Answer: 49
Step-by-step explanation:
There would be 49 dots because each number is a square number. You skip 1 so every square‘s number is one less than the square root of the number of dots.
hope this helps
Okay, So what you need to do first is divide 228 by 30 we get 7.6 so let’s just say 6 Buses because there is no such thing as half students lol. Then you would times 6 by 30 which is 180. We would have 6 vans which hold 8 students 6*8 is 48. Then we could add 180 +48 which is 228.
To sum it up
6 Vans
6 Buses
Hope you have a wonderful day~ <3
If you want a answer for this you need to show the graph to us
Question:
Which is equivalent to
after it has been simplified completely?
Answer:
![\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}](https://tex.z-dn.net/?f=%5Csqrt%7B180x%5E%7B11%7D%7D%20%3D%206x%5E%7B5%7D%5Csqrt%7B5x%7D)
Step-by-step explanation:
Given
![\sqrt{180x^{11}}](https://tex.z-dn.net/?f=%5Csqrt%7B180x%5E%7B11%7D%7D)
Required
Simplify
We start by splitting the square root
![\sqrt{180x^{11}} = \sqrt{180} * \sqrt{x^{11}}](https://tex.z-dn.net/?f=%5Csqrt%7B180x%5E%7B11%7D%7D%20%3D%20%5Csqrt%7B180%7D%20%2A%20%5Csqrt%7Bx%5E%7B11%7D%7D)
Replace 180 with 36 * 5
![\sqrt{180x^{11}} = \sqrt{36 * 5} * \sqrt{x^{11}}](https://tex.z-dn.net/?f=%5Csqrt%7B180x%5E%7B11%7D%7D%20%3D%20%5Csqrt%7B36%20%2A%205%7D%20%2A%20%20%5Csqrt%7Bx%5E%7B11%7D%7D)
Further split the square roots
![\sqrt{180x^{11}} = \sqrt{36} *\sqrt{5} * \sqrt{x^{11}}](https://tex.z-dn.net/?f=%5Csqrt%7B180x%5E%7B11%7D%7D%20%3D%20%5Csqrt%7B36%7D%20%2A%5Csqrt%7B5%7D%20%2A%20%20%5Csqrt%7Bx%5E%7B11%7D%7D)
![\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{11}}](https://tex.z-dn.net/?f=%5Csqrt%7B180x%5E%7B11%7D%7D%20%3D%206%2A%5Csqrt%7B5%7D%20%2A%20%20%5Csqrt%7Bx%5E%7B11%7D%7D)
Replace power of x; 11 with 10 + 1
![\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10 + 1}}](https://tex.z-dn.net/?f=%5Csqrt%7B180x%5E%7B11%7D%7D%20%3D%206%2A%5Csqrt%7B5%7D%20%2A%20%20%5Csqrt%7Bx%5E%7B10%20%2B%201%7D%7D)
From laws of indices; ![a^{m+n} = a^m * a^n](https://tex.z-dn.net/?f=a%5E%7Bm%2Bn%7D%20%3D%20a%5Em%20%2A%20a%5En)
So, we have
![\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10} * x^1}](https://tex.z-dn.net/?f=%5Csqrt%7B180x%5E%7B11%7D%7D%20%3D%206%2A%5Csqrt%7B5%7D%20%2A%20%20%5Csqrt%7Bx%5E%7B10%7D%20%2A%20x%5E1%7D)
![\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10} * x}](https://tex.z-dn.net/?f=%5Csqrt%7B180x%5E%7B11%7D%7D%20%3D%206%2A%5Csqrt%7B5%7D%20%2A%20%20%5Csqrt%7Bx%5E%7B10%7D%20%2A%20x%7D)
Further split the square roots
![\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10}} * \sqrt{x}](https://tex.z-dn.net/?f=%5Csqrt%7B180x%5E%7B11%7D%7D%20%3D%206%2A%5Csqrt%7B5%7D%20%2A%20%20%5Csqrt%7Bx%5E%7B10%7D%7D%20%2A%20%5Csqrt%7Bx%7D)
From laws of indices; ![\sqrt{a} = a^{\frac{1}{2}}](https://tex.z-dn.net/?f=%5Csqrt%7Ba%7D%20%3D%20a%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D)
So, we have
![\sqrt{180x^{11}} = 6*\sqrt{5} * x^{10*\frac{1}{2}} * \sqrt{x}](https://tex.z-dn.net/?f=%5Csqrt%7B180x%5E%7B11%7D%7D%20%3D%206%2A%5Csqrt%7B5%7D%20%2A%20%20x%5E%7B10%2A%5Cfrac%7B1%7D%7B2%7D%7D%20%2A%20%5Csqrt%7Bx%7D)
![\sqrt{180x^{11}} = 6*\sqrt{5} * x^{\frac{10}{2}} * \sqrt{x}](https://tex.z-dn.net/?f=%5Csqrt%7B180x%5E%7B11%7D%7D%20%3D%206%2A%5Csqrt%7B5%7D%20%2A%20%20x%5E%7B%5Cfrac%7B10%7D%7B2%7D%7D%20%2A%20%5Csqrt%7Bx%7D)
![\sqrt{180x^{11}} = 6*\sqrt{5} * x^{5} * \sqrt{x}](https://tex.z-dn.net/?f=%5Csqrt%7B180x%5E%7B11%7D%7D%20%3D%206%2A%5Csqrt%7B5%7D%20%2A%20%20x%5E%7B5%7D%20%2A%20%5Csqrt%7Bx%7D)
Rearrange Expression
![\sqrt{180x^{11}} = 6 * x^{5} * \sqrt{5} * \sqrt{x}](https://tex.z-dn.net/?f=%5Csqrt%7B180x%5E%7B11%7D%7D%20%3D%206%20%2A%20%20x%5E%7B5%7D%20%2A%20%5Csqrt%7B5%7D%20%2A%20%5Csqrt%7Bx%7D)
![\sqrt{180x^{11}} = 6x^{5} * \sqrt{5} * \sqrt{x}](https://tex.z-dn.net/?f=%5Csqrt%7B180x%5E%7B11%7D%7D%20%3D%206x%5E%7B5%7D%20%2A%20%5Csqrt%7B5%7D%20%2A%20%5Csqrt%7Bx%7D)
From laws of indices; ![\sqrt{a} *\sqrt{b} = \sqrt{a*b} = \sqrt{ab}](https://tex.z-dn.net/?f=%5Csqrt%7Ba%7D%20%2A%5Csqrt%7Bb%7D%20%3D%20%5Csqrt%7Ba%2Ab%7D%20%3D%20%5Csqrt%7Bab%7D)
So, we have
![\sqrt{180x^{11}} = 6x^{5} * \sqrt{5*x}](https://tex.z-dn.net/?f=%5Csqrt%7B180x%5E%7B11%7D%7D%20%3D%206x%5E%7B5%7D%20%2A%20%5Csqrt%7B5%2Ax%7D)
![\sqrt{180x^{11}} = 6x^{5} * \sqrt{5x}](https://tex.z-dn.net/?f=%5Csqrt%7B180x%5E%7B11%7D%7D%20%3D%206x%5E%7B5%7D%20%2A%20%5Csqrt%7B5x%7D)
![\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}](https://tex.z-dn.net/?f=%5Csqrt%7B180x%5E%7B11%7D%7D%20%3D%206x%5E%7B5%7D%5Csqrt%7B5x%7D)
<em>The expression can no longer be simplified</em>
Hence,
is equivalent to ![6x^{5}\sqrt{5x}](https://tex.z-dn.net/?f=6x%5E%7B5%7D%5Csqrt%7B5x%7D)
Answer:
- 2 8/25
Step-by-step explanation:
Hope this helps! If it does, please mark me brainliest because it will help me. Thank you so much! ;) :)