5% sales tax would be $0.70
The domain of the function is given by (–∞, –3) ∪ (–3, 2) ∪ (2, ∞)
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The function is given by:
![g(x) = \frac{x^2 + 3x}{x^2 + x - 6}, x < 3](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7Bx%5E2%20%2B%203x%7D%7Bx%5E2%20%2B%20x%20-%206%7D%2C%20x%20%3C%203)
![g(x) = \log_{2}{x + 5}, x \geq 3](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Clog_%7B2%7D%7Bx%20%2B%205%7D%2C%20x%20%5Cgeq%203)
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- For the second definition, the restriction is that x + 5 has to be positive. Since the definition is only valid for
, this will <u>always be true.</u> - In the second definition, the denominator cannot be zero, thus the <u>zeros of the denominator will be outside the domain.</u>
These zeros are found using Bhaskara, we have the quadratic function
, thus the coefficients are
.
![\Delta = b^2 - 4ac = (1)^2 - 4(1)(-6) = 25](https://tex.z-dn.net/?f=%5CDelta%20%3D%20b%5E2%20-%204ac%20%3D%20%281%29%5E2%20-%204%281%29%28-6%29%20%3D%2025)
![x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{-1 + 5}{2} = 2](https://tex.z-dn.net/?f=x_1%20%3D%20%5Cfrac%7B-b%20%2B%20%5Csqrt%7B%5CDelta%7D%7D%7B2a%7D%20%3D%20%5Cfrac%7B-1%20%2B%205%7D%7B2%7D%20%3D%202)
![x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{-1 - 5}{2} = -3](https://tex.z-dn.net/?f=x_2%20%3D%20%5Cfrac%7B-b%20-%20%5Csqrt%7B%5CDelta%7D%7D%7B2a%7D%20%3D%20%5Cfrac%7B-1%20-%205%7D%7B2%7D%20%3D%20-3)
Thus, <u>x = 2 and x = -3 are outside the</u> domain, which is given by:
(–∞, –3) ∪ (–3, 2) ∪ (2, ∞)
A similar problem is given at brainly.com/question/13136492
1. find slope
x=tickets sold
y=money made
slope=(y2-y1)/(x2-x1)
take any point
(5,23.75) and (10,47.50)
input (note, (x,y))
(47.50-23.75)/(10-5)=23.75/5=4.75
slope=4.75
y=mx+b
m=slope
b=yintercept
y=4.75x+b
input
47.5=4.75(10)+b
47.5=47.5+b
b=0
equation is y=4.75x
if ticket sold is 24 then x=24
y=4.75(24)
y=114
answer is $114
2. points
(0,56.00) and (3,45.5)
slope=(y2-y1)/(x2-x1)
slope=(45.5-56.00)/(3-0)=-3.5
y=-3.5x
slope=-3.5
logic it yourself
equation is
y=-3.5x+0
y intercept is when x=0 so when the start of it was or when time=0
x intercept is when y=0 is when he has no money left
1.a. rate of change=4.75
b. $114
2. a.do this yourself, (desmos graphing calculator)
b. slope=-3.5 (duh, means money goes down with time)
c. equaiton is y=-3.5x+0, xint meanss when he has no money, y int means when time=0 or when it started
3x^2-2x should be the correct answer