Answer:

General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Algebra I</u>
<u>Calculus</u>
Implicit Differentiation
The derivative of a constant is equal to 0
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Product Rule: ![\frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)](https://tex.z-dn.net/?f=%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)
Chain Rule: ![\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
Quotient Rule: ![\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5B%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D%20%5D%3D%5Cfrac%7Bg%28x%29f%27%28x%29-g%27%28x%29f%28x%29%7D%7Bg%5E2%28x%29%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
-xy - 2y = -4
Rate of change of the tangent line at point (-1, 4)
<u>Step 2: Differentiate Pt. 1</u>
<em>Find 1st Derivative</em>
- Implicit Differentiation [Product Rule/Basic Power Rule]:                             
- [Algebra] Isolate <em>y'</em> terms:                                                                                
- [Algebra] Factor <em>y'</em>:                                                                                        
- [Algebra] Isolate <em>y'</em>:                                                                                          
- [Algebra] Rewrite:                                                                                            
<u>Step 3: Find </u><em><u>y</u></em>
- Define equation:                     
- Factor <em>y</em>:                                  
- Isolate <em>y</em>:                                  
- Simplify:                                  
<u>Step 4: Rewrite 1st Derivative</u>
- [Algebra] Substitute in <em>y</em>:                                                                                
- [Algebra] Simplify:                                                                                          
<u>Step 5: Differentiate Pt. 2</u>
<em>Find 2nd Derivative</em>
- Differentiate [Quotient Rule/Basic Power Rule]:                                          ![y'' = \frac{0(x+2)^2 - 8 \cdot 2(x + 2) \cdot 1}{[(x + 2)^2]^2}](https://tex.z-dn.net/?f=y%27%27%20%3D%20%5Cfrac%7B0%28x%2B2%29%5E2%20-%208%20%5Ccdot%202%28x%20%2B%202%29%20%5Ccdot%201%7D%7B%5B%28x%20%2B%202%29%5E2%5D%5E2%7D) 
- [Derivative] Simplify:                                                                                       
<u>Step 6: Find Slope at Given Point</u>
- [Algebra] Substitute in <em>x</em>:                                                                                
- [Algebra] Evaluate:                                                                                        
 
        
                    
             
        
        
        
Answer:
Answer: 42.5
Step-by-step explanation:
It says 1 inch equals 5 feet. So, every inch is on the map is an extra 5 feet in real space. So if you think about it, all this is is a simple multiplication problem. 
Here is the math:
8.5 * 5 = 42.5
Think about it, for every inch there is on the map there is an extra 5 feet in real space. There is 8 inches, so we need 5 extra feet for each of those 8 inches. So what we get for 1 inch is 5 feet, for 2 inches 10 feet, 3 inches 15 feet, etc etc until we reach 8 inches. For the 0.5 inches alone that would equal 2.5 feet in real life since 1 inch is 5 feet.
Ez pz
 
        
             
        
        
        
Answer:
3 points = 2
2 points = 6
1 point = 8
Step-by-step explanation:
Given that:
Total point scored = 26
Let number of 3 point basket = x
Number of 2 point basket = x + 4
Number of free throws = x + x + 4 = 2x + 4
Hence, 
Total 3 points = 3x
Total 2 points 2(x + 4)
Total free throw points = 2x + 4
3x + 2(x + 4) + 2x + 4 = 26
3x + 2x + 8 + 2x + 4 = 26
7x + 12 = 26
7x = 26 - 12
7x = 14
x = 2
Number of 3 points = x = 2
2 points = (x+4) = 2+4 = 6
1 point = (2x+ 4) = 2(2) + 4 = 8
 
        
                    
             
        
        
        
The markdown price
 = the percent × regular price
the sale price 
 = regular price - markdown price
 = regular price - the percent × regular price
 = regular price×(1 - the percent)
        
             
        
        
        
Answer:
x=9
Step-by-step explanation: