Answer:
Answer is 9
Step-by-step explanation:
Remember PEMDAS???
"parenthesis, exponents, multiplication, division, addition, subtraction"
you would first solve the addition inside of the parentheses (1 + 2 = 3), and from there finish the equation as it's written from left to right.
Option C:
![$\frac{\sqrt[3]{100 x}}{5}=\sqrt[3]{\frac{4 x}{5}}](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Csqrt%5B3%5D%7B100%20x%7D%7D%7B5%7D%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B4%20x%7D%7B5%7D%7D)
Solution:
Given expression is
![$\sqrt[3]{\frac{4 x}{5}}](https://tex.z-dn.net/?f=%24%5Csqrt%5B3%5D%7B%5Cfrac%7B4%20x%7D%7B5%7D%7D)
Note: ![\sqrt[3]{125}=\sqrt[3]{{5^3}} = 5](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B125%7D%3D%5Csqrt%5B3%5D%7B%7B5%5E3%7D%7D%20%20%3D%205)
To find the correct expression for the above simplified expression.
Option A: ![\frac{\sqrt[3]{4 x}}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B4%20x%7D%7D%7B5%7D)
5 can be written as
.
![$\frac{\sqrt[3]{4 x}}{5}=\frac{\sqrt[3]{4 x}}{\sqrt[3]{125} }](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Csqrt%5B3%5D%7B4%20x%7D%7D%7B5%7D%3D%5Cfrac%7B%5Csqrt%5B3%5D%7B4%20x%7D%7D%7B%5Csqrt%5B3%5D%7B125%7D%20%7D)
![$=\sqrt[3]{\frac{4x}{125} }](https://tex.z-dn.net/?f=%24%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B4x%7D%7B125%7D%20%7D)
It is not the given simplified expression.
Option B: ![\frac{\sqrt[3]{20 x}}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B20%20x%7D%7D%7B5%7D)
![$\frac{\sqrt[3]{20 x}}{5}=\frac{\sqrt[3]{20 x}}{\sqrt[3]{125} }](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Csqrt%5B3%5D%7B20%20x%7D%7D%7B5%7D%3D%5Cfrac%7B%5Csqrt%5B3%5D%7B20%20x%7D%7D%7B%5Csqrt%5B3%5D%7B125%7D%20%7D)
![$=\sqrt[3]{\frac{20x}{125} }](https://tex.z-dn.net/?f=%24%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B20x%7D%7B125%7D%20%7D)
Cancel the common factor in both numerator and denominator.
![$=\sqrt[3]{\frac{4x}{25} }](https://tex.z-dn.net/?f=%24%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B4x%7D%7B25%7D%20%7D)
It is not the given simplified expression.
Option C: ![\frac{\sqrt[3]{100 x}}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B100%20x%7D%7D%7B5%7D)
![$\frac{\sqrt[3]{100 x}}{5}=\frac{\sqrt[3]{100 x}}{\sqrt[3]{125} }](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Csqrt%5B3%5D%7B100%20x%7D%7D%7B5%7D%3D%5Cfrac%7B%5Csqrt%5B3%5D%7B100%20x%7D%7D%7B%5Csqrt%5B3%5D%7B125%7D%20%7D)
![$=\sqrt[3]{\frac{100x}{125} }](https://tex.z-dn.net/?f=%24%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B100x%7D%7B125%7D%20%7D)
Cancel the common factor in both numerator and denominator.
![$=\sqrt[3]{\frac{4 x}{5}}](https://tex.z-dn.net/?f=%24%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B4%20x%7D%7B5%7D%7D)
It is the given simplified expression.
Option D: ![\frac{\sqrt[3]{100 x}}{125}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B100%20x%7D%7D%7B125%7D)
![$\frac{\sqrt[3]{100 x}}{125}=\frac{\sqrt[3]{100 x}}{5^3}](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Csqrt%5B3%5D%7B100%20x%7D%7D%7B125%7D%3D%5Cfrac%7B%5Csqrt%5B3%5D%7B100%20x%7D%7D%7B5%5E3%7D)
It is not the given simplified expression.
Hence Option C is the correct answer.
![$\frac{\sqrt[3]{100 x}}{5}=\sqrt[3]{\frac{4 x}{5}}](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Csqrt%5B3%5D%7B100%20x%7D%7D%7B5%7D%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B4%20x%7D%7B5%7D%7D)
Answer:
8
Step-by-step explanation:
total number of pencils = 186
number of students = 23
number of pencils each student gets = number of pencils ÷ number of pencils
=186/23
=8.08
so each student gets 8 pencils
Answer:
C
Step-by-step explanation:
The number of points either side of the line of best fit are equal (3 points either side) and the line is the line of best fit.
The value is 333
<h3>How to determine the function</h3>
From the information given, we have:
- x = - 8
- 1/3*h(x) = x^2-5x+7
Now, let's substitute the value of 'x' in the function:
1/3*h(x) = x^2-5x+7
1/ 3 × h(-8) = ( - 8)² - 5 ( -8) + 7
Make 'h ( -8)' the subject of formula
h ( -8) = 
h ( -8) = 
Take the sum of the numerator
h ( -8) = 
Take the inverse of the denominator and multiply
h ( -8) = 111 × 3/ 1
h ( -8) = 333
We can see that through the substitute of the value of x as - 8, we get 333
Thus, the value is 333
Learn more about algebraic expressions here:
brainly.com/question/723406
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