Answer:
n=12
Step-by-step explanation:
7n-18 =5n+6
+18 to both sides
7n=5n+24
-5n from both sides
2n=24
divide by 2
n=12
 
        
                    
             
        
        
        
Answer:
x = 6
Step-by-step explanation:
Given
6x² - 2x + 36 = 5x² + 10x ( subtract 5x² + 10x from both sides )
x² - 12x + 36 = 0 ← in standard form
This is a perfect square of the form
(x - a)² = x² - 2ax + a²
36 = 6² ⇒ a = 6 and 2ax = (2 × 6)x = 12x, hence
(x - 6)² = 0
x - 6 = 0 ⇒ x = 6
 
        
             
        
        
        
Answer:

General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]:                                                           ![\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bcf%28x%29%5D%20%3D%20c%20%5Ccdot%20f%27%28x%29) 
  
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Product Rule]:                                                                             ![\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bf%28x%29g%28x%29%5D%3Df%27%28x%29g%28x%29%20%2B%20g%27%28x%29f%28x%29)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>

<u>Step 2: Differentiate</u>
- [Function] Derivative Rule [Product Rule]:                                                   ![\displaystyle f'(x) = \frac{d}{dx}[9x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B9x%5E%7B10%7D%5D%20%5Ctan%5E%7B-1%7D%28x%29%20%2B%209x%5E%7B10%7D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B%5Ctan%5E%7B-1%7D%28x%29%5D) 
- Rewrite [Derivative Property - Multiplied Constant]:                                  ![\displaystyle f'(x) = 9 \frac{d}{dx}[x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%209%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%5E%7B10%7D%5D%20%5Ctan%5E%7B-1%7D%28x%29%20%2B%209x%5E%7B10%7D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B%5Ctan%5E%7B-1%7D%28x%29%5D) 
- Basic Power Rule:                                                                                         ![\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%2090x%5E9%20%5Ctan%5E%7B-1%7D%28x%29%20%2B%209x%5E%7B10%7D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B%5Ctan%5E%7B-1%7D%28x%29%5D) 
- Arctrig Derivative:                                                                                          
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
 
        
             
        
        
        
Answer:
domain will be ( -∞, ∞)
Step-by-step explanation:
The given functions are f(x) = x² - 1 and g(x) = 2x - 3
We have to find domain of (fog)(x)
We will find the function (fg)(x) first.
(fog)(x) = f[g(x)]
          = (2x - 3)²
          = 4x² + 9 - 12x - 1
         = 4x² - 12x + 8
        = 4 (x² - 3x + 2)
The given function is defined for all values of x.
Therefore, domain will be ( -∞, ∞)
<u>brainly.com/question/2458431</u>
 
        
             
        
        
        
Answer:
The new points to the triangle will be:

Step-by-step explanation:
Because the reflection point is at  , all x values will subtract their distances from
, all x values will subtract their distances from  to get their new values. The y values remain the same.
 to get their new values. The y values remain the same.
The starting values are:

Point  is 1 unit away from
 is 1 unit away from  , so we'll subtract 1 from 2 to get the new x value:
, so we'll subtract 1 from 2 to get the new x value:  , so
, so  .
.
  
Point  is also 1 unit away from
 is also 1 unit away from  , so we'll subtract 1 from 2 to get the new x value:
, so we'll subtract 1 from 2 to get the new x value:  , so
, so  .
.
Point  is 3 units away from
 is 3 units away from  , so we'll subtract 3 from 2 to get the new x value:
, so we'll subtract 3 from 2 to get the new x value:  , so
, so  .
.