Answer:
It has been proved that T is compact
Step-by-step explanation:
To prove this using the definition of compactness, let's assume that T is
not compact. Now, if that be the case, an open cover of T will exist. Let's call this open cover "A". Now, this open cover will have no finite subcover.
Now, from the question, since T is closed, it’s complement R\T will be open.
Therefore, if we add the set R\T to the collection of sets A, then we'll have an open cover of R and also of S.
Due to the fact that S is compact, this
cover will have a finite sub - cover which we will call B.
Finally, either B itself or B\{R\T} would be a finite sub - cover of A. This is a contradiction.
Thus, it proves that T has to be compact if S is to be a compact subset of R and T is to be a closed subset of S.
Find the equation of the line
slope=(y2-y1)/(x2-x1)
slope=(6-2)/(7-(-3))=4/10=2/5
slope is 2/5
y=mx+b
y=2/5x+b find b
input a point
6=2/5(7)+b
6=14/5+b
minus 14/5 from both sides
3 and 1/5=b
16/5=b
xintercept is when y=0
0=2/5x+16/5
minus 16/5 from both sides
-16/5=2/5x
times both sides by 5/2 to clear fraction
-8=x
xintercept is -8 or (-8,0)
120.25 I just divided the figure into smaller shapes, found the value and then I added the areas together! :)
I'm assuming you didn't mean to repeat each number 3 times.
If she did 184 jumping jacks in 4 minutes that means she did 46 jumping jacks per minute.
Answer:
the number doesnt represent an integer?
A. 3
B. 20.1
C. -10
D. 20/4
Step-by-step explanation:
We call integers the “counting numbers, their negatives and zero”. I.e. 0,1,−1,2,−2,3,−3,.. etc.
non-integers means “everything except integers”. Which is not well-defined (i.e. nonsense). Why? Because nobody said what “everything” is.
Therefore, when somebody says “non-integer” he has to specify how he defines “everything”. In this case, our “everything” is probably “real numbers”.
Real numbers have an interesting definition concerning an abstract mathematical object called “field” . Let’s forget about that and let’s focus on a high school definition: Real numbers are probably all the numbers you know. They are those represented by a decimal and their negatives e.g. 345.232… and −243.13242240… where there are “infinitely many” digits at the end. Note that 2.5 is also a real number. Integers are too. Basically, real numbers are the numbers used to measure distances and their negatives.
To summirize, your answer is the following:
“non integers” means everything except the integers, where everything is defined however we want. The most common definition of everything in this case is “real numbers” and therefore the most common interpretation of “non integers” is “reals which are not integers”.
Examples of “reals which are not integers”: 1.5,2.88,1.3333… etc
the answer is
B. 20.1
