Answer:
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Step-by-step explanation:
Answer:
r + c ≤12
r > 3
c > 2
Step-by-step explanation:
Jennifer is putting together a selection of flowers that has at most 12 flowers in it.
r = number of roses she uses
c = the number of carnations
At also means Less than or equal to.
It is represented by ≤
She is choosing either roses or carnations. She wants to pick at least three roses
r > 3
and at least two carnations.
= c > 2
Therefore, the system of inequality that represents this scenario is written as:
r + c ≤ 12
r > 3
c > 2
We first have to find the first derivative before we can find the second. First derivative with respect to x is

so

and

. That's the first derivative. Now for the second it's probably easiest to use the quotient rule, even though it's usually long and drawn out. That looks like this:
![\frac{dy}{dx}= \frac{4y^2(-6x)-[-3x^2(8y \frac{dy}{dx})] }{(4y^2)^2}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%3D%20%5Cfrac%7B4y%5E2%28-6x%29-%5B-3x%5E2%288y%20%5Cfrac%7Bdy%7D%7Bdx%7D%29%5D%20%7D%7B%284y%5E2%29%5E2%7D%20%20)
which simplifies a bit to

. We will multiply both sides by that denominator to get rid of it which leaves us with

. Get both dy/dx terms on the same side, and then factor it out.

. Divide to isolate the dy/dx:

. There's no simplifying you could do after that that would make any significant difference.
Answer:
f(7) = -196
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = -3x² - 7x
f(7) is x = 7
<u>Step 2: Evaluate</u>
- Substitute in <em>x</em>: f(7) = -3(7)² - 7(7)
- Exponents: f(7) = -3(49) - 7(7)
- Multiply: f(7) = -147 - 49
- Add: f(7) = -196