Solution :
We have to prove that [tex]$\overline{A \cup B} = \overline{A} \cap \overline{B}$[/tex] (De-Morgan's law)
Let [tex]$x \in \bar{A} \cap \bar{B}, $[/tex] then [tex]$x \in \bar{A}$[/tex] and [tex]$x \in \bar{B} $[/tex]
and so [tex]$x \notin \bar{A}$[/tex] and [tex]$x \notin \bar{B} $[/tex].
Thus, [tex]$x \notin A \cup B$[/tex] and so [tex]$x \in \overline{A \cup B}$[/tex]
Hence, [tex]$\bar{A} \cap \bar{B} \subset \overline{A \cup B}$[/tex] .........(1)
Now we will show that [tex]$\overline{A \cup B} \subset \overline{A} \cap \overline{B}$[/tex]
Let [tex]$x \in \overline{A \cup B}$[/tex] ⇒ [tex]$x \notin A \cup B$[/tex]
Thus x is present neither in the set A nor in the set B, so by definition of the union of the sets, by definition of the complement.
[tex]$x \in \overline{A}$[/tex] and [tex]$x \in \overline{B}$[/tex]
Therefore, [tex]$x \in \overline{A} \cap \overline{B}$[/tex] and we have [tex]$\overline{A \cup B} \subset \overline{A} \cap \overline{B}$[/tex] .............(2)
From (1) and (2),
[tex]$\overline{A \cup B} = \overline{A} \cap \overline{B}$[/tex]
Hence proved.
Simplify:
3 (2x - 4)
Answer:
Step-by-step explanation:
In Kelsey’s pencil case, she has 2 highlighters for every 7 pencils. What is the ratio of pencils to highlighters?
Answer:
7:2
Step-by-step explanation:
Answer:
7:2
Step-by-step explanation:
What features do all right trlangles have in common?
Answer:
all right trigangles must have a 90 degress angle
Step-by-step explanation:
no
A square has legs of 11, what is the measure of its hypotenuse
A.) 9.4 or B.)15.6
15.6 is the measure of the hypotenuse of the square.
What is a square?A square is a two-dimensional closed shape with 4 equal sides and 4 vertices.
Given that one side of the square is 11.
The diagonal is the hypotenuse of the square.
Since square have equal sides, the hypotenuse can be obtained using Pythagorean theorem.
i.e. 11² + 11² = (hypotenuse)²
i,.e. (hypotenuse)² = 121+121 =242
Therefore, hypotenuse = √242 = 15.6
Hence, the measure of the hypotenuse of the square is 15.6
To learn more about square, use the link given below:
https://brainly.com/question/11800577
#SPJ2
the 100th term of the sequence with the term -1-4n
Given:
The terms of a sequence are given by
[tex]a_n=-1-4n[/tex]
To find:
The 100th term of the sequence.
Solution:
We have,
[tex]a_n=-1-4n[/tex]
Putting n=100, we get
[tex]a_{100}=-1-4(100)[/tex]
[tex]a_{100}=-1-400[/tex]
[tex]a_{100}=-401[/tex]
Therefore, the 100th term of the given sequence is -401.
i need help, may someone help please..
Answer:
if line p is going through the middle x is equal to 5
Here are the prices of some items and the amount of sales tax charged on each in Nevada. Cost of Item $10; Tax .57 Cost of Item $50; Tax 2.85 What is the sales tax rate in Nevada?
2.5% 7%
4.8% 5.7%
Using the figure below determine the following ratios. sin A cos A tan A sin B tan B
What is the slope of the line that passes through the points (4, 6) and (-16, -18)? In the simplest form.
Answer:
[tex]\displaystyle m=\frac{6}{5}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Slope Formula: [tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (4, 6)
Point (-16, -18)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m=\frac{-18-6}{-16-4}[/tex][Fraction] Subtract: [tex]\displaystyle m=\frac{-24}{-20}[/tex][Fraction] Simplify: [tex]\displaystyle m=\frac{6}{5}[/tex]Under her cell phone plan, Aubrey pays a flat cost of $57.50 per month and $4 per gigabyte . She wants to keep her bill at $75.10 per month . Write and solve an equation which can be used to determine the number of gigabytes of data Aubrey can use while staying within her budget .
Answer:
57.50+4x=75.10
x=4.4
So she can use up to 4.4 gigabytes of data
multiple choice! please help me :)
Complete the table:
a. 1
c. 2
b. -1
d. 0
Answer:
cos0 = 1
cos90 =0
so a for the first one and d for the other
Answer:
The answer is -1
Step-by-step explanation:
:)
Point VV is located at (-5,3)(−5,3) on the coordinate plane. Point VV is reflected over the yy-axis to create point V'V ′ . Point V'V ′ is then reflected over the xx-axis to create point V''V ′′ . What ordered pair describes the location of V''?V ′′ ?
Given:
Point V is located at (-5,3) on the coordinate plane.
It is reflected over the y-axis to create point V'.
Point V' is then reflected over the x-axis to create point V''.
To find:
The location of point V''.
Solution:
We have,
Point V= (-5,3)
If point V reflected over the y-axis, then
[tex](x,y)\to (-x,y)[/tex]
[tex]V(-5,3)\to V'(5,3)[/tex]
If point V' reflected over the x-axis, then
[tex](x,y)\to (x,-y)[/tex]
[tex]V'(5,3)\to V''(5,-3)[/tex]
Therefore, the ordered pair (5,-3) describes the location of V''.
Answer:
5,3
Step-by-step explanation:
Point VV is located at (-4,6)(−4,6) on the coordinate plane. Point VV is reflected over the xx-axis to create point V'V
′
. What ordered pair describes the location of V'?V
′
?
Encuentra el mínimo común múltiplo para cada par de números.
1) 3, 24
2) 24, 4
3) 8, 2
4) 5,30
5) 3, 40
Solve the system using substitution.
6x+8y=30 y=1/2x
Answer:
(3, 1.5)Step-by-step explanation:
Given the system:
6x + 8y = 30 y=1/2xSubstitute y and solve for x:
6x + 8y = 306x + 8(1/2x) = 306x + 4x = 3010x = 30x = 3Find y:
y = 1/2xy = 1/2(3)y = 1.5Solution is (3, 1.5)
the product of two numbers is -72. one of the factors -9, what is the other factor?
1.A rectangular room contains 600m cube of air and its height is 5m.
(i) Find the area of its floor.
(ii) Find the cost of carpeting its floor at Rs 60 per sq.m.
Answer:
24 m square
1,440 RS
Step-by-step explanation:
Volume is height x area
600= 5 x area => area = 600/5 = 24 m2
24 sqm x 60 RS/ sqm = 1,440 RS
The boundary line of a linear inequality passes through the points (3,0) and (0,6). The points (3,0) and (2,6) are not solutions of the inequality. Write the linear inequality
Answer:
[tex]y<-2x+6[/tex]
Step-by-step explanation:
The boundary line of a linear inequality passes through the points (3, 0) and (0, 6).
The points (3, 0) and (2, 6) are not solutions of the inequality.
We want to find the equation of the linear inequality.
First, we will simply find the line that crosses the points (3, 0) and (0, 6).
We can determine the slope to be:
[tex]\displaystyle \frac{6-0}{0-3}=\frac{6}{-3}=-2[/tex]
Notice that (0, 6) is the y-intercept.
Then by the slope-intercept form:
[tex]y=mx+b[/tex]
Our equation will be:
[tex]y=-2x+6[/tex]
Now, we will need to determine our inequality sign.
First, (3,0) is on the boundary line yet it is not a solution. Therefore, our line is dotted. That is: we do not have the "or equal to" statement.
So, our inequality signs can only be either < or >.
We are given that (2, 6) is not a solution.
So, we can test for the sign. Substitute 2 for x and 6 for y:
[tex]\displaystyle 6\text{ }?\text{ }-2(2)+6[/tex]
Evaluate:
[tex]\displaystyle 6\text{ } ?\text{ } 2[/tex]
Since 6 is not a solution, the above statement needs to be false.
It will be false is the sign is <, since 2 is not greater than 6.
Therefore, our sign is <.
And our inequality is:
[tex]y<-2x+6[/tex]
Can someone help me on this
Answer:
um what???????
Step-by-step explanation:
An hour before showtime only 105 people have a ride for a concert according to sales 95% of the people have yet to arrive how many tickets were sold for the concert explain
Given:
An hour before showtime only 105 people have arrived for a concert.
According to sales 95% of the people have yet to arrive.
To find:
The total number of tickets sold.
Solution:
Let x be the total number of tickets sold.
According to sales 95% of the people have yet to arrive.
[tex]100\%-95\%=5\%[/tex]
It means, only 5% people have arrived.
[tex]\dfrac{5}{100}x=105[/tex]
[tex]\dfrac{1}{20}x=105[/tex]
[tex]x=105\times 20[/tex]
[tex]x=2100[/tex]
Therefore, the total 2100 tickets were sold.
Mel cleans houses. She earns $7.50 every hour she dusts. She earns $10.00 every hour that
she scrubs floors. She scrubbed floors for 1.5 hours and dusted for 2 hours. How much money
did Mel earn?
5x+3y-z-4x-3y-z help please
The simplified version of this x-2z
Step-by-step explanation:
You need to start by combining like terms. You can start with the terms that have the variable x in them. By combining those terms, the equation becomes x+3y-z-3y-z.
From here, you can combine the terms 3y and -3y, which bring the equation to x-z-z.
From here, combine the terms with the variable z. This would bring the equation down too x-2z, your final answer.
erin has 40,000 in a savings account that earns 15% interest per year. the interest is not compounded. how much will she have in 3 months?
Answer:
$41500
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 15%/100 = 0.15 per year,
putting time into years for simplicity,
3 months ÷ 12 months/year = 0.25 years,
then, solving our equation
I = 40000 × 0.15 × 0.25 = 1500
I = $ 1,500.00
The simple interest accumulated
on a principal of $ 40,000.00
at a rate of 15% per year
for 0.25 years (3 months) is $ 1,500.00.
Sanaa went into a t-shirt store and purchased 2 t-shirts for $30. The store is having a sale for 40% off. What is the amount of money she will save with the sale?
Answer:
$12
Step-by-step explanation:
$30 x .40 = $12
Kathy distributes jelly beans among her friends. Alia gets 42 fewer jelly beans than Kelly, who gets 33 jelly beans. How many jelly beans does Alia get?
A.
42 − 33
B.
33 + 42
C.
4 − 33
D.
33 − 42
E.
32 − 43
Help fast It's do today
Answer:
D. 33 - 42
Step-by-step explanation:
Kathy distributes jelly beans among her friends.
Number of jelly beans received by Kelly after distribution of Jellies by Kathy = 33
Also, Alia gets 42 fewer jelly beans than Kelly
Now, we need to find the number of jelly beans received by Alia
So, Number of jelly beans received by Alia = No. of jelly beans received by Kelly - 33
⇒ Number of jelly beans received by Alia = 42 - 33
Therefore, The correct answer is D. 33 - 42
Answer:
The answer is D. i took the test and got it right brainlist plssssssssssss
Step-by-step explanation:
There are 30 pieces of fruit in a bowl and 12 of them are oranges. What percentage of the pieces of fruit in the bowl are oranges?
Answer:
40% of the fruit in the bowl are oranges.
Step-by-step explanation:
12/30=0.4
Find the least common denominator 1/3 1/5
=
What is the value of the expression below when w=
3?
5w + 2
Answer:
17
Step-by-step explanation:
5w+2
Substitute w as 3
5(3)+2
Multiply
15+2
Add
17
I hope this helps!
what is the reciprocal of 5 1/4
Complete the table by entering the correct value in each blank. (Enter fractional answers like
as 1/5.)
Expression Value
A
B
C
D
Answer:
D
O
N
T
KNOW
Step-by-step explanation:
Y
O
U ARE
W
E
L
C
O
M
E