Answer: It will take 7 stages for all 19,530 families to be called.
In the first stage, only 5 families are called.
In the second stage, we would have 5 x 5 = 25 families being called.
In the third stage, we would have 5 x 5 x 5 = 125 families being called.
We can use exponents to finish the list and see when our goal is reached.
4th stage: 5^4 = 625
5th stage: 5^5 = 3125
6th stage: 5^6 = 15625
7th stage: 5^7 = 78,125
Divide 324 by 24. Which is 13.5
If the polygons are similar then the sides are in proportion.
![\dfrac{32}{24}=\dfrac{32:8}{24:8}=\dfrac{4}{3}](https://tex.z-dn.net/?f=%5Cdfrac%7B32%7D%7B24%7D%3D%5Cdfrac%7B32%3A8%7D%7B24%3A8%7D%3D%5Cdfrac%7B4%7D%7B3%7D)
Therefore we have the equations:
![\dfrac{x-1}{6}=\dfrac{4}{3}\qquad\text{cross multiply}\\\\3(x-1)=(4)(6)\\\\3x-3=24\qquad\text{add 3 to both sides}\\\\3x=27\qquad\text{divide both sides by 3}\\\\\boxed{x=9}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx-1%7D%7B6%7D%3D%5Cdfrac%7B4%7D%7B3%7D%5Cqquad%5Ctext%7Bcross%20multiply%7D%5C%5C%5C%5C3%28x-1%29%3D%284%29%286%29%5C%5C%5C%5C3x-3%3D24%5Cqquad%5Ctext%7Badd%203%20to%20both%20sides%7D%5C%5C%5C%5C3x%3D27%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%203%7D%5C%5C%5C%5C%5Cboxed%7Bx%3D9%7D)
![\dfrac{y+1}{21}=\dfrac{4}{3}\qquad\text{cross multiply}\\\\3(y+1)=(21)(4)\\\\3y+3=84\qquad\text{subtract 3 from both sides}\\\\3y=81\qquad\text{divide both sides by 3}\\\\\boxed{y=27}](https://tex.z-dn.net/?f=%5Cdfrac%7By%2B1%7D%7B21%7D%3D%5Cdfrac%7B4%7D%7B3%7D%5Cqquad%5Ctext%7Bcross%20multiply%7D%5C%5C%5C%5C3%28y%2B1%29%3D%2821%29%284%29%5C%5C%5C%5C3y%2B3%3D84%5Cqquad%5Ctext%7Bsubtract%203%20from%20both%20sides%7D%5C%5C%5C%5C3y%3D81%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%203%7D%5C%5C%5C%5C%5Cboxed%7By%3D27%7D)
The divide and simplify of the equation √36 x⁴ / √9 x⁶ will result to ![\frac{2}{x^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7Bx%5E%7B2%7D%20%7D)
Let's begin by simplifying the equation;
Simplify the equation by finding the square root of both 36 and 9
The square root of 36= 6
The square root of 9= 3
= ![\frac{6x^{4} }{3x^{6} }](https://tex.z-dn.net/?f=%5Cfrac%7B6x%5E%7B4%7D%20%7D%7B3x%5E%7B6%7D%20%7D)
The above equation can also be written as;
= ![6x^{4} * 3x^{-6}](https://tex.z-dn.net/?f=6x%5E%7B4%7D%20%20%2A%203x%5E%7B-6%7D)
The next step is to solve the powers, that is,
= ![\frac{6x^{4} }{3x^{6} }](https://tex.z-dn.net/?f=%5Cfrac%7B6x%5E%7B4%7D%20%7D%7B3x%5E%7B6%7D%20%7D)
Cancel out 6 by 3 and get 2
The result is,
= ![\frac{2}{x^{6-4} }](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7Bx%5E%7B6-4%7D%20%7D)
The final submission result is,
=
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Answer:
2. and 4.
Step-by-step explanation: