Answer:
100,000
Step-by-step explanation:
We are given a function: f(t) = 100,000, where,
f(t) is a function that tells us about the number of people who will be infected in t weeks. Here t that is number of week is the independent variable and f(t) is the dependent variable.
We observe that f(t) is a constant function that is it does not depend on the value of t. Whatever may be the value of t it will always take the constant value of 100,000.
So, after ten weeks that is we put t = 10, we get,
f(10) = 100,000
Thus, after 10 weeks 100,000 people will be infected.
For this case we have a system of two equations with two unknowns.
To solve, we equate both equations:
![2x-2 = x ^ 2-x-6\\x ^ 2-3x-4 = 0](https://tex.z-dn.net/?f=2x-2%20%3D%20x%20%5E%202-x-6%5C%5Cx%20%5E%202-3x-4%20%3D%200)
We have a quadratic equation of the form:
![x ^ 2 + bx + c = 0](https://tex.z-dn.net/?f=x%20%5E%202%20%2B%20bx%20%2B%20c%20%3D%200)
Where:
![a = 1\\b = -3\\c = -4](https://tex.z-dn.net/?f=a%20%3D%201%5C%5Cb%20%3D%20-3%5C%5Cc%20%3D%20-4)
Its roots are given by:
![x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}\\x = \frac {- (- 3) \pm \sqrt {(- 3) ^ 2-4 (1) (- 4)}} {2 (1)}\\x = \frac {3 \pm \sqrt {9 + 16}} {2}\\x = \frac {3 \pm \sqrt {25}} {2}\\x = \frac {3 \pm5} {2}\\](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%20%7B-b%20%5Cpm%20%5Csqrt%20%7Bb%20%5E%202-4%20%28a%29%20%28c%29%7D%7D%20%7B2a%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B-%20%28-%203%29%20%5Cpm%20%5Csqrt%20%7B%28-%203%29%20%5E%202-4%20%281%29%20%28-%204%29%7D%7D%20%7B2%20%281%29%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B3%20%5Cpm%20%5Csqrt%20%7B9%20%2B%2016%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B3%20%5Cpm%20%5Csqrt%20%7B25%7D%7D%20%7B2%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B3%20%5Cpm5%7D%20%7B2%7D%5C%5C)
We have two roots:
![x_ {1} = \frac {3 + 5} {2} = 4\\x_ {2} = \frac {3-5} {2} = - 1](https://tex.z-dn.net/?f=x_%20%7B1%7D%20%3D%20%5Cfrac%20%7B3%20%2B%205%7D%20%7B2%7D%20%3D%204%5C%5Cx_%20%7B2%7D%20%3D%20%5Cfrac%20%7B3-5%7D%20%7B2%7D%20%3D%20-%201)
Thus, we look for the values of y, by substituting any of the equations:
![For\ x_ {1} = 4,\ y_ {1} = 2 (4) -2 = 6\\For\ x_ {2} = - 1,\ y_ {2} = 2 (-1) -2 = -4](https://tex.z-dn.net/?f=For%5C%20x_%20%7B1%7D%20%3D%204%2C%5C%20y_%20%7B1%7D%20%3D%202%20%284%29%20-2%20%3D%206%5C%5CFor%5C%20x_%20%7B2%7D%20%3D%20-%201%2C%5C%20y_%20%7B2%7D%20%3D%202%20%28-1%29%20-2%20%3D%20-4)
Answer:
![(x_ {1}, y_ {1}) = (4,6)\\(x_ {2}, y_ {2}) (- 1, -4)](https://tex.z-dn.net/?f=%28x_%20%7B1%7D%2C%20y_%20%7B1%7D%29%20%3D%20%284%2C6%29%5C%5C%28x_%20%7B2%7D%2C%20y_%20%7B2%7D%29%20%28-%201%2C%20-4%29)
Option B
Before we solve anything, we need to know how many cups there are in a gallon.
There are 16 cups in 1 gallon.
We have 1.5 gallons.
There is a shortcut to finding the 0.5 extra gallons;
Divide the amount of cups per gallon by 2. This will give us an equivalent of 0.5 gallons.
16 / 2 = 8.
There are 8 cups per 0.5gal.
Now that we have our gallons translated into cups, let's sum up.
16 + 8 = 24.
There are 24 cups in 1.5 gallons.
The chef can get 24 1-cup servings out of the pot.
I hope this helps!
Answer:
the y-intercept
Step-by-step explanation:
brainliest plz
#3
<span>The marketing firm is observing and measuring specific characteristics of the subjects, but is not attempting to modify the subjects.</span>