Answer:
![f(x)=(x-1)(x-2)(x-3)](https://tex.z-dn.net/?f=f%28x%29%3D%28x-1%29%28x-2%29%28x-3%29)
Step-by-step explanation:
we know that
The x-intercepts or the roots of the function are the values of x when the value of the function is equal to zero
so
In this problem
Observing the graph
The x-intercepts are the points
![(1,0),(2,0),(3,0)](https://tex.z-dn.net/?f=%281%2C0%29%2C%282%2C0%29%2C%283%2C0%29)
so
![x=1\\ x-1=0](https://tex.z-dn.net/?f=x%3D1%5C%5C%20x-1%3D0)
![x=2\\ x-2=0](https://tex.z-dn.net/?f=x%3D2%5C%5C%20x-2%3D0)
![x=3\\ x-3=0](https://tex.z-dn.net/?f=x%3D3%5C%5C%20x-3%3D0)
therefore
The equation of the graph in factored form is equal to
![f(x)=(x-1)(x-2)(x-3)](https://tex.z-dn.net/?f=f%28x%29%3D%28x-1%29%28x-2%29%28x-3%29)
220= 45*x. I hope you are satisfied with my answer.
Answer: ![14*\sqrt[3]{x^{10}}](https://tex.z-dn.net/?f=14%2A%5Csqrt%5B3%5D%7Bx%5E%7B10%7D%7D)
Step-by-step explanation:
First, let's remember the rules:
![x^{1/n} = \sqrt[n]{x}](https://tex.z-dn.net/?f=x%5E%7B1%2Fn%7D%20%3D%20%5Csqrt%5Bn%5D%7Bx%7D)
such that:
![\sqrt[n]{x^m} = x^{m/n}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%5Em%7D%20%3D%20x%5E%7Bm%2Fn%7D)
![(x^a)^b = x^{a*b}](https://tex.z-dn.net/?f=%28x%5Ea%29%5Eb%20%3D%20x%5E%7Ba%2Ab%7D)
![x^a*x^b = x^{a + b}](https://tex.z-dn.net/?f=x%5Ea%2Ax%5Eb%20%3D%20x%5E%7Ba%20%2B%20b%7D)
Now we have the equation:
![4*\sqrt[3]{x^{10}} + 5*x^3*\sqrt[3]{8*x}](https://tex.z-dn.net/?f=4%2A%5Csqrt%5B3%5D%7Bx%5E%7B10%7D%7D%20%2B%205%2Ax%5E3%2A%5Csqrt%5B3%5D%7B8%2Ax%7D)
First, let's rewrite the roots as we saw above:
![4*x^{10/3} + 5*x^3*\sqrt[3]{8}*x^{1/3} = 4*x^{10/3} + 5*\sqrt[3]{8}*x^{3 + 1/3}](https://tex.z-dn.net/?f=4%2Ax%5E%7B10%2F3%7D%20%2B%205%2Ax%5E3%2A%5Csqrt%5B3%5D%7B8%7D%2Ax%5E%7B1%2F3%7D%20%3D%204%2Ax%5E%7B10%2F3%7D%20%2B%205%2A%5Csqrt%5B3%5D%7B8%7D%2Ax%5E%7B3%20%2B%201%2F3%7D)
We also know that: ![\sqrt[3]{8} = 2](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B8%7D%20%3D%202)
and that: ![3 + 1/3 = 9/3 + 1/3 = 10/3](https://tex.z-dn.net/?f=3%20%2B%201%2F3%20%3D%209%2F3%20%2B%201%2F3%20%3D%2010%2F3)
Replacing those two things in our equation, we get:
![4*x^{10/3} + 5*\sqrt[3]{8}*x^{3 + 1/3} = 4*x^{10/3} + 5*2*x^{10/3} = (4 + 5*2)*x^{10/3}](https://tex.z-dn.net/?f=4%2Ax%5E%7B10%2F3%7D%20%2B%205%2A%5Csqrt%5B3%5D%7B8%7D%2Ax%5E%7B3%20%2B%201%2F3%7D%20%3D%204%2Ax%5E%7B10%2F3%7D%20%2B%205%2A2%2Ax%5E%7B10%2F3%7D%20%3D%20%284%20%2B%205%2A2%29%2Ax%5E%7B10%2F3%7D)
![(4 + 10)*x^{10/3} = 14*\sqrt[3]{x^{10}}](https://tex.z-dn.net/?f=%284%20%2B%2010%29%2Ax%5E%7B10%2F3%7D%20%3D%2014%2A%5Csqrt%5B3%5D%7Bx%5E%7B10%7D%7D)
Where in the final step, I returned to the cubic root form.
Like... 276 divided by 4... My 4th grade teacher is teaching us a way of long division, here are the steps. Divide, Multiply, Subtract Bring down, Repeat... Here is the example. 4 to 2, I cant make 2 with 4. 4 is too big, then i go to 27. the closest i can get is 6x4 to make 24. then on top i put 6, then i multiply 4x6 and put 24 down below 27. Then I subtract then bring down the 6. Next step, repeat. Do 4 divided by 3, the closest i can get to 4 is by doing 3x1 so i put the 1 up by the 6 then multiply 1x4. Which is 4, then i bring it down then subtract 36 - 4. You get 61 with a remainder of 4. :) Hope that helped and isn't too confusing!
They will be in debt cause coins don't translate into real life currency.