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3 years ago

12x−39≤9 AND−4x+3<−6

Mathematics

2 answers:

nignag [31]3 years ago

8 0

Answer:

2 1/4 < x ≤ 4

Step-by-step explanation:

12x−39≤9 AND−4x+3<−6

Solve them separately and then put back together

12x−39≤9

Add 39 to each side

12x−39+39≤9+39

12x ≤48

Divide by 12

12x/12 ≤48/12

x ≤4

Now the other inequality

−4x+3<−6

Subtract 3 from each side

−4x+3-3<−6-3

-4x < -9

Divide by -4, remembering to flip the inequality

-4x/-4 > -9/-4

x > 2 1/4

put back together

x > 2 1/4 and x ≤4

2 1/4 < x ≤ 4

densk [106]3 years ago

5 0

Answer:

2.25<x≤4

Step-by-step explanation:

12x−39≤9 ⇒ 12x≤ 48 ⇒ x≤4

−4x+3<−6 ⇒ -4x < -9 ⇒ x> 9/4= 2.25

2.25<x≤4

x= (2.25, 4]

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A space is totally disconnected if its connected spaces are one-point-sets.Show that a finite Hausdorff space is totally disconn

marysya [2.9K]

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 $x_1, x_2, ..., x_n$ . So there are disjoint open neighborhoods $U_{12}$ and $U_2$ , of $x_1$ and $x_2$ respectively (that's the definition of Hausdorff space). There are also open disjoint neighborhoods $U_{13}$ and $U_3$ of $x_1$ and $x_3$ respectively, and disjoint open neighborhoods $U_{14}$ and $U_4$ of $x_1$ and $x_4$ , and so on, all the way to disjoint open neighborhoods $U_{1n}$ , and $U_n$ of $x_1$ and $x_n$ respectively. So $U=U_2 \cup U_3 \cup ... \cup U_n$ has every element of $X$ in it, except for $x_1$ . Since $U$ is union of open sets, it is open, and so $U^c$ , which is the singleton $\{ x_1\}$ , is closed. Therefore every singleton is closed.

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4 0

4 years ago

Find the mean absolute deviation of the following numbers. 10, 8, 5, 12, 20

kicyunya [14]

The mean absolute deviation of the following set of data is 4.5
Step-by-step explanation:
We need to find the mean absolute deviation of the following set of data.
10,20,12,4,18,8,14,18
For finding mean absolute deviation, first we need to find the mean of the given data set.
The formula used to calculate mean is:
Sum of all data points: 10+20+12+4+18+8+14+18 = 104
Number of data points = 8
So, mean is:

Now, we will subtract 13 from the given data points:
10 - 13 = -3
20 - 13 = 7
12 - 13 = -1
4 - 13 = -9
18 -13 = 5
8 - 13 = -5
14 - 13 = 1
18 - 13 = 5
We will take absolute values i.e |-a|=a
So, now the numbers will be:
3,7,1,9,5,5,1,5
We will now find absolute mean deviation by finding mean of newly calculate values
Sum of all data points = 3+7+1+9+5+5+1+5
Number of data points = 8

So, the mean absolute deviation of the following set of data is 4.5

4 0

3 years ago

There..?

QveST [7]

The answer should be:

Domain: All real

numbers

greater than or

equal to 0 and

less than or

equal to 100

Range: all real

numbers

greater than or

equal to 0 and

less than or

equal to 50

3 0

3 years ago

Which expression represents 36x^2-100y^2 factored completely

Citrus2011 [14]

36 and 100 are both perfect squares
the factorization of x^2-y^2 is (x+y)(x-y)
substitute x^2 with 36x^2 and y^2 with 100y^2:
<span>36x^2-100y^2=
(6x+10y)(6x-10y) or
4(3x+5y)(3x-5y)</span>

7 0

3 years ago

My question is what is x-4<6 i dont know inequalities

PolarNik [594]

Answer:

x=6+4

x<10

(-∞,10)

Step-by-step explanation:

Inequalities are the greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

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3 years ago