Answer:
See explanation
Step-by-step explanation:
1. Given the expression
![\dfrac{\sqrt[7]{x^5} }{\sqrt[4]{x^2} }](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%5B7%5D%7Bx%5E5%7D%20%7D%7B%5Csqrt%5B4%5D%7Bx%5E2%7D%20%7D)
Note that
![\sqrt[7]{x^5}=x^{\frac{5}{7}} \\ \\\sqrt[4]{x^2}=x^{\frac{2}{4}}=x^{\frac{1}{2}}](https://tex.z-dn.net/?f=%5Csqrt%5B7%5D%7Bx%5E5%7D%3Dx%5E%7B%5Cfrac%7B5%7D%7B7%7D%7D%20%5C%5C%20%5C%5C%5Csqrt%5B4%5D%7Bx%5E2%7D%3Dx%5E%7B%5Cfrac%7B2%7D%7B4%7D%7D%3Dx%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D)
When dividing
by
we have to subtract powers (we cannot subtract 4 from 7, because then we get another expression), so

and the result is ![x^{\frac{3}{14}}=\sqrt[14]{x^3}](https://tex.z-dn.net/?f=x%5E%7B%5Cfrac%7B3%7D%7B14%7D%7D%3D%5Csqrt%5B14%5D%7Bx%5E3%7D)
2. Given equation ![3\sqrt[4]{(x-2)^3} -4=20](https://tex.z-dn.net/?f=3%5Csqrt%5B4%5D%7B%28x-2%29%5E3%7D%20-4%3D20)
Add 4:
![3\sqrt[4]{(x-2)^3} -4+4=20+4\\ \\3\sqrt[4]{(x-2)^3}=24](https://tex.z-dn.net/?f=3%5Csqrt%5B4%5D%7B%28x-2%29%5E3%7D%20-4%2B4%3D20%2B4%5C%5C%20%5C%5C3%5Csqrt%5B4%5D%7B%28x-2%29%5E3%7D%3D24)
Divide by 3:
![\sqrt[4]{(x-2)^3} =8](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%28x-2%29%5E3%7D%20%3D8)
Rewrite the equation as:

Hence,

Find a ∩ b if a = {2, 5, 8, 11, 14} and b = {1, 3, 5, 7}. {1, 2, 3, 5, 7, 8, 11, 14} {5}
Maslowich
The intersection of given set a and b is a∩b = {5}.
According to the given question.
We have two sets a and b.
a = {2, 5, 8, 11, 14}
And, b = {1, 3, 5, 7}
As, we know that "the intersection of two sets A and B is the set of all those elements which are common to both A and B. Symbolically, we can represent the intersection of A and B as A ∩ B".
Since, only the element which is common to set a and set b is 5.
Thereofore, the intersection of given set a and b is given by
a∩b = {5}
Find out more information about intersection of sets here:
brainly.com/question/14679547
#SPJ4
Hmm, I believe the answer is 80%.
It is a decrease.
30 - 6 = 24.
24/30 = 80% decrease from Wednesday.
Answer:
c) 82
Step-by-step explanation:
<ABE and <BEC are supplementary because they form a line.
<ABE + <BEC = 180
116+ x = 180
Subtract 116 from each side.
116-116+x = 180 -116
x = 64
The angles in triangle ECB add to 180 because it is a triangle
<BEC + <ECB + <CBE = 180
x + 34+y = 180
64 + 34+ y = 180
98 + y = 180
Subtract 98 from each side.
98-98+y = 180-98
y = 82
Using the formula for interest:
F = P (1 + r/n)^t
Where:
F = future value
P = Principal value
r = interest rate per year
n = interest period
t = duration
Substituting the given values:
F = 200 (1 + 0.32/12)^1
F = 205.33
To obtain the interest, we subtract the principal value from the future value. This is shown below:
Interest = 205.33 - 200 = 5.33
Among the choices, the answer is A.