Step-by-step explanation:
im not going to go in to detail but the answer is c
Answer:
I would say the answer is c
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:

To match the number with the opposite, we are flipping the sign. If the sign is originally a negative, it would become a positive, and vice versa.
Term: 3.2 Match (Opposite): B) - 3.2
Term: -2.3 Match (Opposite): D) 2.3
Term: -1.5 Match (Opposite): C) 1.5
Term: 5.1 Match (Opposite): A) -5.1
~
Answer: 8 whole gallons.
Step-by-step explanation: If you have only $27.00 and you need to buy gas, but each gallon is $3.15, then you just need to divide your total amount ($27.00) by your cost per gallon ($3.15), and you will get about 8.6 gallons, however this question asks for how many WHOLE gallons you can get, so all you need to do is round down to fit your budget, leaving money for only 8 whole gallons.
WORK: ($27.00) / ($3.15) = 8.6 gallons