Answer:
C
Step-by-step explanation:
We know it's direct variation using the direct variation equation.
![y=kx](https://tex.z-dn.net/?f=y%3Dkx)
Where k is the constant.
Since 7 times x is the y values, ![k=7](https://tex.z-dn.net/?f=k%3D7)
Now we can substitute 7 into k of the direct variation equation.
![y=7x](https://tex.z-dn.net/?f=y%3D7x)
We need to simplify
![\frac{ \sqrt{14x^3} }{ \sqrt{18x} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%7B14x%5E3%7D%20%7D%7B%20%5Csqrt%7B18x%7D%20%7D%20)
First lets factor
![\sqrt{14x^3}](https://tex.z-dn.net/?f=%20%5Csqrt%7B14x%5E3%7D%20)
![\sqrt{14x^3}](https://tex.z-dn.net/?f=%20%5Csqrt%7B14x%5E3%7D%20)
=
![\sqrt{14} \sqrt{x^3}](https://tex.z-dn.net/?f=%20%5Csqrt%7B14%7D%20%20%5Csqrt%7Bx%5E3%7D)
![\sqrt{14} = \sqrt{2} \sqrt{7}](https://tex.z-dn.net/?f=%20%5Csqrt%7B14%7D%20%3D%20%20%5Csqrt%7B2%7D%20%5Csqrt%7B7%7D%20)
by applying the radical rule
![\sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b}](https://tex.z-dn.net/?f=%20%5Csqrt%5Bn%5D%7Bab%7D%20%3D%20%20%5Csqrt%5Bn%5D%7Ba%7D%20%5Csqrt%5Bn%5D%7Bb%7D%20)
![\sqrt{x^3} = x^{3/2}](https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%5E3%7D%20%3D%20x%5E%7B3%2F2%7D)
By applying the radical rule
![\sqrt[n]{x^m} = x^{m/n}](https://tex.z-dn.net/?f=%20%5Csqrt%5Bn%5D%7Bx%5Em%7D%20%3D%20x%5E%7Bm%2Fn%7D)
So
![\sqrt{14x^3}](https://tex.z-dn.net/?f=%20%5Csqrt%7B14x%5E3%7D%20)
=
![\sqrt{14} \sqrt{x^3}](https://tex.z-dn.net/?f=%20%5Csqrt%7B14%7D%20%20%5Csqrt%7Bx%5E3%7D)
=
![\sqrt{2} \sqrt{7}x^{3/2}](https://tex.z-dn.net/?f=%20%5Csqrt%7B2%7D%20%5Csqrt%7B7%7Dx%5E%7B3%2F2%7D%20%20)
Now let's factor
![\sqrt{18x}](https://tex.z-dn.net/?f=%20%5Csqrt%7B18x%7D%20)
By applying the radical rule
![\sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b}](https://tex.z-dn.net/?f=%20%5Csqrt%5Bn%5D%7Bab%7D%20%3D%20%20%5Csqrt%5Bn%5D%7Ba%7D%20%20%5Csqrt%5Bn%5D%7Bb%7D%20)
,
![\sqrt{18x} = \sqrt{18} \sqrt{x}](https://tex.z-dn.net/?f=%5Csqrt%7B18x%7D%20%3D%20%20%5Csqrt%7B18%7D%20%5Csqrt%7Bx%7D%20%20)
So
![\sqrt{18x}](https://tex.z-dn.net/?f=%20%5Csqrt%7B18x%7D%20)
=
![\sqrt{2}*3 \sqrt{x}](https://tex.z-dn.net/?f=%20%5Csqrt%7B2%7D%2A3%20%5Csqrt%7Bx%7D%20)
So
![\frac{ \sqrt{14x^3} }{ \sqrt{18x} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%7B14x%5E3%7D%20%7D%7B%20%5Csqrt%7B18x%7D%20%7D%20)
=
![\frac{ \sqrt{2} \sqrt{7} x^{3/2} }{ \sqrt{2}*3 \sqrt{x} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%7B2%7D%20%5Csqrt%7B7%7D%20x%5E%7B3%2F2%7D%20%7D%7B%20%5Csqrt%7B2%7D%2A3%20%5Csqrt%7Bx%7D%20%20%7D%20)
We know that
![\sqrt[n]{x} = x^{1/n}](https://tex.z-dn.net/?f=%20%5Csqrt%5Bn%5D%7Bx%7D%20%3D%20x%5E%7B1%2Fn%7D)
so
![\sqrt{x} = x^{1/2}](https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%7D%20%3D%20x%5E%7B1%2F2%7D)
We now have
We know that
So
![\frac{x^{3/2}}{x^{1/2}} = x^{3/2 - 1/2} = x](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%5E%7B3%2F2%7D%7D%7Bx%5E%7B1%2F2%7D%7D%20%3D%20x%5E%7B3%2F2%20-%201%2F2%7D%20%3D%20x)
We now got
![\frac{ \sqrt{2} \sqrt{7} x^{3/2} }{ \sqrt{2}*3x^{1/2}} = \frac{ \sqrt{2} \sqrt{7} x }{ \sqrt{2}*3} ](https://tex.z-dn.net/?f=%5Cfrac%7B%20%5Csqrt%7B2%7D%20%5Csqrt%7B7%7D%20x%5E%7B3%2F2%7D%20%7D%7B%20%5Csqrt%7B2%7D%2A3x%5E%7B1%2F2%7D%7D%20%3D%20%5Cfrac%7B%20%5Csqrt%7B2%7D%20%5Csqrt%7B7%7D%20x%20%7D%7B%20%5Csqrt%7B2%7D%2A3%7D%0A)
We can notice that the numerator and the denominator both got √2 in a multiplication, so we can simplify them, and we get:
![\frac{ \sqrt{2} \sqrt{7} x }{ \sqrt{2}*3} = \frac{ \sqrt{7}x }{3}](https://tex.z-dn.net/?f=%5Cfrac%7B%20%5Csqrt%7B2%7D%20%5Csqrt%7B7%7D%20x%20%7D%7B%20%5Csqrt%7B2%7D%2A3%7D%20%3D%20%20%20%5Cfrac%7B%20%5Csqrt%7B7%7Dx%20%7D%7B3%7D%20)
All in All, we get
![\frac{ \sqrt{14x^3} }{ \sqrt{18x} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%7B14x%5E3%7D%20%7D%7B%20%5Csqrt%7B18x%7D%20%7D%20)
=
![\frac{ \sqrt{7}x }{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%7B7%7Dx%20%7D%7B3%7D%20)
Hope this helps! :D
Solution:
The terms shown both are <u>common</u> with "x". Thus, x can be <u>factored.</u>
- => x² + x/5
- => (x × x + 1/5 × x)
- => x(x + 1/5)
Nothing further can be done with this <u>expression.</u>
The factorized expression is x(x + 1/5).
I’m pretty sure 17.3 because of you do a^2+b^2=c^2 you get a^2= 10 square root 3 and that in a decimal is 17.3205
Answer: 4 quarts of milk
Step-by-step explanation: if you buy 3 quarts it won't be enough since 6 pints is not equal to or more than 7 pints but 4 quarts (8 pints) is more than 7 pints so it is more than enough which means you will still have one pint extra after making whatever you need.