Show that if U is open in X, and A is closed in X, then UA is open in X, and A\U is closed in X.
Answers
The intersection of N(x) and N'(x), denoted by N(x)∩N'(x), is an open neighborhood of x. Since N(x)∩N'(x) ⊆ N(x) ⊆ U and N(x)∩N'(x) ⊆ N'(x) ⊆ X\U, we can conclude that N(x)∩N'(x) ⊆ UA.
Since N(x)∩A is a non-empty set contained in A\U, we have shown that every point in (A\U)' has a neighborhood contained in A\U. Therefore, (A\U)' is open in X, which implies that A\U is closed in X.
To show that if U is open in X and A is closed in X, then UA is open in X and A\U is closed in X, we need to prove two statements:
UA is open in X.A\U is closed in X.Let's prove these statements one by one:
To show that UA is open in X, we need to prove that for every point x in UA, there exists an open neighborhood around x that is completely contained within UA.Let x be an arbitrary point in UA. Since x is in UA, it must belong to U as well as A. Since U is open in X, there exists an open neighborhood N(x) of x that is completely contained within U. Now, since x is in A, it is also in X\U (complement of U in X). As A is closed in X, X\U is closed in X, which means its complement, U, is open in X. Therefore, there exists an open neighborhood N'(x) of x that is completely contained within X\U.
Now, consider the intersection of N(x) and N'(x), denoted by N(x)∩N'(x). This intersection is an open neighborhood of x. Since N(x)∩N'(x) ⊆ N(x) ⊆ U and N(x)∩N'(x) ⊆ N'(x) ⊆ X\U, we can conclude that N(x)∩N'(x) ⊆ UA.
Since N(x)∩N'(x) is an open neighborhood of x completely contained within UA, we have shown that UA is open in X.
To show that A\U is closed in X, we need to prove that its complement, (A\U)', is open in X.Let x be an arbitrary point in (A\U)'. Since x is not in A\U, it means that x must either be in A or in U (or both). If x is in A, then x is not in A\U. Therefore, x is in U.
Since x is in U and U is open in X, there exists an open neighborhood N(x) of x that is completely contained within U. Now, consider the intersection of N(x) and A. Since x is in A, N(x)∩A is a non-empty set. Let y be any point in N(x)∩A.
We know that N(x)∩A ⊆ U∩A ⊆ A\U, because if y was in U, it would contradict the assumption that y is in A. Therefore, N(x)∩A is a subset of A\U.
Since N(x)∩A is a non-empty set contained in A\U, we have shown that every point in (A\U)' has a neighborhood contained in A\U. Therefore, (A\U)' is open in X, which implies that A\U is closed in X.
Hence, we have shown that if U is open in X and A is closed in X, then UA is open in X, and A\U is closed in X.
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Related Questions
Q1 - Multiplying one equation
Work these simultaneous equations out
on paper and write down your answers.
p
4p + 2q = 28
13p + 69 = 88
9 =
3s + 4t = 31
S =o
88 + 8t = 72
t =
a =
4a + 3b = 45
16a + 4b = 124
b =
5m + 6n = 61
m =
15m + 4n = 99
n =
Answers
Answer:
p = 4
q = 6
s = 5
t = 4
a = 6
b = 7
m = 5
n = 6
Need 6 and 7 done please and thank you
Answers
Answer:
black
black
Step-by-step explanation:
A tree branch is observed to bend as the fruit growing on it increase in size. By estimating the mass of the developing fruit and plotting the data over time, a student finds that the height h in metres of the branch end above the ground is closely approximated by the function h=2-0.2×1.60.2m where m is the estimated mass, in kilograms, of fruit on the branch.
(a) Sketch the graph of h against m.
Answers
The graph of h against m is plotted in form of a curve.
Given:
A tree branch is observed to bend as the fruit growing on it increases in size.
The height h in metres of the branch end above the ground is closely approximated by the function \(h=2-0.2*1.60^{0.2m}\) where m is the estimated mass, in kilograms, of fruit on the branch.
We have to sketch the graph of h against m.
The x-axis represents the mass in kg while the y-axis represents the height of the branch above the ground in metres.
Hence a curved graph is obtained by plotting the function.
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Which angle has sides DB and DC? Select all that apply.
Answers
No, rectangle DABC is not the result of a dilation of rectangle HEFG with a center of dilation at the origin.
What is dilation?Dilation is a geometrical transformation that changes the size of a shape or figure. It is one of the four basic transformations of geometry alongside translation, rotation, and reflection. Dilation involves resizing a shape by a scale factor and keeping its overall shape intact. The scale factor is the ratio of the size of the image to the size of the original figure.
Dilation involves a scaling of a shape, where each point on the shape is moved away from or closer to the center of dilation, proportional to its distance from the center. In this case, the angles of rectangle DABC are different from the angles of rectangle HEFG, so it is not the result of a dilation. The angles of rectangle HEFG are ∠2, ∠33, ∠EDC, whereas the angles of rectangle DABC are ∠ADB, ∠BDC, and ∠CDB.
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Which point is located at (2, 3)?
A
B
C
D
Answers
Answer:
a
Step-by-step explanation:
Is 4.15 larger, smaller or equal to 415 tenths.
Answers
4.15 is smaller than 415 tenths.
We have,
The concept used to compare 4.15 and 415 tenths is the conversion between decimal and fraction forms.
By recognizing that 415 tenths can be expressed as the decimal 41.5, we can directly compare it to 4.15.
Comparing the two decimals, we can determine that 4.15 is smaller than 41.5.
To compare 4.15 and 415 tenths, we can convert 415 tenths to its decimal form.
415 tenths is equal to 415/10 = 41.5.
Now we can see that 4.15 is smaller than 41.5.
Therefore,
4.15 is smaller than 415 tenths.
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help please the picture is here when you click here
Answers
a. By the distributive property, 3x + 7x = (3+7)x = 10x, so this is always true.
b. By the distributive property, 5x-10x = (5-10)x = -5x, which is not necessarily equal to 5x (if you let x equal any value other than zero, you will see that this does not hold).
c. 4(1 + 2x) - 3x is equal to (4 + 8x) - 3x (by the distributive property), which is equal to 4 + 5x. This is equal to 5x + 4 since addition is commutative.
d. 5 - 3(2 - 4x) = 5 - (6 - 12x) = -1 + 12x, so this does hold for all values of x.
An item is marked down to 9 over 10 of its original value and then is further marked down to 7 over 10 of that.
What portion of the value of the item remains?
Answers
Answer:
To find the portion of the value of the item that remains, we need to multiply the two discount percentages:
9/10 * 7/10 = 63/100
This means that 63% of the original value of the item remains after the two discounts have been applied. Alternatively, we can say that the item is being sold for 63% of its original value.
In the diagram, the measures of 22, 23 and 26 are 40°. The measure of 21
is 140°. Are lines cand d parallel?
Answers
Answer:
c. Yes because ∠2 and ∠6 are congruent.
Step-by-step explanation:
From the picture attached,
m(∠2) = m(∠3) = m(∠6) = 40°
m(∠1) = 140°
Since (∠2 ≅ ∠6) (corresponding angles)
Therefore, by the converse theorem of corresponding angles lines c and d are parallel.
Option c is the answer.
Write 99 as a product of primes.
Use index notation when giving your answer.
Do
Answers
Answer:
99 = 3² * 11
Step-by-step explanation:
99 = 3 * 3 * 11
99 = 3² * 11
99 as a product of primes is, 99 = 3² * 11
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
To Write 99 as a product of primes,
we get,
99 = 3 * 3 * 11
99 = 3² * 11
Hence, 99 as a product of primes is, 99 = 3² * 11
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A map of your town has a scale of 1 inch to 0.25 mile. There are two roads that are 5 inches apart on the map.
Answers
can someone help me
Answers
Answer:
KN = LN
Step-by-step explanation:
JN and MN are equal to each other so the other lines KN and LN are also equal to each other
What’s the slope of the line ? Help
Answers
Answer:
3
Step-by-step explanation:
A pair of jeans at a local retail store has a cost of $32.00. If the sales tax is 5.3%, what is the total amount paid for the jeans?
Answers
The total amount that a customer will pay for the jeans is $33.696.
How to calculate the value?From the information given, pair of jeans at a local retail store has a cost of $32.00. If the sales tax is 5.3%,
The value of the sales tax will be:
= Sales percentage × Amount
= 5.3% × $32
= $1.696
The total amount paid will be:
= Cost + Tax
= $32 + $1.696
= $33.696
The amount is $33.696.
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Solve the system using the substitution technique:(−6, −3.6)(0.6, 0.8)(6, 4.4)(−0.6, 0)
Answers
Given
The system of equations,
\(\begin{gathered} -2x+3y=1.2\text{ \_\_\_\_\_}(1) \\ -3x-6y=1.8\text{ \_\_\_\_\_}(2) \end{gathered}\)To find the solution using substitution technique.
Explanation:
It is given that,
\(\begin{gathered} -2x+3y=1.2\text{ \_\_\_\_\_}(1) \\ -3x-6y=1.8\text{ \_\_\_\_\_}(2) \end{gathered}\)That implies,
\(\begin{gathered} (1)\Rightarrow-2x+3y=1.2 \\ \Rightarrow3y=1.2+2x \end{gathered}\)And,
\(\begin{gathered} (2)\Rightarrow-3x-6y=1.8 \\ \Rightarrow-3x-2(3y)=1.8 \end{gathered}\)Substitute 3y=1.2+2x in the above equation.
That implies,
\(\begin{gathered} -3x-2(1.2+2x)=1.8 \\ -3x-2.4-4x=1.8 \\ -7x=1.8+2.4 \\ -7x=4.2 \\ x=\frac{4.2}{-7} \\ x=-0.6 \end{gathered}\)And, substitute x=-0.6 in (1).
That implies,
\(\begin{gathered} (1)\Rightarrow-2(-0.6)+3y=1.2 \\ \Rightarrow1.2+3y=1.2 \\ \Rightarrow3y=1.2-1.2 \\ \Rightarrow3y=0 \\ \Rightarrow y=0 \end{gathered}\)Hence, the solution is (-0.6,0).
The value of almost everything you own assets such as a car computer oar house depreciates goes down overtime when an asset value decreases by a fixed amount each year the depreciation is called straight line depreciation suppose your truck has an initial value of $12,400 depreciates $820 per year write an equation illustrates this function if you plan to keep your truck for seven years and determine the value of the truck at the end of this. Period let v represent the dependent variable in T represent the independent variable
Answers
Answer:
A
Step-by-step explanation:
Trust
The correct equation is,
⇒ y = 12,400 - 820r
And, Amount for 7 years is, $6,660
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
Here, your truck has an initial value of $12,400 depreciates $820 per year.
Let number of years = r
Hence, We get the correct equation is,.
⇒ y = 12,400 - 820r
So, For r = 7 years;
⇒ y = 12400 - 820 x 7
⇒ y = 12400 - 5740
⇒ y = $6,660
Thus, The correct equation is,
⇒ y = 12,400 - 820r
And, Amount for 7 years is, $6,660
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FIND THE HEIGHT OF THE TRAPEZOID A =80 CM2 7CM 9cm what is H
Answers
B = 9
b = 7
A = 80
a = ?
Substitution
\(\begin{gathered} \text{ 80 = }\frac{(9\text{ + 7)}\cdot a}{2} \\ \text{ 80 = }\frac{16a}{2} \\ \text{ 80 = 8a} \\ \text{a = }\frac{80}{8} \\ a\text{ = 10 cm} \end{gathered}\)The height of the trapezoid is 10 cm
the line contains the point (3, 5) and is parallel to the line containing (-4, 0) and (-1, -2)
Answers
To find the equation of the line passing through (3, 5) and parallel to the line containing (-4, 0) and (-1, -2), we need to use the slope-intercept form of a line:
y = mx + b
where m is the slope of the line and b is the y-intercept.
First, we need to find the slope of the line containing (-4, 0) and (-1, -2):
m = (y2 - y1) / (x2 - x1)
m = (-2 - 0) / (-1 - (-4))
m = -2 / 3
Since the line we're looking for is parallel to this line, it will have the same slope.
Now we can use the point-slope form of a line to find the equation of the line passing through (3, 5) with slope -2/3:
y - y1 = m(x - x1)
y - 5 = (-2/3)(x - 3)
Simplifying and rearranging, we get:
y = (-2/3)x + 7
So the equation of the line containing the point (3, 5) and parallel to the line containing (-4, 0) and (-1, -2) is y = (-2/3)x + 7.
I Believe This is the answer
Answer: The line through (-4, -6, 1) and (-2, 0, -3), is parallel to the line through (10, 18, 4) and (5, 3, 14).
Step-by-step explanation:
Have a Great Day
I need to know this right now :(
Answers
Answer:
40000
400
Step-by-step explanation:
40000 because 4000 * 10 = 40000
400 because 1 / 10 of 4000 = 400
Answer:
ok so 1/2 is your answer 1/4 divide = 1//2 !
Step-by-step explanation:
Can someone please help me ASAP? It’s due today!! Read the question. I will give brainliest if it’s all correct
Answers
The order from least to greatest is:
Neither the letters nor the numbers can be repeated.The letters can repeat, but the numbers cannot repeat.The number can repeat, but the letters cannot repeat.The letter "O" cannot be used, but there are no restrictions on repeating the other letters or numbers.What are the possible license situation?The number of possible license plates for each situation:
Neither the letters nor the numbers can be repeated: 26 x 25 x 9 x 8 x 7 = 327,600
The letters can repeat, but the numbers cannot repeat: 26 x 26 x 9 x 8 x 7 = 405,504
The number can repeat, but the letters cannot repeat: 26 x 25 x 9³ = 5,153,250
The letter "O" cannot be used, but there are no restrictions on repeating the other letters or numbers: 25 x 25 x 9 x 9 x 9 = 15,187,500
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Image transcribed:
Use the arrows to move each item into the correct order. Click the "up" arrow to move the item up, or click the "down" arrow to move the item down. Once all the items are in the correct order, submit your response.
A bike license consists of 2 letters, using any of the 26 letters in the alphabet, followed by 3 digits from 1 to 9. Calculate the number of possible license plates in each situation, then order them from least to greatest.
↑ ↓The letters can repeat, but the numbers cannot repeat.
↑ ↓The numbers can repeat, but the letters cannot repeat.
↑ ↓Neither the letters nor the numbers can be repeated.
↑ ↓The letter "o" cannot be used, but there are no restrictions on repeating the other letters or numbers.
Harish has dug out a cuboidal well with dimensions 2m x 1.5m x 10m in his field. Find
the cost of cementing the walls of the well at the rate Rs 52 per m2
Answers
The cost of cementing the walls of the cuboidal well is Rs 3640.
How is the surface area of a cuboid determined?A three-dimensional solid form with six rectangular sides is called a cuboid. It also goes by the name rectangular prism. The shapes and sizes of the faces on either side of each other are identical.
A cuboid's surface area is the sum of all of its faces. We can determine the area of each face and put them together to determine the cuboid's surface area.
Given that, the cost of cementing the walls of the well at the rate Rs 52 per square m.
Thus,
Area of one rectangular face = length x height = 2 x 10 = 20m².
Area of the other rectangular face = width x height = 1.5 x 10 = 15m².
Total surface area of the walls = 2(20) + 2(15) = 70m².
Now, the cost of cementing the walls of the well at the rate of Rs 52 per m² is:
Cost = 70m x Rs 52 = Rs 3640
Hence, the cost of cementing the walls of the well is Rs 3640.
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Which equation represents a line that passes through (4, 1/3) and has a slope of 3/4
Answers
Answer:
y-y1=m(x-x1)
y-1/3=3/4(x-4)
y=3/4x-8/3
-x/5-8=12
Show work
And check
Answers
Answer:
\(\huge\boxed{\sf x = -100}\)
Step-by-step explanation:
Given equation:\(\displaystyle -\frac{x}{5} -8=12\\\\Add \ 8 \ to \ both \ sides\\\\-\frac{x}{5} = 12+ 8\\\\-\frac{x}{5} = 20\\\\Multiply \ both\ sides \ by \ 5\\\\-x = 20 \times 5\\\\-x = 100\\\\Multiply\ both \ sides \ by\ -1\\\\x = -100\\\\\rule[225]{225}{2}\)
f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6
where c is constant
Answers
The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.
Given a function:
f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6
where c is a constant.
The solution to the question is shown below.
Step 1: We have given a function:
f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6
We have to find the number of words we have to write to express this function in words.
Step 2: Solution
f(t) = et5+4t + ln(t²+3c)⁷ +te-1+5e⁶
Where,
et5+4t = exponential function
ln(t²+3c)⁷ = natural logarithmic function
te-1 = linear function
e⁶ = exponential function
Therefore, f(t) can be expressed in words as:
The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.
Step 3: Conclusion
Hence, the function f(t) can be expressed in words with:The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.
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the correlation coefficient may assume any value between : -1, and 1. 0 and 1. 0 and 8. -1, and 0. -infinity and infinity.
Answers
The correlation coefficient may assume any value between -1 and 1. Correct answer option A.
This means that the coefficient might be negative, zero, or positive, with -1 being a perfect negative correlation, 0 representing no connection, and 1 representing a perfect positive correlation.
The correlation coefficient is a numerical measure of two variables' linear connection. It is a measure of the strength of the link between two variables. A correlation coefficient of 1 indicates that there is a perfect positive connection, a coefficient of -1 indicates that there is a perfect negative correlation, and a coefficient of 0 shows that there is no correlation between the two variables.
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Can you find the slope and type the correct code? Please remember to type in ALL CAPS with no spaces.
Answers
Yes, I can find the slope of a line and type the correct code. The SLOPE function will return the slope of the linear regression line that best fits the data.
The slope of a line is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. The formula for finding the slope of a line is (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line.
The slope is a measure of how steep the line is. It can be positive, negative, zero, or undefined. The code for finding the slope of a line in ALL CAPS with no spaces is SLOPE.
To use this function in Excel, you need to provide the range of x-values and the range of y-values.
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the average number of shoppers at a particular grocery store in one day is 505, and the standard deviation is 115. the number of shoppers is normally distributed. for a random day, what is the probability that there are between 250 and 450 shoppers at the grocery store?
Answers
For a random day with the standard deviation, the probability that there are less than 300 shoppers on a random day, is 0.00585.
Probability is a measure of the likelihood that an event will occur.
Many events cannot be predicted with absolute certainty. We can only predict the probability that an event will occur, i.e. how likely it is to occur, using it.The average total number of shoppers on a grocery store in 1 day is 505; the standard deviation is 115.
Let, X be the random variable denoting the number of shoppers on a random day.
Then, X follows normal with mean 505 and standard deviation of 115.
Then, we can say that,
Z=(X-505)/115 follows standard normal with mean 0 and standard deviation of 1.
We have to find
P (250 <X< 450)
= P {(250-505)/155} < Z < {(450-505)/155}
= P (-1.64 <Z< -0.03)
Where, Z is the standard normal variate.
ρ = -1.64 <ρ< -0.03
Where, ρ is the distribution function of the standard normal variate.
From the standard normal table, this becomes
=0.00585
For a random day, the probability that there are less than 300 shoppers on a random day, is 0.00585.
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for each number on the numberline, write an abosolute value equation in the form |x-c|=d, where c and d are some numbers to satisfy the given solution set.
-8 and -4
Answers
The absolute value equation in the form |x-c|=d is |x + 6| = 2
How to write an abosolute value equation in the form |x-c|=dFrom the question, we have the following parameters that can be used in our computation:
Solution = -8 and -4
This means that
x = -8 and -4
The midpoint of the above solutions are
Mid = 1/2(-8 - 4)
Mid = -6
So, we have
|x + 6| = d
Using the solution -8, we have
|-8 + 6| = d
This gives
d = 2
So, we have
|x + 6| = 2
Hence, the absolute value equation in the form |x-c|=d is |x + 6| = 2
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Find the digit 5 in each of these numbers.
15.2
3.5
The 5 in 3.5 is 1 place to the right of the 5 in 15.2.
Which sentence correctly compares the values?
Answers
each number has its place on the number line so true
Step-by-step explanation:
and 5 is one place to the left in 15.2
Antoine has a total of 34 coins. He has 20 quarters and his remaining coins are dimes. What is the ratio of dimes to total coins?
Answers
Answer:
14:34
Step-by-step explanation:
34-20 gets your dime count which is 14 and then to total coins the answer equals 14:34