Answer:

Step-by-step explanation:
What is the cube root of
? This is the question.
We can write:
![\sqrt[3]{27a^{12}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B27a%5E%7B12%7D%7D)
We will use the below property to simplify:
![\sqrt[n]{a*b}=\sqrt[n]{a} \sqrt[n]{b}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Ba%2Ab%7D%3D%5Csqrt%5Bn%5D%7Ba%7D%20%20%5Csqrt%5Bn%5D%7Bb%7D)
So, we have:
![\sqrt[3]{27a^{12}} =\sqrt[3]{27} \sqrt[3]{a^{12}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B27a%5E%7B12%7D%7D%20%3D%5Csqrt%5B3%5D%7B27%7D%20%5Csqrt%5B3%5D%7Ba%5E%7B12%7D%7D)
We will now use below property to further simplify:
![\sqrt[n]{x} =x^{\frac{1}{n}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%7D%20%3Dx%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D)
Thus, we have:
![\sqrt[3]{27} \sqrt[3]{a^{12}} =3*(a^{12})^{\frac{1}{3}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B27%7D%20%5Csqrt%5B3%5D%7Ba%5E%7B12%7D%7D%20%3D3%2A%28a%5E%7B12%7D%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
We know power to the power rule: 
Now, we have:

This is the correct answer: 
Question number b is the correct one
Answer:
letter C: 100
Step-by-step explanation:
This problem can be configured as an arithmetic progression:
The first value is 10, the ratio is also 10 (the multiples of ten are 20, 30, 40, ...) and the number of terms is 19 (10, 20, 30, ... , 180, 190 -> total of 19 numbers).
So, we can use the following formula to calculate the sum of all these numbers:
Sn = n(a1 + an)
/2
where Sn is the sum, n is the number of terms, a1 is the first term and an is the last one.
The result we want is the average of the sum, so we need to divide Sn by n:
Average = Sn/n = n(a1 + an)
/2n = (a1 + an)
/2 = (10+190)/2 = 200/2 = 100
The correct option is letter C.
Answer:
y = 2x + 20


Step-by-step explanation:
Vlad spent 20 minutes on history. Then Vlad spent 2 minutes on each math problem for homework, this is 2x. So in total, he spent 20+2x on homework. Depending on how many problems he did, the total time y can be found. This is the equation 20+2x=y.
If Vlad did 0 math problems then he spent at least 20 minutes on homework from history. This is the constraint
.
We also know Vlad can do many math problems but the least amount he did was 0, so the second constraint is
.