X-5) = 2(x-1)
3x-15 = 2x - 2
x - 15 = -2
x = 13
Answer:
67
Step-by-step explanation:
A linear pair is two angles which form a straight angle when combined (or 180 degrees). Thus do 180 - 113 to get 67 degrees for Angle 2
The answer is 1.
EXPLANATION
The commutative property of multiplication states that two numbers can be multiplied in either order.
Multiply both the numerator and denominator by
, which is called the "conjugate" of
:
![\dfrac{5+\sqrt3}{2-\sqrt3}\cdot\dfrac{2+\sqrt3}{2+\sqrt3}](https://tex.z-dn.net/?f=%5Cdfrac%7B5%2B%5Csqrt3%7D%7B2-%5Csqrt3%7D%5Ccdot%5Cdfrac%7B2%2B%5Csqrt3%7D%7B2%2B%5Csqrt3%7D)
Why do we pick this number? Recall the difference of squares factorization:
![a^2-b^2=(a-b)(a+b)](https://tex.z-dn.net/?f=a%5E2-b%5E2%3D%28a-b%29%28a%2Bb%29)
Now replace
and
. Then
![(2-\sqrt3)(2+\sqrt3)=2^2-(\sqrt3)^2=4-3=1](https://tex.z-dn.net/?f=%282-%5Csqrt3%29%282%2B%5Csqrt3%29%3D2%5E2-%28%5Csqrt3%29%5E2%3D4-3%3D1)
So in your fraction, you end up with
![\dfrac{5+\sqrt3}{2-\sqrt3}=\dfrac{(5+\sqrt3)(2+\sqrt3)}1=(5+\sqrt3)(2+\sqrt3)](https://tex.z-dn.net/?f=%5Cdfrac%7B5%2B%5Csqrt3%7D%7B2-%5Csqrt3%7D%3D%5Cdfrac%7B%285%2B%5Csqrt3%29%282%2B%5Csqrt3%29%7D1%3D%285%2B%5Csqrt3%29%282%2B%5Csqrt3%29)
Finally, just expand the product.
![(5+\sqrt3)(2+\sqrt3)=10+7\sqrt3+(\sqrt3)^2=\boxed{13+7\sqrt3}](https://tex.z-dn.net/?f=%285%2B%5Csqrt3%29%282%2B%5Csqrt3%29%3D10%2B7%5Csqrt3%2B%28%5Csqrt3%29%5E2%3D%5Cboxed%7B13%2B7%5Csqrt3%7D)
The one above me is correct