Step-by-step explanation:
If X is a finite Hausdorff space then every two points of X can be separated by open neighborhoods. Say the points of X are 
. So there are disjoint open neighborhoods 
and 
, of 
and 
respectively (that's the definition of Hausdorff space). There are also open disjoint neighborhoods 
and 
of and 
respectively, and disjoint open neighborhoods 
and 
of and 
, and so on, all the way to disjoint open neighborhoods 
, and 
of and 
respectively. So 
has every element of 
in it, except for . Since 
is union of open sets, it is open, and so 
, which is the singleton 
, is closed. Therefore every singleton is closed.
Now, remember finite union of closed sets is closed, so 
is closed, and so its complemented, which is is open. Therefore every singleton is also open.
That means any two points of belong to different connected components (since we can express X as the union of the open sets 
, so that is in a different connected component than 
, and same could be done with any 
), and so each point is in its own connected component. And so the space is totally disconnected.
0.1/0.4 converted to a decimal is 0.25 :) hope this helps
Problem: 2x^2+3x-9
For a polynomial of the form, ax^2+bx+c rewrite the middle term as the sum of two terms whose product a·c=2·-9=-18 and whose sum is b=3.
Factor 3 out of 3x
2x^2+3(x)-9
Rewrite 3 as -3 plus 6.
2x^2+(-3+6)x-9
Apply the distributive property
2x^2(-3x+6x)-9
Remove the parentheses
2x^2-3x+6x-9
Factor out the greatest common factor from each group
Group the first two terms and the last two terms
(2x^2-3x) (6x-9)
Factor out the greatest common factor in each group.
x(2x-3)+3(2x-3)
Factor the polynomial by factoring out the greatest common factor, 2x-3
(x+3) (2x-3). So, the quotient is 2x-3
Answer:
x=7
Step-by-step explanation:
I got this because it is rise over run
The missing number would be 3, and if you add that three to 4 you get 7. which means that the answer is...
(7,12)
<h2>Hope this helps you!!!</h2>
For direct variation:
y = kx
9 = 12k
k = 9/12 = 3/4
