The value of n in the given equation is -2.6
Step-by-step explanation:
Given,
10 = ![\frac{2}{3n+8}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3n%2B8%7D)
To find the value of n
10 = ![\frac{2}{3n+8}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3n%2B8%7D)
or, 10(3n+8) = 2 [ by cross multiplication]
or, 30n + 80 = 2
or, 30n = 2-80 [ taking the constant values in one side]
or, 30n = -78
or, n = ![\frac{-78}{30}](https://tex.z-dn.net/?f=%5Cfrac%7B-78%7D%7B30%7D)
or, n = -2.6
Answer:
![\huge\boxed{x=1\ \vee\ x=2}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7Bx%3D1%5C%20%5Cvee%5C%20x%3D2%7D)
Step-by-step explanation:
![3^{2x}-4\cdot3^{x+1}+27=0\\\\\text{use}\ (a^n)^m=a^{nm}\ \text{and}\ a^n\cdot a^m=a^{n+m}\\\\\left(3^x\right)^2-4\cdot3^x\cdot3^1+27=0\\\\\left(3^x\right)^2-12\cdot3^x+27=0\\\\\text{substitute}\ 3^x=t>0\\\\t^2-12t+27=0\\\\t^2-3t-9t+27=0\\\\t(t-3)-9(t-3)=0\\\\(t-3)(t-9)+0\iff t-3=0\ \vee\ t-9=0\\\\t-3=0\qquad\text{add 3 to both sides}\\\boxed{t=3}\\\\t-9=0\qquad\text{add 9 to both sides}\\\boxed{t=9}](https://tex.z-dn.net/?f=3%5E%7B2x%7D-4%5Ccdot3%5E%7Bx%2B1%7D%2B27%3D0%5C%5C%5C%5C%5Ctext%7Buse%7D%5C%20%28a%5En%29%5Em%3Da%5E%7Bnm%7D%5C%20%5Ctext%7Band%7D%5C%20a%5En%5Ccdot%20a%5Em%3Da%5E%7Bn%2Bm%7D%5C%5C%5C%5C%5Cleft%283%5Ex%5Cright%29%5E2-4%5Ccdot3%5Ex%5Ccdot3%5E1%2B27%3D0%5C%5C%5C%5C%5Cleft%283%5Ex%5Cright%29%5E2-12%5Ccdot3%5Ex%2B27%3D0%5C%5C%5C%5C%5Ctext%7Bsubstitute%7D%5C%203%5Ex%3Dt%3E0%5C%5C%5C%5Ct%5E2-12t%2B27%3D0%5C%5C%5C%5Ct%5E2-3t-9t%2B27%3D0%5C%5C%5C%5Ct%28t-3%29-9%28t-3%29%3D0%5C%5C%5C%5C%28t-3%29%28t-9%29%2B0%5Ciff%20t-3%3D0%5C%20%5Cvee%5C%20t-9%3D0%5C%5C%5C%5Ct-3%3D0%5Cqquad%5Ctext%7Badd%203%20to%20both%20sides%7D%5C%5C%5Cboxed%7Bt%3D3%7D%5C%5C%5C%5Ct-9%3D0%5Cqquad%5Ctext%7Badd%209%20to%20both%20sides%7D%5C%5C%5Cboxed%7Bt%3D9%7D)
![\text{We return to substitution:}\\\\3^x=t\\\\3^x=3\ \vee\ 3^x=9\\\\3^x=3^1\ \vee\ 3^x=3^2\\\\\boxed{x=1}\ \vee\ \boxed{x=2}](https://tex.z-dn.net/?f=%5Ctext%7BWe%20return%20to%20substitution%3A%7D%5C%5C%5C%5C3%5Ex%3Dt%5C%5C%5C%5C3%5Ex%3D3%5C%20%5Cvee%5C%203%5Ex%3D9%5C%5C%5C%5C3%5Ex%3D3%5E1%5C%20%5Cvee%5C%203%5Ex%3D3%5E2%5C%5C%5C%5C%5Cboxed%7Bx%3D1%7D%5C%20%5Cvee%5C%20%5Cboxed%7Bx%3D2%7D)
Answer:
y=2 x=3 i think
Step-by-step explanation:
2y+3=y+5
y=5-3
y=2
4x-3=4y+1
4x-3=4×2+1
4x-3=9
4x=9+3
4x=12
x=12/4
×=3
Answer:
The bill excluding tax is $31.21 and the 20% tip was $6.24.