Step 1 ) Move all terms right side of the equation.
![\displaystyle\ x^{2} + 6x = -18](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%5C%20x%5E%7B2%7D%20%2B%206x%20%3D%20-18%20)
![\displaystyle\ x^{2} + 6x + 18 = -18 + 18](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%5C%20x%5E%7B2%7D%20%2B%206x%20%2B%2018%20%3D%20-18%20%2B%2018%20)
![\displaystyle\ x^{2} +6x + 18 = 0](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%5C%20x%5E%7B2%7D%20%2B6x%20%2B%2018%20%3D%200%20)
Step 2 ) Apply quadratic formula. (Note: There are 2 solutions)
![\displaystyle\ x^{2} +6x + 18 = 0](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%5C%20x%5E%7B2%7D%20%2B6x%20%2B%2018%20%3D%200%20)
![\displaystyle\ x = \frac{-b\sqrt{b^{2}-4ac}}{2a}, \displaystyle\ x = \frac{-b-\sqrt{b^{2}-4ac}}{2a}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%5C%20x%20%3D%20%5Cfrac%7B-b%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%7D%7B2a%7D%2C%20%5Cdisplaystyle%5C%20x%20%3D%20%5Cfrac%7B-b-%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%7D%7B2a%7D%20)
![\displaystyle\ x = \frac{-6+\sqrt{6^{2}-4 * 18}}{2} , \displaystyle\ x = \frac{-6-\sqrt{6^{2}-4*18}}{2}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%5C%20x%20%3D%20%5Cfrac%7B-6%2B%5Csqrt%7B6%5E%7B2%7D-4%20%2A%2018%7D%7D%7B2%7D%20%2C%20%5Cdisplaystyle%5C%20x%20%3D%20%5Cfrac%7B-6-%5Csqrt%7B6%5E%7B2%7D-4%2A18%7D%7D%7B2%7D%20)
,
![\displaystyle\ x = \frac{-6-6i}{2}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%5C%20x%20%3D%20%5Cfrac%7B-6-6i%7D%7B2%7D%20%20)
Step 3 ) Simplify.
,
![\displaystyle\ x = \frac{-6-6i}{2}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%5C%20x%20%3D%20%5Cfrac%7B-6-6i%7D%7B2%7D%20%20)
,
![\displaystyle\ x = -3 - 3i](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%5C%20x%20%3D%20-3%20-%203i%20)
Since the options only provide one of the answer we found, the answer is...
![\displaystyle\ x = -3 - 3i](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%5C%20x%20%3D%20-3%20-%203i%20)
•
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- <em>Marlon Nunez</em>
Answer:
commission rate of Maurice is 12%
Step-by-step explanation:
Maurice earns commission = $6,048
Lexus priced at = $50,400
Maurice's commission rate =
=![\frac {commision}{rate} \times 100](https://tex.z-dn.net/?f=%5Cfrac%20%7Bcommision%7D%7Brate%7D%20%5Ctimes%20100)
=![\frac{6048}{50400} \times 100](https://tex.z-dn.net/?f=%5Cfrac%7B6048%7D%7B50400%7D%20%5Ctimes%20100)
=12 %
hence the commission rate of Maurice is 12%
It is around 1.81 kilograms
Answer:
The correct option is;
Use a scale factor of 2
Step-by-step explanation:
The parameters given are;
A = (1, -6)
B = (5, -6)
C = (6, -2)
D = (0, -2)
A'' = (1.5, 4)
B'' = (3.5, 4)
C'' = (4, 2)
D'' = ( 1, 2)
We note that the length of side AB in polygon ABCD = √((5 -1)² + (-6 - (-6))²) = 4
The length of side A''B'' in polygon A''B''C''D'' = √((3.5 -1.5)² + (4 - 4)²) = 2
Which gives;
AB/A''B'' = 4/2 = 2
Similarly;
The length of side BC in polygon ABCD = √((6 -5)² + (-2 - (-6))²) = √17
The length of side B''C'' in polygon A''B''C''D'' = √((4 -3.5)² + (2 - 4)²) = (√17)/2
Also we have;
The length of side CD in polygon ABCD = √((6 -0)² + (-2 - (-2))²) = 6
The length of side C''D'' in polygon A''B''C''D'' = √((4 -1)² + (2 - 2)²) = 3
For the side DA and D''A'', we have;
The length of side DA in polygon ABCD = √((1 -0)² + (-6 - (-2))²) = √17
The length of side D''A'' in polygon A''B''C''D'' = √((1.5 -1)² + (4 - 2)²) = (√17)/2
Therefore the Polygon A B C D can be obtained from polygon A''B''C''D'' by multiplying each side of polygon A''B''C''D'' by 2
The correct option is therefore;
Use a scale factor of 2.