You could buy the Magnet and the Postcard and get 19 cents!
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:
B. FOIL
Step-by-step explanation:
FOIL stands for Firsts, Outsides, Insides, and Lasts
This is a mnemonic to help you to remember how to multiply two binomials
From the image, we can see that the on the right side of the equals,
is the product of the <u>firsts</u> of the binomials
is the product of the <u>outsides</u> of the binomials
is the product of the <u>insides</u> of the binomials
is the product of the<u> lasts</u> of the binomials.
Nate's package is 8 kilograms. This is because, if there are 1,000 grams in 1 kilogram, 8,000/ 1,000= 8 Therefore, the mass of his package is 8 kilograms.
Have a Merry Christmas!