Answer:
Horizontal distance = 0 m and 6 m
Step-by-step explanation:
Height of a rider in a roller coaster has been defined by the equation,
y = 
Here x = rider's horizontal distance from the start of the ride
i). 

![=\frac{1}{3}[x^{2}-2(3x)+9-9+24]](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B3%7D%5Bx%5E%7B2%7D-2%283x%29%2B9-9%2B24%5D)
![=\frac{1}{3}[(x^{2}-2(3x)+9)+15]](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B3%7D%5B%28x%5E%7B2%7D-2%283x%29%2B9%29%2B15%5D)
![=\frac{1}{3}[(x-3)^2+15]](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B3%7D%5B%28x-3%29%5E2%2B15%5D)

ii). Since, the parabolic graph for the given equation opens upwards,
Vertex of the parabola will be the lowest point of the rider on the roller coaster.
From the equation,
Vertex → (3, 5)
Therefore, minimum height of the rider will be the y-coordinate of the vertex.
Minimum height of the rider = 5 m
iii). If h = 8 m,


(x - 3)² = 9
x = 3 ± 3
x = 0, 6 m
Therefore, at 8 m height of the roller coaster, horizontal distance of the rider will be x = 0 and 6 m
The net pay is the amount left after taxes and deductions have been removed from the gross pay.
Her monthly gross pay is: $4111.93
The deductions are:



Let her gross pay be x.
So, we have:

So, we have:

Express percentage as decimals


Add 102 to both sides


Divide both sides by 0.95

Rewrite as:

Hence, her monthly gross pay is: $4111.93
Read more about gross and net pay at:
brainly.com/question/8952173
One way is to:
First, multiply 2 by the term inside the parenthesis.
Second, add eleven on both sides.
Third, divide using 4x on both sides.
This will give you your first method.
Answer:

Step-by-step explanation:
We are asked to divide our given fraction:
.
We will simplify our division problem using rules of exponents.
Using product rule of exponents
we can write:


Substituting these values in our division problem we will get,

Using power rule of exponents
we will get,


Using quotient rule of exponent
we will get,


Using product rule of exponents
we will get,


Upon canceling out
we will get,

Using power rule of exponents
we will get,


Therefore, our resulting quotient will be
.
I think the answer is the third one