Question:
Which expression is equivalent to
![\frac{\sqrt{2}}{\sqrt[3]{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D)
Answer:
![\frac{\sqrt{2}}{\sqrt[3]{2}} =2^{\frac{1}{6}} = \sqrt[6]{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%20%3D2%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D%20%3D%20%5Csqrt%5B6%5D%7B2%7D)
Step-by-step explanation:
Given
![\frac{\sqrt{2}}{\sqrt[3]{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D)
Required
Simplify
From laws of indices;
![\sqrt[n]{x} =x^{\frac{1}{n}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%7D%20%3Dx%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D)
So, the expression can be rewritten as
![\frac{\sqrt{2}}{\sqrt[3]{2}} = \frac{{2^{\frac{1}{2}}}}{2^{\frac{1}{3}}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%20%3D%20%5Cfrac%7B%7B2%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%7D%7B2%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%7D)
Also, from laws of indices

So, the expression is further solved to:
![\frac{\sqrt{2}}{\sqrt[3]{2}} =2^{\frac{1}{2} - \frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%20%3D2%5E%7B%5Cfrac%7B1%7D%7B2%7D%20-%20%5Cfrac%7B1%7D%7B3%7D)
Solve exponents as fraction
![\frac{\sqrt{2}}{\sqrt[3]{2}} =2^{\frac{3-2}{6}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%20%3D2%5E%7B%5Cfrac%7B3-2%7D%7B6%7D%7D)
![\frac{\sqrt{2}}{\sqrt[3]{2}} =2^{\frac{1}{6}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%20%3D2%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D)
This can be rewritten as
![\frac{\sqrt{2}}{\sqrt[3]{2}} =2^{\frac{1}{6}} = \sqrt[6]{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%20%3D2%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D%20%3D%20%5Csqrt%5B6%5D%7B2%7D)
To find the total of what you sold for each package, you'll need to write two equations. Know that x = paper plate packages and y = utensil packages.
First, x + y = 15 shows that there has to be fifteen packages, and 8x + 5y = 90 shows the $ made from selling a certain number of packages.
Next, you can solve by substitution, so change x + y = 15 to y = 15 - x.
To find our x, substitute the y in 8x + 5y = 90 to get
8x + 5(15 - x) = 90
Distribute: 8x + 75 - 5x = 90
Combine the X's and subtract the 75: 3x = 15
Divide the 3: x = 5
Now with our x, we can put 5 into the original equation x + y = 15 to get 5 + y = 15. Subtracting the 5, we get y = 10.
So, you have delivered 5 paper plate packages and 10 utensil packages.
Answer:
A
Step-by-step explanation:
Im good at math
Answer:

Step-by-step explanation:
Let x be the number of days you want to rent
The flat rate for car rental is $35 a day
As for insurance, $10 for 3 days or fewer, and $5 per day if more than 3 days that is

Combine this with the flat rental rate $35 a day and we have
