Answer:
{
}
The number line is attached.
Step-by-step explanation:
By definition Set-builder notation is a mathematical shorthand used to provide specific details about a set.
In this case, you have the following interval:
![(-6,2]](https://tex.z-dn.net/?f=%28-6%2C2%5D)
You can obsseve that the left hand contains a parentheses, which means that -6 it is not included, then:
The right hand contains a bracket, which means that 2 is included:
The inequality is:
Therefore, in Set-builder notation this is:
{}
Observe the number line attached. Since -6 is not included, you must use an unfilled circle. Since 2 is included, you must use a filled circle.
Answer:
![\sqrt[6]{432}](https://tex.z-dn.net/?f=%5Csqrt%5B6%5D%7B432%7D)
Step-by-step explanation:
![\sqrt[3]{4}\cdot\sqrt{3}=4^{\frac{1}{3}}\cdot3^\frac{1}{2}=(2^2)^\frac{1}{3}\cdot3^\frac{1}{2}=(2^\frac{4}{3})^\frac{1}{2}\cdot3^\frac{1}{2}=(2^\frac{4}{3}\cdot3)^\frac{1}{2}=(2^4\cdot27)^\frac{1}{6}=432^\frac{1}{6}=\sqrt[6]{432}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B4%7D%5Ccdot%5Csqrt%7B3%7D%3D4%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Ccdot3%5E%5Cfrac%7B1%7D%7B2%7D%3D%282%5E2%29%5E%5Cfrac%7B1%7D%7B3%7D%5Ccdot3%5E%5Cfrac%7B1%7D%7B2%7D%3D%282%5E%5Cfrac%7B4%7D%7B3%7D%29%5E%5Cfrac%7B1%7D%7B2%7D%5Ccdot3%5E%5Cfrac%7B1%7D%7B2%7D%3D%282%5E%5Cfrac%7B4%7D%7B3%7D%5Ccdot3%29%5E%5Cfrac%7B1%7D%7B2%7D%3D%282%5E4%5Ccdot27%29%5E%5Cfrac%7B1%7D%7B6%7D%3D432%5E%5Cfrac%7B1%7D%7B6%7D%3D%5Csqrt%5B6%5D%7B432%7D)
Using the distributive property is done by multiplying the factor (outside the parentheses) to each term within it. In this case, 8(3 + 4), we multiply the 8 by 3, and then add it to the product of 8 x 4:
8(3 + 4) = 8 x 3 + 8 x 4 = 24 + 32
If we need to simplify further, this adds up to 56.
we will check each options
option-A:
For solving any equations , we always isolate variables on anyone side
For exp: x+7=1
so, this is TRUE
option-B:
For solving system of equations
For exp:
x-y=1
x+y=3
If we use addition , we could easily solve for x and y
so, this is TRUE
option-C:
We always solve problems using conventional method
we do not guess
so, this is FALSE
option-D:
We often reverse order of operation
For exp:
(x-2)^2-3=0
so, this is TRUE
option-E:
For linear equations , we always get one solution , infinite solutions or no solutions
so, this is FALSE
