Answer:
x ≈ 83.533
y = 9105.13
Step-by-step explanation:
Step 1: Substitution
109x = 79x + 2506
30x = 2506
x = 83.533
Step 2: Plug <em>x</em> in
y = 109(83.533)
y = 9105.13
Graphically:
Move the dot twice to the right
Answer:
x=1 -3(1+4)=-15
Step-by-step explanation:
-3(x+4)=-15
---------------
-3 -3
x+4= 5
-4=-4
x=1
That should be right
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