<em>Note: </em><em>You seem to have missed entering the complete question. I am assuming you want to get the simplified version of the stated expression. So, I will solve it accordingly.</em>
<em />
Answer:
The simplification of the expression is:
![3\left(4h+2k\right)\cdot \:3=\:36h+18k](https://tex.z-dn.net/?f=3%5Cleft%284h%2B2k%5Cright%29%5Ccdot%20%5C%3A3%3D%5C%3A36h%2B18k)
Step-by-step explanation:
Given the expression
![3\left(4h+2k\right)3](https://tex.z-dn.net/?f=3%5Cleft%284h%2B2k%5Cright%293)
simplifying the expression
![3\left(4h+2k\right)3](https://tex.z-dn.net/?f=3%5Cleft%284h%2B2k%5Cright%293)
![=3\left(4h+2k\right)\cdot \:3](https://tex.z-dn.net/?f=%3D3%5Cleft%284h%2B2k%5Cright%29%5Ccdot%20%5C%3A3)
![=3\cdot \:3\left(4h+2k\right)](https://tex.z-dn.net/?f=%3D3%5Ccdot%20%5C%3A3%5Cleft%284h%2B2k%5Cright%29)
![\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Athe%5C%3Adistributive%5C%3Alaw%7D%3A%5Cquad%20%5C%3Aa%5Cleft%28b%2Bc%5Cright%29%3Dab%2Bac)
![=3\cdot \:3\cdot \:4h+3\cdot \:3\cdot \:2k](https://tex.z-dn.net/?f=%3D3%5Ccdot%20%5C%3A3%5Ccdot%20%5C%3A4h%2B3%5Ccdot%20%5C%3A3%5Ccdot%20%5C%3A2k)
![\mathrm{Multiply\:the\:numbers:}\:3\cdot \:3\cdot \:4=36](https://tex.z-dn.net/?f=%5Cmathrm%7BMultiply%5C%3Athe%5C%3Anumbers%3A%7D%5C%3A3%5Ccdot%20%5C%3A3%5Ccdot%20%5C%3A4%3D36)
![=36h+3\cdot \:3\cdot \:2k](https://tex.z-dn.net/?f=%3D36h%2B3%5Ccdot%20%5C%3A3%5Ccdot%20%5C%3A2k)
![\mathrm{Multiply\:the\:numbers:}\:3\cdot \:3\cdot \:2=18](https://tex.z-dn.net/?f=%5Cmathrm%7BMultiply%5C%3Athe%5C%3Anumbers%3A%7D%5C%3A3%5Ccdot%20%5C%3A3%5Ccdot%20%5C%3A2%3D18)
![=36h+18k](https://tex.z-dn.net/?f=%3D36h%2B18k)
Therefore, the simplification of the expression is:
![3\left(4h+2k\right)\cdot \:3=\:36h+18k](https://tex.z-dn.net/?f=3%5Cleft%284h%2B2k%5Cright%29%5Ccdot%20%5C%3A3%3D%5C%3A36h%2B18k)
Answer:
1 no
2 yes
3 yes
4 no
5 no
6 yes
explanation:
sooooooo just
2 and 3 and 6 :D have a nice thanks giving
This involves a quick application of the power rule, which is
![f'(x)=nx^{n-1}](https://tex.z-dn.net/?f=f%27%28x%29%3Dnx%5E%7Bn-1%7D)
.
First, it is helpful to rewrite
![f(x)=\sqrt{x}](https://tex.z-dn.net/?f=f%28x%29%3D%5Csqrt%7Bx%7D)
as
![f(x)=x^{\frac{1}{2}}](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D)
. Remember that these are equivalent forms, but the latter is easier to use with the power rule.
We apply the power rule and simply:
Answer:
![f(-1) =\boxed{-11}\\ f(0) =\boxed{-4}\\f(2) =\boxed{14}](https://tex.z-dn.net/?f=%20f%28-1%29%20%3D%5Cboxed%7B-11%7D%5C%5C%20f%280%29%20%3D%5Cboxed%7B-4%7D%5C%5Cf%282%29%20%3D%5Cboxed%7B14%7D)
Step-by-step explanation:
![f(x)=\begin{cases} 9x -2 \:\: x < 0\\ 9x-4 \:\: x \geq 0\end{cases}\\\\\because \; -1 \: is \: less\: than \: zero\\\therefore f(-1) \: lies \: in \: the \: interval\: x](https://tex.z-dn.net/?f=f%28x%29%3D%5Cbegin%7Bcases%7D%209x%20-2%20%5C%3A%5C%3A%20x%20%3C%200%5C%5C%209x-4%20%5C%3A%5C%3A%20x%20%5Cgeq%200%5Cend%7Bcases%7D%5C%5C%5C%5C%5Cbecause%20%5C%3B%20-1%20%5C%3A%20is%20%5C%3A%20less%5C%3A%20than%20%5C%3A%20zero%5C%5C%5Ctherefore%20f%28-1%29%20%5C%3A%20lies%20%5C%3A%20in%20%5C%3A%20the%20%5C%3A%20interval%5C%3A%20x%3C0%5C%5C%5C%5Cf%28-1%29%20%3D%209%28-1%29%20-2%20%3D%20-9-2%20%3D%20-11%5C%5Cf%28-1%29%3D%5Cboxed%7B-11%7D%5C%5C%5C%5CSimilarly%2C%5C%3A%20%20f%280%29%20%5C%3A%5C%26%5C%3A%20f%282%29%5C%3A%20lies%20%5C%3A%20in%20%5C%3A%20the%20%5C%3A%20interval%5C%3A%20x%5Cgeq%200%5C%5C%5C%5Cf%280%29%20%3D%209x-4%20%3D%209%280%29%20-%204%20%3D%200-4%20%3D%20-4%5C%5Cf%280%29%20%3D%20%5Cboxed%7B-4%7D%5C%5C%5C%5Cf%282%29%3D9x-4%20%3D%209%282%29-4%20%3D%2018-4%20%3D%2014%5C%5C%5C%5Cf%282%29%3D%5Cboxed%7B14%7D)