Answer:
OPTION C
Step-by-step explanation:
We have the following rules:
![$ \sqrt[a]{x} = x^{\frac{1}{a} $](https://tex.z-dn.net/?f=%24%20%5Csqrt%5Ba%5D%7Bx%7D%20%3D%20x%5E%7B%5Cfrac%7B1%7D%7Ba%7D%20%24)
and
OPTION A: ![$ x \sqrt[7]{x} $](https://tex.z-dn.net/?f=%24%20x%20%5Csqrt%5B7%5D%7Bx%7D%20%24)
= 
= 
So, it can be eliminated.
OPTION B: ![$ \bigg ( \frac{1}{\sqrt[7]{x}} \bigg )^9 $](https://tex.z-dn.net/?f=%24%20%5Cbigg%20%28%20%5Cfrac%7B1%7D%7B%5Csqrt%5B7%5D%7Bx%7D%7D%20%5Cbigg%20%29%5E9%20%24)
= 
= 
= 
So, this option is also eliminated.
OPTION C: ![$ x . \sqrt[7]{x} $](https://tex.z-dn.net/?f=%24%20x%20.%20%5Csqrt%5B7%5D%7Bx%7D%20%24)
= 
= 
= 
So, OPTION C is the answer.
For the carpet:
Given:
Area = x^2 + x - 20 ft^2
Length = x+ 5 ft
As a carpet is rectangular, the area is defined as the product of the length and the width. To obtain an expression of the carpet's width, the area is to be divided by the length, which is shown below:
__x_-_4___x + 5|x^2 + x - 20 x^2 + 5x -------- -4x - 20 -4x - 20 -------- 0
Therefore, the expression of width = x - 4.
Applying the value of x = 20 to obtain the measurements of the carpet, we obtain the following:
Width = x - 4 = 20 - 4 = 16ft
Length = x+ 5 = 20 + 5 = 25ft.
Therefore, the carpet is 25ft x 16ft.
For the wall:
The same principles apply to the wall as it is also assumed to be rectangular.
Given:
Area = <span>x^2 + 17x + 30 ft^2
Width = x + 2
To obtain the expression for the wall's length, Area is to be divided by the Width, which is shown below:
__x_+_15______x + 2|x^2 + 17x + 30 x^2 + 2x -------- 15x + 30 15x + 30 --------- 0
Therefore, the expression for the wall's length is x + 15.
Applying the value of x = 20 to obtain the wall's dimensions:
Length = x + 15 = 20 + 15 = 35ft.
Width = x + 2 = 20 + 2 = 22ft.
Therefore the wall has measurements of 35ft x 22ft.</span>
Replace every n with 15 to get 15*(15-1)/2 = 15*14/2 = 15*7 = 105
Answer is choice C
A)
The relationship between the amount of hours
spent studying and the test scores increase with time in a positive direction showing a positive correlation.
B) Y=8x+40
Y=8(3) +40
Y=24+40
Y= 64
C)
The 40 stands for the initial score the student
can get without any studying
