Answer: k = 63
Step-by-step explanation: You need to multiply the left side by its reciprocal to move the numbers to the right. You also need to multiply by k on the right side to get it alone on the left. This will result in
(9/3)(3/9) = (21/k)(9/3) simplified
1 = 189/3k • k then multiply by k
k = 189/3 simplify
k = 63
Answer:

General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Terms/Coefficients
- Anything to the 0th power is 1
- Exponential Rule [Rewrite]:
- Exponential Rule [Root Rewrite]:
<u>
</u>
<u>Calculus</u>
Derivatives
Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Chain Rule]: ![\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
<em />
<em />
<em />
<u>Step 2: Differentiate</u>
- Chain Rule:
![\displaystyle y' = 2(x + \sqrt{x})^{2 - 1} \cdot \frac{d}{dx}[x + \sqrt{x}]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%202%28x%20%2B%20%5Csqrt%7Bx%7D%29%5E%7B2%20-%201%7D%20%5Ccdot%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%20%2B%20%5Csqrt%7Bx%7D%5D)
- Rewrite [Exponential Rule - Root Rewrite]:
![\displaystyle y' = 2(x + x^{\frac{1}{2}})^{2 - 1} \cdot \frac{d}{dx}[x + x^{\frac{1}{2}}]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%202%28x%20%2B%20x%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%29%5E%7B2%20-%201%7D%20%5Ccdot%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%20%2B%20x%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5D)
- Simplify:
![\displaystyle y' = 2(x + x^{\frac{1}{2}}) \cdot \frac{d}{dx}[x + x^{\frac{1}{2}}]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%202%28x%20%2B%20x%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%29%20%5Ccdot%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%20%2B%20x%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5D)
- Basic Power Rule:

- Simplify:

- Rewrite [Exponential Rule - Rewrite]:

- Multiply:
![\displaystyle y' = 2[(x + x^{\frac{1}{2}}) + \frac{x + x^{\frac{1}{2}}}{2x^{\frac{1}{2}}}]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%202%5B%28x%20%2B%20x%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%29%20%2B%20%5Cfrac%7Bx%20%2B%20x%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%7B2x%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%5D)
- [Brackets] Add:

- Multiply:

- Rewrite [Exponential Rule - Root Rewrite]:

Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
Don’t try to fall for people that are using links they r trying to scam
Answer:
-3x² - 10x - 16 r. 
Step-by-step explanation:
You can easily do this through synthetic division:
First step is to get all the numeric coefficients of the expression and write them down. Don't forget to bring their signs along with them.
-3x³ - 4x² + 4x +3
| -3 -4 +4 +3
|______________
Next we find the root that is associated with the divisor:
x - 2 = 0
x = 2
We use this and put it outside:
2 | -3 -4 +4 +3
|______________
Okay now we bring down the first coefficient:
2 | -3 -4 +4 +3
|______________
-3
Then we multiply it by the root and put the product under the next coefficient:
2 x - 3 = -6
2 | -3 -4 +4 +3
|<u> -6 </u>
-3
Then we add them:
2 | -3 -4 +4 +3
|<u> -6 </u>
-3 -10
Do the same steps until the end:
2 | -3 -4 +4 +3
|<u> -6 -20 -32 </u>
-3 -10 -16 -29
Now that you have that, remember that since the divisor is in the 1st degree, quotient will have a degree will be one degree below as well.
-3x² - 10x - 26
Your last coefficient is going to be your remainder:
-3x² - 10x - 16 r. 