I think its -40 because it looks like you have negative 40 then ur adding 10
Answer:
10 red apples and 6 green apples
Step-by-step explanation:
first you multiply 5×2 to get 10 apples
then you multiply 3×2 to get 6 apples
Answer:
![\huge\boxed{\sqrt{25-10\sqrt3+3}=5-\sqrt3}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7B%5Csqrt%7B25-10%5Csqrt3%2B3%7D%3D5-%5Csqrt3%7D)
Step-by-step explanation:
![\sqrt{25-10\sqrt3+3}=(*)\\\\25=5^2\\3=(\sqrt3)^2\\10\sqrt3=(2)(5)(\sqrt3)\\\\(*)=\sqrt{5^2-(2)(5)(\sqrt3)+(\sqrt3)^2}\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=\sqrt{(5-\sqrt3)^2}\\\\\text{use}\ \sqrt{a^2}=|a|\\\\=|5-\sqrt3|=5-\sqrt3\\\\^{\text{because}\ 5>\sqrt3\to5-\sqrt3>0}](https://tex.z-dn.net/?f=%5Csqrt%7B25-10%5Csqrt3%2B3%7D%3D%28%2A%29%5C%5C%5C%5C25%3D5%5E2%5C%5C3%3D%28%5Csqrt3%29%5E2%5C%5C10%5Csqrt3%3D%282%29%285%29%28%5Csqrt3%29%5C%5C%5C%5C%28%2A%29%3D%5Csqrt%7B5%5E2-%282%29%285%29%28%5Csqrt3%29%2B%28%5Csqrt3%29%5E2%7D%5C%5C%5C%5C%5Ctext%7Buse%7D%5C%20%28a-b%29%5E2%3Da%5E2-2ab%2Bb%5E2%5C%5C%5C%5C%3D%5Csqrt%7B%285-%5Csqrt3%29%5E2%7D%5C%5C%5C%5C%5Ctext%7Buse%7D%5C%20%5Csqrt%7Ba%5E2%7D%3D%7Ca%7C%5C%5C%5C%5C%3D%7C5-%5Csqrt3%7C%3D5-%5Csqrt3%5C%5C%5C%5C%5E%7B%5Ctext%7Bbecause%7D%5C%205%3E%5Csqrt3%5Cto5-%5Csqrt3%3E0%7D)
For this case we have, by definition:
![a^{-b} =\frac{1}{a ^ b}](https://tex.z-dn.net/?f=a%5E%7B-b%7D%20%3D%5Cfrac%7B1%7D%7Ba%20%5E%20b%7D)
So, we have:
![\frac{1}{4}^{-\frac{1}{2}}=\frac{1}{(\frac{1}{4})^{\frac{1}{2}}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%3D%5Cfrac%7B1%7D%7B%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D)
On the other hand we have that by definition:
![a^{\frac{1}{2}}=\sqrt{a}](https://tex.z-dn.net/?f=a%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D%5Csqrt%7Ba%7D)
Thus, the expression can be written as:
![\frac{1}{\sqrt {\frac{1}{4}}} =](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Csqrt%20%7B%5Cfrac%7B1%7D%7B4%7D%7D%7D%20%3D)
![\frac{1}{\frac{1}{\sqrt{4}}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Cfrac%7B1%7D%7B%5Csqrt%7B4%7D%7D%7D)
![\frac{1}{\frac{1}{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Cfrac%7B1%7D%7B2%7D%7D)
![\frac{1*2}{1*1}=2](https://tex.z-dn.net/?f=%5Cfrac%7B1%2A2%7D%7B1%2A1%7D%3D2)
So, we have:
![\frac{1}{4}^{-\frac{1}{2}}= 2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%3D%202)
Answer:
![\frac{1}{4}^{-\frac{1}{2}}= 2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%3D%202)