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MrMuchimi
3 years ago
12

Which graph represents the compound inequality​

Mathematics
1 answer:
Sergio039 [100]3 years ago
7 0

Answer: C

Step-by-step explanation:

When looking at compound inequalities, the inequalities are very important. You can see that on the graphs, there are some points that have a white open circle and others have blue, closed circle. The 2 different circles tells you the inequality itself. If you see ≤ or ≥, it is a closed circle. This is a closed circle because it is less than/greater than or equal to. That means it is also equal to the point, therefore it is a closed circle. If you see < or >, it is an open circle. That means it is not closed because it is greater than. It is not equal to on that specific point.

Now that we have covered the basics, we can start to eliminate. our first condition is n<-2. Above, we have established that < is an open circle. We can eliminate A and B because the points on -2 are both closed circles.

That leaves us with C and D. Since C and D both follow the points, let's look carefully at what the inequality tells us. n<-2 means n is less than -2. This means the arros should be pointing in the left side. As you go more towards the negative, the smaller the number becomes.

We can eliminate D because at -2, the numbers are going towards the right, not the left.

Therefore, our answer is C.

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N is a positive integer
Murrr4er [49]

Part (1)

n is some positive integer. Let's say for now that n is even. So n = 2k, for some integer k

This means n-1 = 2k-1 is odd since subtracting 1 from an even number leads to an odd number.

Now multiply n with n-1 to get

n(n-1) = 2k(2k-1) = 2m

where m = k(2k-1) is an integer

The result 2m is even showing that n(n-1) is even

------------

Let's say that n is odd this time. That means n = 2k+1 for some integer k

And also n-1 = 2k+1-1 = 2k showing n-1 is even

Now multiply n and n-1

n(n-1) = (2k+1)(2k) = 2k(2k+1) = 2m

where m = k(2k+1) is an integer

We've shown that n(n-1) is even here as well.

------------

So overall, n(n-1) is even regardless if n is even or if n is odd.

Either n or n-1 will be even. If you multiply an even number with any number, the result will be even.

=======================================================

Part (2)

n is some positive integer

2n is always even since 2 is a factor of 2n

2n+1 is always odd because we're adding 1 to an even number. The sequence of integers goes even,odd,even,odd, etc and it does this forever.

-----------

Another way to see how 2n+1 is odd is to divide 2n+1 over 2 and you'll find that we get (2n+1)/2 = 2n/2+1/2 = n+0.5

The 0.5 at the end is not an integer, so there's no way that (2n+1)/2 is an integer; therefore 2n+1 is odd.

6 0
2 years ago
What percent of 80 is 28
serious [3.7K]

Answer:

35%

Step-by-step explanation:

easy way to remember: \frac{28}{80} *1 00

= 0.35 *100

= 35%

5 0
3 years ago
Read 2 more answers
What is the domain of f?
larisa86 [58]

Answer:

\huge \boxed{\mathrm{A}}

Step-by-step explanation:

The domain of a function is all possible values for the value of x.

The denominator in a rational function cannot equal to 0.

x+2\neq 0

Subtracting 2 from both sides.

x\neq -2

The domain of the function is all real numbers except -2.

7 0
3 years ago
What are the coordinates of the endpoints A'B after a reflection of segment AB over the line y = - x?
kupik [55]

Answer:

by reflection, if you mean swapped, then the answers are A'(1,-6) and B'(4,2)

i hope these are the answers you are looking for

Step-by-step explanation:

6 0
3 years ago
Can someone help me with this question please?
Paladinen [302]
60 movies ------ 100%
9 movies -------- x%
__________________
60*x=9*100%
60x=900%   |:60
x=15%

The answer is 15%
:)
7 0
3 years ago
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