180537.5 simplified is 180538
X=2
2
−
3
(
|
x
−
2
|
)
−
4
x
=
−
6
−
3
(
|
x
−
2
|
)
−
4
x
+
2
=
−
6
Step 1: Add 4x to both sides.
−
3
(
|
x
−
2
|
)
−
4
x
+
2
+
4
x
=
−
6
+
4
x
−
3
(
|
x
−
2
|
)
+
2
=
4
x
−
6
Step 2: Add -2 to both sides.
−
3
(
|
x
−
2
|
)
+
2
+
−
2
=
4
x
−
6
+
−
2
−
3
(
|
x
−
2
|
)
=
4
x
−
8
Step 3: Divide both sides by -3.
−
3
(
|
x
−
2
|
)
−
3
=
4
x
−
8
−
3
|
x
−
2
|
=
−
4
3
x
+
8
3
Step 4: Solve Absolute Value.
|
x
−
2
|
=
−
4
3
x
+
8
3
We know either
x
−
2
=
−
4
3
x
+
8
3
or
x
−
2
=
−
(
−
4
3
x
+
8
3
)
x
−
2
=
−
4
3
x
+
8
3
(Possibility 1)
x
−
2
+
4
3
x
=
−
4
3
x
+
8
3
+
4
3
x
(Add 4/3x to both sides)
7
3
x
−
2
=
8
3
7
3
x
−
2
+
2
=
8
3
+
2
(Add 2 to both sides)
7
3
x
=
14
3
(
3
7
)
*
(
7
3
x
)
=
(
3
7
)
*
(
14
3
)
(Multiply both sides by 3/7)
x
=
2
x
−
2
=
−
(
−
4
3
x
+
8
3
)
(Possibility 2)
x
−
2
=
4
3
x
+
−
8
3
(Simplify both sides of the equation)
x
−
2
−
4
3
x
=
4
3
x
+
−
8
3
−
4
3
x
(Subtract 4/3x from both sides)
−
1
3
x
−
2
=
−
8
3
−
1
3
x
−
2
+
2
=
−
8
3
+
2
(Add 2 to both sides)
−
1
3
x
=
−
2
3
(
3
−
1
)
*
(
−
1
3
x
)
=
(
3
−
1
)
*
(
−
2
3
)
(Multiply both sides by 3/(-1))
x
=
2
−
3
(
|
x
−
2
|
)
−
4
x
=
−
6
−
3
(
|
x
−
2
|
)
−
4
x
+
2
=
−
6
Step 1: Add 4x to both sides.
−
3
(
|
x
−
2
|
)
−
4
x
+
2
+
4
x
=
−
6
+
4
x
−
3
(
|
x
−
2
|
)
+
2
=
4
x
−
6
Step 2: Add -2 to both sides.
−
3
(
|
x
−
2
|
)
+
2
+
−
2
=
4
x
−
6
+
−
2
−
3
(
|
x
−
2
|
)
=
4
x
−
8
Step 3: Divide both sides by -3.
−
3
(
|
x
−
2
|
)
−
3
=
4
x
−
8
−
3
|
x
−
2
|
=
−
4
3
x
+
8
3
Step 4: Solve Absolute Value.
|
x
−
2
|
=
−
4
3
x
+
8
3
We know either
x
−
2
=
−
4
3
x
+
8
3
or
x
−
2
=
−
(
−
4
3
x
+
8
3
)
x
−
2
=
−
4
3
x
+
8
3
(Possibility 1)
x
−
2
+
4
3
x
=
−
4
3
x
+
8
3
+
4
3
x
(Add 4/3x to both sides)
7
3
x
−
2
=
8
3
7
3
x
−
2
+
2
=
8
3
+
2
(Add 2 to both sides)
7
3
x
=
14
3
(
3
7
)
*
(
7
3
x
)
=
(
3
7
)
*
(
14
3
)
(Multiply both sides by 3/7)
x
=
2
x
−
2
=
−
(
−
4
3
x
+
8
3
)
(Possibility 2)
x
−
2
=
4
3
x
+
−
8
3
(Simplify both sides of the equation)
x
−
2
−
4
3
x
=
4
3
x
+
−
8
3
−
4
3
x
(Subtract 4/3x from both sides)
−
1
3
x
−
2
=
−
8
3
−
1
3
x
−
2
+
2
=
−
8
3
+
2
(Add 2 to both sides)
−
1
3
x
=
−
2
3
(
3
−
1
)
*
(
−
1
3
x
)
=
(
3
−
1
)
*
(
−
2
3
)
(Multiply both sides by 3/(-1))
x
=
2
Answer:
Step-by-step explanation:
Given that the Martian Colonies elect their government through a lottery. There are 100,000 people living on Mars
every year, a council of 99 co-equal leaders is randomly selected from the population.
Since these are members, order of selection of not important
So combinations woul dbe used here.
Total number of persons avaiiable = 100,000
No of persons to be selected = 999
No of ways this can be done =
999 out of 100,000
=
Answer:
Step-by-step explanation:
a)
![\sqrt[3]{81}=\sqrt[3]{3^4}=\sqrt[3]{(3^3)(3)}=3\sqrt[3]{3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B81%7D%3D%5Csqrt%5B3%5D%7B3%5E4%7D%3D%5Csqrt%5B3%5D%7B%283%5E3%29%283%29%7D%3D3%5Csqrt%5B3%5D%7B3%7D)
This is irrational.
__
b)
![\sqrt[3]{-64}=\sqrt[3]{(-4)^3}=-4](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B-64%7D%3D%5Csqrt%5B3%5D%7B%28-4%29%5E3%7D%3D-4)
This is rational.
_____
Please be aware that 3 square root of 81 is not the same as cube root of 81.
![3\sqrt{81}\ne\sqrt[3]{81}](https://tex.z-dn.net/?f=3%5Csqrt%7B81%7D%5Cne%5Csqrt%5B3%5D%7B81%7D)
You can call a cube root what it is.
