Answer:
The triangle is 1, since 10 - 1 is 9.
Hope that helps!
Step-by-step explanation:
7 multiplied by 11 is 77. And to get 462, (and based on the given information), we can conclude that it is 3*2*7*11.
Whee
remember
![(x^m)(x^n)=x^{m+n}](https://tex.z-dn.net/?f=%28x%5Em%29%28x%5En%29%3Dx%5E%7Bm%2Bn%7D)
multiply both sides by 2^x
![(2^{2x})+(2^0)=3(2^x)](https://tex.z-dn.net/?f=%282%5E%7B2x%7D%29%2B%282%5E0%29%3D3%282%5Ex%29)
![2^{2x}+1=3(2^x)](https://tex.z-dn.net/?f=2%5E%7B2x%7D%2B1%3D3%282%5Ex%29)
minus 3(2)^x from both sides
![2^{2x}-3(2^x)+1=0](https://tex.z-dn.net/?f=2%5E%7B2x%7D-3%282%5Ex%29%2B1%3D0)
we can use the quadratic formula
use u subsitution where u=2ˣ
![1(2^x)^2-3(2^x)+1=0](https://tex.z-dn.net/?f=1%282%5Ex%29%5E2-3%282%5Ex%29%2B1%3D0)
![1(u)^2-3(u)+1=0](https://tex.z-dn.net/?f=1%28u%29%5E2-3%28u%29%2B1%3D0)
![u^2-3u+1=0](https://tex.z-dn.net/?f=u%5E2-3u%2B1%3D0)
use quadratic formula
![u=\frac{3+\sqrt{5}}{2}](https://tex.z-dn.net/?f=u%3D%5Cfrac%7B3%2B%5Csqrt%7B5%7D%7D%7B2%7D)
and
![u=\frac{3-\sqrt{5}}{2}](https://tex.z-dn.net/?f=u%3D%5Cfrac%7B3-%5Csqrt%7B5%7D%7D%7B2%7D)
solve
subsitte and solve
u=2ˣ
![2^x=\frac{3+\sqrt{5}}{2}](https://tex.z-dn.net/?f=2%5Ex%3D%5Cfrac%7B3%2B%5Csqrt%7B5%7D%7D%7B2%7D)
take ln of both sides
![x(ln(2))=ln(\frac{3+\sqrt{5}}{2})](https://tex.z-dn.net/?f=x%28ln%282%29%29%3Dln%28%5Cfrac%7B3%2B%5Csqrt%7B5%7D%7D%7B2%7D%29)
divide both sides by ln(2)
![x=\frac{ln(\frac{3+\sqrt{5}}{2})}{ln(2)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7Bln%28%5Cfrac%7B3%2B%5Csqrt%7B5%7D%7D%7B2%7D%29%7D%7Bln%282%29%7D)
for other one
![2^x=\frac{3-\sqrt{5}}{2}](https://tex.z-dn.net/?f=2%5Ex%3D%5Cfrac%7B3-%5Csqrt%7B5%7D%7D%7B2%7D)
take ln of both sides
![x(ln(2))=ln(\frac{3-\sqrt{5}}{2})](https://tex.z-dn.net/?f=x%28ln%282%29%29%3Dln%28%5Cfrac%7B3-%5Csqrt%7B5%7D%7D%7B2%7D%29)
divide both sides by ln(2)
![x=\frac{ln(\frac{3-\sqrt{5}}{2})}{ln(2)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7Bln%28%5Cfrac%7B3-%5Csqrt%7B5%7D%7D%7B2%7D%29%7D%7Bln%282%29%7D)
so
![x=\frac{ln(\frac{3+\sqrt{5}}{2})}{ln(2)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7Bln%28%5Cfrac%7B3%2B%5Csqrt%7B5%7D%7D%7B2%7D%29%7D%7Bln%282%29%7D)
and
![x=\frac{ln(\frac{3-\sqrt{5}}{2})}{ln(2)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7Bln%28%5Cfrac%7B3-%5Csqrt%7B5%7D%7D%7B2%7D%29%7D%7Bln%282%29%7D)
those are the 2 solutions
aprox x=1.38848 and x=-1.338848
Move the decimal point to the right (add a zero), therefore, 825,740