1. m
2. One set of ordered pairs
3. b
To show why this is, I’m going to explain how to write the equation for a linear function with two random sets of ordered pairs - (1,0) and (5, 8).
First, find the slope. The formula for slope is m = (y2 - y1)/(x2-x1) where m is the slope and (x1, y1) and (x2, y2) are two sets of points.
This is why #1 is m. M is the letter used when finding slope.
To find m, I plug in the two sets of ordered pairs.
m = (8-0)/(5-1)
m = 8/4
m = 2
An equation for a line (linear function) is written in something called slope-intercept form. It looks like y = mx + b. m is the slope and b is the y-intercept (number y equals when x = 0). If m = 3 and b = 1, the equation would be y = 3x + 1.
Here, you have just solved for m and know it equals 2. Plug that value in for m.
y = 2x + b
To solve for b, plug one ordered pair in for x and y. I will use (1,0)
0 = 2(1) + b
0 = 2 + b
-2 = b
Now that you know b = -2, plug that in for b.
y = 2x - 2. Now you have the equation fo the line.
Answer:
b. 
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Functions
- Function Notation
- 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>
- Rewrite function [Exponential Rule - Root Rewrite]:
![\displaystyle H(x) = [F(x)]^\bigg{\frac{1}{3}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20H%28x%29%20%3D%20%5BF%28x%29%5D%5E%5Cbigg%7B%5Cfrac%7B1%7D%7B3%7D%7D)
- Chain Rule:
![\displaystyle H'(x) = \frac{d}{dx} \bigg[ [F(x)]^\bigg{\frac{1}{3}} \bigg] \cdot \frac{d}{dx}[F(x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20H%27%28x%29%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5BF%28x%29%5D%5E%5Cbigg%7B%5Cfrac%7B1%7D%7B3%7D%7D%20%5Cbigg%5D%20%5Ccdot%20%5Cfrac%7Bd%7D%7Bdx%7D%5BF%28x%29%5D)
- Basic Power Rule:
![\displaystyle H'(x) = \frac{1}{3}[F(x)]^\bigg{\frac{1}{3} - 1} \cdot F'(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20H%27%28x%29%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5BF%28x%29%5D%5E%5Cbigg%7B%5Cfrac%7B1%7D%7B3%7D%20-%201%7D%20%5Ccdot%20F%27%28x%29)
- Simplify:
![\displaystyle H'(x) = \frac{F'(x)}{3}[F(x)]^\bigg{\frac{-2}{3}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20H%27%28x%29%20%3D%20%5Cfrac%7BF%27%28x%29%7D%7B3%7D%5BF%28x%29%5D%5E%5Cbigg%7B%5Cfrac%7B-2%7D%7B3%7D%7D)
- Rewrite [Exponential Rule - Rewrite]:
![\displaystyle H'(x) = \frac{F'(x)}{3[F(x)]^\bigg{\frac{2}{3}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20H%27%28x%29%20%3D%20%5Cfrac%7BF%27%28x%29%7D%7B3%5BF%28x%29%5D%5E%5Cbigg%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D)
<u>Step 3: Evaluate</u>
- Substitute in <em>x</em> [Derivative]:
![\displaystyle H'(5) = \frac{F'(5)}{3[F(5)]^\bigg{\frac{2}{3}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20H%27%285%29%20%3D%20%5Cfrac%7BF%27%285%29%7D%7B3%5BF%285%29%5D%5E%5Cbigg%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D)
- Substitute in function values:

- Exponents:

- Multiply:

- Simplify:

Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
Answer:
Sam initially made 45 bread rolls
Step-by-step explanation:
Let x = total number of bread rolls made by Sam. He gives 2/5 of the bread to his neighbor. This means he gave 2/5 × x =
2x/5 bread rolls to his neighbor.
The remainder would be x - 2x/5 =3x/5
He gave 4/9 of the remainder to his cousin = 4/9 ×3x/5=12x/45
=4x/15
He has 15 bread rolls left
Total number of bread rolls = what he has left + what he gave his cousin + what he gave his neighbor
x = 15 + 4x/15 + 2x/5
Taking LCM of 15 and cross multiplying
15x= 225+4x + 6x
15x = 225 +10x
15x-10x = 225
5x = 225
x = 225/5 =45
Sam initially made 45 bread rolls
Answer:
Do you mean what is the square root?
Step-by-step explanation:
1.73205080757
2
2.2360679775
Just find something close if those aren't answer choices
Answer: 125 centimeters
1,250 millimeters
Step-by-step explanation:
'centi' means hundred. 100 centimeters go into a meter.
'milli' means thousand. 1,000 millimeters go into a meter. Easy math from there.