The answer is (5n+6)(n-2)
Answer:
C
Step-by-step explanation:
81x-64-49x-27
81x-49x-64-27
32x-91 (C)
Answer:
Please check the step-by-step explanation for the answer.
Step-by-step explanation:
Considering the trigonometric expression
![6sin^2\left(3x\right)=-3](https://tex.z-dn.net/?f=6sin%5E2%5Cleft%283x%5Cright%29%3D-3)
Steps
![\mathrm{Let:\:}\sin \left(3x\right)=u](https://tex.z-dn.net/?f=%5Cmathrm%7BLet%3A%5C%3A%7D%5Csin%20%5Cleft%283x%5Cright%29%3Du)
![6u^2=-3](https://tex.z-dn.net/?f=6u%5E2%3D-3)
![\mathrm{Divide\:both\:sides\:by\:}6](https://tex.z-dn.net/?f=%5Cmathrm%7BDivide%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A%7D6)
![\frac{6u^2}{6}=\frac{-3}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B6u%5E2%7D%7B6%7D%3D%5Cfrac%7B-3%7D%7B6%7D)
![u^2=-\frac{1}{2}](https://tex.z-dn.net/?f=u%5E2%3D-%5Cfrac%7B1%7D%7B2%7D)
![\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}](https://tex.z-dn.net/?f=%5Cmathrm%7BFor%5C%3A%7Dx%5E2%3Df%5Cleft%28a%5Cright%29%5Cmathrm%7B%5C%3Athe%5C%3Asolutions%5C%3Aare%5C%3A%7Dx%3D%5Csqrt%7Bf%5Cleft%28a%5Cright%29%7D%2C%5C%3A%5C%3A-%5Csqrt%7Bf%5Cleft%28a%5Cright%29%7D)
![u=\sqrt{-\frac{1}{2}},\:u=-\sqrt{-\frac{1}{2}}](https://tex.z-dn.net/?f=u%3D%5Csqrt%7B-%5Cfrac%7B1%7D%7B2%7D%7D%2C%5C%3Au%3D-%5Csqrt%7B-%5Cfrac%7B1%7D%7B2%7D%7D)
![\mathrm{Simplify}\:\sqrt{-\frac{1}{2}}](https://tex.z-dn.net/?f=%5Cmathrm%7BSimplify%7D%5C%3A%5Csqrt%7B-%5Cfrac%7B1%7D%7B2%7D%7D)
![\mathrm{Apply\:radical\:rule}:\quad \sqrt{-a}=\sqrt{-1}\sqrt{a}](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Aradical%5C%3Arule%7D%3A%5Cquad%20%5Csqrt%7B-a%7D%3D%5Csqrt%7B-1%7D%5Csqrt%7Ba%7D)
![=\sqrt{-1}\sqrt{\frac{1}{2}}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B-1%7D%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7D%7D)
![\mathrm{Apply\:imaginary\:number\:rule}:\quad \sqrt{-1}=i](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Aimaginary%5C%3Anumber%5C%3Arule%7D%3A%5Cquad%20%5Csqrt%7B-1%7D%3Di)
![=i\sqrt{\frac{1}{2}}](https://tex.z-dn.net/?f=%3Di%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7D%7D)
Similarly,
![-\sqrt{-\frac{1}{2}}=\quad -i\sqrt{\frac{1}{2}}](https://tex.z-dn.net/?f=-%5Csqrt%7B-%5Cfrac%7B1%7D%7B2%7D%7D%3D%5Cquad%20-i%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7D%7D)
So,
![u=i\sqrt{\frac{1}{2}},\:u=-i\sqrt{\frac{1}{2}}](https://tex.z-dn.net/?f=u%3Di%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7D%7D%2C%5C%3Au%3D-i%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7D%7D)
![\mathrm{Substitute\:back}\:u=\sin \left(3x\right)](https://tex.z-dn.net/?f=%5Cmathrm%7BSubstitute%5C%3Aback%7D%5C%3Au%3D%5Csin%20%5Cleft%283x%5Cright%29)
![\sin \left(3x\right)=i\sqrt{\frac{1}{2}},\:\sin \left(3x\right)=-i\sqrt{\frac{1}{2}}](https://tex.z-dn.net/?f=%5Csin%20%5Cleft%283x%5Cright%29%3Di%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7D%7D%2C%5C%3A%5Csin%20%5Cleft%283x%5Cright%29%3D-i%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7D%7D)
So,
![\sin \left(3x\right)=i\sqrt{\frac{1}{2}}\quad :\quad \mathrm{No\:Solutions}](https://tex.z-dn.net/?f=%5Csin%20%5Cleft%283x%5Cright%29%3Di%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7D%7D%5Cquad%20%3A%5Cquad%20%5Cmathrm%7BNo%5C%3ASolutions%7D)
and
![\sin \left(3x\right)=-i\sqrt{\frac{1}{2}}\quad :\quad \mathrm{No\:Solutions}](https://tex.z-dn.net/?f=%5Csin%20%5Cleft%283x%5Cright%29%3D-i%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7D%7D%5Cquad%20%3A%5Cquad%20%5Cmathrm%7BNo%5C%3ASolutions%7D)
![\mathrm{Combine\:all\:the\:solutions}](https://tex.z-dn.net/?f=%5Cmathrm%7BCombine%5C%3Aall%5C%3Athe%5C%3Asolutions%7D)
![\mathrm{No\:Solution\:for}\:x\in \mathbb{R}](https://tex.z-dn.net/?f=%5Cmathrm%7BNo%5C%3ASolution%5C%3Afor%7D%5C%3Ax%5Cin%20%5Cmathbb%7BR%7D)
Keywords: trigonometric equation, solution
Learn more about trigonometric equation solution from brainly.com/question/1687218
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Answer:
12-12
Step-by-step explanation:
hope this helps tell me if it's right
12/66--->x/22
12/66--->4/22 (almost 4/20 if you know what I mean)