5x+15(greater than or equal to symbol) $210
210-15=195
195 divided by 5=39
So it will take her atleast 39 weeks to save up for the game
Using the commutative property would be: 4*9=36
Answer:
(a) -12
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
<u>Calculus</u>
Integrals
Integration Rule [Reverse Power Rule]: 
Integration Property [Swapping Limits]: 
Integration Property [Multiplied Constant]:
Integration Property [Addition/Subtraction]: ![\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%7B%5Bf%28x%29%20%5Cpm%20g%28x%29%5D%7D%20%5C%2C%20dx%20%3D%20%5Cint%20%7Bf%28x%29%7D%20%5C%2C%20dx%20%5Cpm%20%5Cint%20%7Bg%28x%29%7D%20%5C%2C%20dx)
Integration Property [Splitting Integral]: 
Integration Rule [Fundamental Theorem of Calculus 1]:
Step-by-step explanation:
<u>Step 1: Define</u>
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<u>Step 2: Solve Pt. 1</u>
- [Integral] Rewrite [Integration Property - Addition]:
![\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = \int\limits^{10}_6 {4f(x)} \, dx + \int\limits^{10}_6 {10} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5E%7B10%7D_6%20%7B%5B4f%28x%29%20%2B%2010%5D%7D%20%5C%2C%20dx%20%3D%20%5Cint%5Climits%5E%7B10%7D_6%20%7B4f%28x%29%7D%20%5C%2C%20dx%20%2B%20%5Cint%5Climits%5E%7B10%7D_6%20%7B10%7D%20%5C%2C%20dx)
- [Integral] Rewrite [Integration Property - Multiplied Constant]:
![\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4\int\limits^{10}_6 {f(x)} \, dx + 10\int\limits^{10}_6 {} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5E%7B10%7D_6%20%7B%5B4f%28x%29%20%2B%2010%5D%7D%20%5C%2C%20dx%20%3D%204%5Cint%5Climits%5E%7B10%7D_6%20%7Bf%28x%29%7D%20%5C%2C%20dx%20%2B%2010%5Cint%5Climits%5E%7B10%7D_6%20%7B%7D%20%5C%2C%20dx)
<u>Step 3: Redefine</u>
<em>Manipulate the given integral values.</em>
- [Integrals] Combine [Integration Property - Splitting Integral]:

- [Integral] Rewrite:

- [Integral] Substitute in integrals:

- [Integral] Add:

- [Integral] Rewrite [Integration Property - Swapping Limits]:

- [Integral] [Division Property of Equality] Isolate integral:

<u>Step 4: Solve Pt. 2</u>
- [Integral] Substitute in integral:
![\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10\int\limits^{10}_6 {} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5E%7B10%7D_6%20%7B%5B4f%28x%29%20%2B%2010%5D%7D%20%5C%2C%20dx%20%3D%204%28-13%29%20%2B%2010%5Cint%5Climits%5E%7B10%7D_6%20%7B%7D%20%5C%2C%20dx)
- [Integral] Integrate [Integration Rule - Reverse Power Rule]:
![\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10(x) \bigg| \limits^{10}_6](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5E%7B10%7D_6%20%7B%5B4f%28x%29%20%2B%2010%5D%7D%20%5C%2C%20dx%20%3D%204%28-13%29%20%2B%2010%28x%29%20%5Cbigg%7C%20%5Climits%5E%7B10%7D_6)
- [Integral] Evaluate [Integration Rule - FTC 1]:
![\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10(10 - 6)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5E%7B10%7D_6%20%7B%5B4f%28x%29%20%2B%2010%5D%7D%20%5C%2C%20dx%20%3D%204%28-13%29%20%2B%2010%2810%20-%206%29)
- [Integral] (Parenthesis) Subtract:
![\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10(4)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5E%7B10%7D_6%20%7B%5B4f%28x%29%20%2B%2010%5D%7D%20%5C%2C%20dx%20%3D%204%28-13%29%20%2B%2010%284%29)
- [Integral] Multiply:
![\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = -52 + 40](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5E%7B10%7D_6%20%7B%5B4f%28x%29%20%2B%2010%5D%7D%20%5C%2C%20dx%20%3D%20-52%20%2B%2040)
- [Integral] Add:
![\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = -12](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5E%7B10%7D_6%20%7B%5B4f%28x%29%20%2B%2010%5D%7D%20%5C%2C%20dx%20%3D%20-12)
Topic: AP Calculus AB/BC
Unit: Integration
Book: College Calculus 10e
30% of 60 is 30/100 or 3/10 f 60
3/10 times 60=180/10=18
he gave 18