Answer with explanation:
When a die is thrown once, total possible outcome ={1,2,3,4,5,6}=6
Total number of odd number in total possible outcome when a die is thrown once ={1,3,5}=3
Probability of an event
![=\frac{\text{Total Possible Outcome}}{\text{Total favorable outcome}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Ctext%7BTotal%20Possible%20Outcome%7D%7D%7B%5Ctext%7BTotal%20favorable%20outcome%7D%7D)
Probability of getting an Odd number when a Dice is thrown once
![=\frac{3}{6}\\\\=\frac{1}{2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B3%7D%7B6%7D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B2%7D)
So, When a two fair six sided dice is rolled, the probability that both dice show an odd number
![=\frac{1}{2}\times \frac{1}{2}\\\\=\frac{1}{4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B4%7D)
A plane consists of an infinite set of points.
A point's location on the coordinate plane is indicated by an ordered pair, (x, y).
Step-by-step explanation:
The undefined terms in geometry are points, lines and planes.
- A point's location on the coordinate plane is indicated by an ordered pair, (x, y). TRUE. In R², the ordered pairs (x,y) is used to defined the location of a point.
- The second statement is false because a point has no dimension.
- The third statement is also false because a line has only one dimension which is length.
- The fourth statement is not true because distance between two points must have a beginning and an end.
- A plane consists of an infinite set of points. TRUE .The plane is a home of infinitely many points.
Answer:
I don't know please ask from someone else
Answer:
x = 45
Step-by-step explanation:
x and 3x are adjacent angles and the form a straight line. Their sum will be 180 degrees
x +3x = 180
Combine like terms
4x = 180
Divide each side by 4
4x/4 = 180/4
x =45
Answer:
For ![x \in\mathbb{C}](https://tex.z-dn.net/?f=x%20%5Cin%5Cmathbb%7BC%7D)
![x = -2i](https://tex.z-dn.net/?f=x%20%3D%20-2i)
![x = 2i](https://tex.z-dn.net/?f=x%20%3D%202i)
![x = 7](https://tex.z-dn.net/?f=x%20%3D%207)
Step-by-step explanation:
![f(x)=x^3-7x^2+4x-28](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E3-7x%5E2%2B4x-28)
For ![f(x) = 0](https://tex.z-dn.net/?f=f%28x%29%20%3D%200)
![x^3-7x^2+4x-28 = 0](https://tex.z-dn.net/?f=x%5E3-7x%5E2%2B4x-28%20%3D%200)
We can easily factor the expression
by grouping.
![x^3-7x^2+4x-28 = (x^3-7x^2)+(4x-28) = x^2(x-7)+4(x-7) = \boxed{(x^2+4)(x-7) }](https://tex.z-dn.net/?f=x%5E3-7x%5E2%2B4x-28%20%3D%20%28x%5E3-7x%5E2%29%2B%284x-28%29%20%3D%20x%5E2%28x-7%29%2B4%28x-7%29%20%3D%20%5Cboxed%7B%28x%5E2%2B4%29%28x-7%29%20%7D)
Now we have
![(x^2+4)(x-7) = 0](https://tex.z-dn.net/?f=%28x%5E2%2B4%29%28x-7%29%20%3D%200)
Therefore,
![x^2+4 = 0 \text{ or } x-7 = 0](https://tex.z-dn.net/?f=x%5E2%2B4%20%3D%200%20%5Ctext%7B%20or%20%7D%20x-7%20%3D%200)
So,
![x^2 = -4 \implies x = \pm\sqrt{-4}](https://tex.z-dn.net/?f=x%5E2%20%3D%20-4%20%5Cimplies%20x%20%3D%20%5Cpm%5Csqrt%7B-4%7D)
Once ![\sqrt{-1} = i](https://tex.z-dn.net/?f=%5Csqrt%7B-1%7D%20%3D%20i)
![x = \pm\sqrt{-4} = \pm\sqrt{4}\sqrt{-1} = \pm 2i](https://tex.z-dn.net/?f=x%20%3D%20%5Cpm%5Csqrt%7B-4%7D%20%3D%20%20%5Cpm%5Csqrt%7B4%7D%5Csqrt%7B-1%7D%20%3D%20%5Cpm%202i)