Answer:
9) five hundred and forty three thousand, six hundred and ninety-eight
500,000 + 40,00+ 3,000+ 600+ 90+ 8 = 543,698
10)forty-five million nine hundred eighty-seven thousand one hundred fifty-nine and nine tenths
40,000,000 + 5,000,000 + 900,000 + 80,000 + 7,000 + 100 + 50 + 9 + 0.9 = 45,987,159.9
Answer:
22 Feet
Step-by-step explanation:
All the lengths of a square are the same length.
The area of a square is the length times the width. The length and the width are the same measurement. So, we are looking for the square root of 479.

21.88606863 is as far as my calculator goes. This is an irrational number. That means that it never repeats or terminates as a decimal. They tell us to answer to the nearest foot. That would be 22 feet.
Answer:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4x^\bigg{\frac{3}{2}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cfrac%7B-1%7D%7B4x%5E%5Cbigg%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
Exponential Properties
- Exponential Property [Rewrite]:

- Exponential Property [Root Rewrite]:
![\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%5Bn%5D%7Bx%7D%20%3D%20x%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D)
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]:
Derivative Rule [Basic Power Rule]:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify.</em>
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D)
<u>Step 2: Differentiate</u>
- Simplify:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \bigg( \frac{1}{2\sqrt{x}} \bigg)'](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cbigg%28%20%5Cfrac%7B1%7D%7B2%5Csqrt%7Bx%7D%7D%20%5Cbigg%29%27)
- Rewrite [Derivative Property - Multiplied Constant]:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{1}{\sqrt{x}} \bigg)'](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cbigg%28%20%5Cfrac%7B1%7D%7B%5Csqrt%7Bx%7D%7D%20%5Cbigg%29%27)
- Rewrite [Exponential Rule - Root Rewrite]:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{1}{x^\Big{\frac{1}{2}}} \bigg)'](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cbigg%28%20%5Cfrac%7B1%7D%7Bx%5E%5CBig%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%20%5Cbigg%29%27)
- Rewrite [Exponential Rule - Rewrite]:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( x^\bigg{\frac{-1}{2}} \bigg)'](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cbigg%28%20x%5E%5Cbigg%7B%5Cfrac%7B-1%7D%7B2%7D%7D%20%5Cbigg%29%27)
- Derivative Rule [Basic Power Rule]:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{-1}{2} x^\bigg{\frac{-3}{2}} \bigg)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cbigg%28%20%5Cfrac%7B-1%7D%7B2%7D%20x%5E%5Cbigg%7B%5Cfrac%7B-3%7D%7B2%7D%7D%20%5Cbigg%29)
- Simplify:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4} x^\bigg{\frac{-3}{2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cfrac%7B-1%7D%7B4%7D%20x%5E%5Cbigg%7B%5Cfrac%7B-3%7D%7B2%7D%7D)
- Rewrite [Exponential Rule - Rewrite]:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4x^\bigg{\frac{3}{2}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cfrac%7B-1%7D%7B4x%5E%5Cbigg%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D)
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
It’s y= 30x + 200 for the linear equation and the answer is 440
Answer: Second, Fourth and Fifth options are correct.
Step-by-step explanation:
F is the incenter because F is the point of intersection of the three angle bisector of the triangle.
As we can see that the angle bisector divides the angles into equal angles.
So, F is the point of concurrency of the angle bisectors of the angle of the triangle.
F is equidistant from the three sides of the triangle.
Hence, Second ,Fourth, Fifth options are correct.