD is a parallelogram
1. AED
2. SAS
3. ACB
4. ALTERNATE INTERIOR ANGLES
Why is understanding mitts important?( Select the best answer)
1.It helps us understand how organisms repair.
2. It helps us understand how organisms grow.
3. It is important for cancer research.
4. All options correct.