Which of the following collections of subsets of the plane, R2
, are partitions?
(a) {{(x; y) | x + y = c}| c  R}
(b) The set of all circles in R2
(c) The set of all circles in R2
centered at the origin together with the set {(0; 0)}
(d) {{(x; y)} | (x; y)  R

Answers

Answer 1
Answer: Choice A

[tex]\{(x,y) | \ \ x+y = c, \ c \in \mathbb{R}\}[/tex]

Explanation:

The notation for choice A basically says "we have a line of the form x+y = c where c is a real number". Then points on the line in the form (x,y) will form a particular partition. A partition is where we break a set up into non-overlapping subsets and there are no gaps. Think of it like breaking up a house into multiple rooms. Each room is a subset of the house. There are no gaps or overlaps (ignore the regions in the walls).

Take note that if a point is on a line like x+y = 5, then it cannot be on any other line of the form x+y = c, where c is not equal to 5. Something like (x,y) = (2,3) is on x+y = 5 and not on any other line. If c is allowed to be any real number, then x+y = c will be able to partition the real numbers.

Put another way, we can pick any real number we want (aka the number c) and break it down into a sum of x and y values. Such a sum cannot yield any other c value. So going back to the house/room analogy, any particular (x,y) ordered pair will belong to one and only one room.

Let's look at an example of a non-answer. Choice B is not correct because it is perfectly possible to have circles intersect. Intersecting circles share at least one common point. Those common points are what break the idea of partitions. This idea also means choice C is false as well.

Choice D can be ruled out because the notation should be (x,y) in R2 and not simply R.

Answer 2

The collections of subsets of the plane, R2 is (a) {{x,y) : x + y = c} : c ∈ R}

What is a subset ?

If X is a subset of Y then all the elements of A also contained in B.

According to the given statement we have o determine which of the following collections of subsets of the plane R2.

R2 defines a two dimension plane.

x+y = c where c is a real number.

Then points on the line in the form (x,y) will form a particular partition. A partition is where we break a set up into non-overlapping subsets and there are no gaps. Think of it like breaking up a house into multiple rooms. Each room is a subset of the house.

Take note that if a point is on a line like x+y = 7, then it cannot be on any other line of the form x+y = c, where c is not equal to 7. Something like (x,y) = (3,4) is on x+y = 7 and not on any other line.

B. Is not correct because it is perfectly possible to have circles intersect. Intersecting circles share at least one common point. Those common points are what break the idea of partitions.

C. is false as well

D. Is ruled out because the notation should be (x,y) in R2 and not simply R.

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Related Questions

log base 4 (x+3)²- log base 4 y² = 0​

Answers

Answer:

x = - |y| - 3

Step-by-step explanation:

Write a two-step equation and solve.

Four more than six times a number is 22

Five less than eleven times a number is 50

Seven less than nine times a number is -16

Answers

Step-by-step explanation:

1) let number=a

six times a number=6a

Condition:

6a+4=22

2) eleven times a number=11a

Condition:

11a-5=50

3) 9 times a number=9a

Condition:

9a-7=-16

Note:if you need to ask any question please let me know.

7. What's the perimeter of a rectangle with length 12 m and width 5 m?
A. 60 m
B. 49 m
C. 34 m
D. 17 m

Answers

Answer:

Option(c) 34m

Step-by-step explanation:

Perimeter of a rectangle = 2(length + breadth)

length = 12m

breadth/width = 5m

Perimeter = 2(12 + 5)

                = 2(17)

                = 34m

Answer:

34

you just add, 12+5+12+5 to get 34

Determine the sum by suitable re arrangement .
a) 6254 + 1297 + 446 + 103 Ans:
b) 1983 + 647 + 217 + 353 2.​

Answers

Answer:

a.8100

b.3200

Step-by-step explanation:

hope you're okay

y=3x+2y is it a function how do you do it

Answers

9514 1404 393

Answer:

  yes

Step-by-step explanation:

Solve for y. You can do this by subtracting 3x+y from both sides of the equation.

  y -(3x+y) = 3x +2y -(3x +y)

  -3x = y

Or ...

  y = -3x

Each value of x maps to a single value of y, so this relation is a function.

_____

This equation is a first-degree polynomial in x. Any polynomial relation y=p(x) is a function, so this is a function.

Select the correct answer.
Based on these segment lengths, which group of segments cannot form a triangle?
OA 12,7,8
OB. 8, 7, 13
OC. 1,2,3
OD. 80,140, 70
Reset
Next
2021 EdimentumAll rights

Answers

Answer:

C

Step-by-step explanation:

If you add up the length of two sides, the sum must be greater than the third side of the triangle.

If you add 1 and 2, it equals 3

But that means it will be equal to the length of the third side, 3

It will be impossible to make a triangle with those lengths of sides no matter how the sides or angles are set.

It's sort of difficult to explain this without any visual

You can look up "triangle inequality" to find out more about this

A triangle has a perimeter of 75 inches. Find the length of three sides
if one side is 15 inches larger than the smallest side, and the third
side is twice the smallest

Answers

9514 1404 393

Answer:

  15 in, 30 in, 30 in

Step-by-step explanation:

Let x represent the length of the smallest side. Then the other two sides are (x+15) and (2x). The perimeter is the sum of the side lengths:

  x +(x +15) +2x = 75

  4x = 60

  x = 15 . . . . . . . . . . . shortest side

  (x+15) = 30 . . . . . . second side

  (2x) = 30 . . . . . . . third side

The shortest side is 15 inches, the second side is 30 inches, and the third side is 30 inches.

3/6, 1/12, 3/6, 3/60 determine the lcd by division of prime number

Answers

Answer:

LCD = 60

BRAINLIEST, PLEASE!

Step-by-step explanation:

All of the denominator numbers are multiples of 60, and since 60 is also equal to the largest denominator number, it's the LCD.

The area of a circle is 78.5 cm^2. What is the diameter of the circle?
-5 cm
-10 cm
-12.5 cm
-39.25 cm

Answers

Answer:

10cm

Step-by-step explanation:

78,5=pi.r^2

Answer5:

Step-by-step explanation:

Need answers in 2 minutes ASAP

Answers

Step-by-step explanation:

f(10)=10

f(-2)=-2

f(a)=a

f(a+b)=a+b

g(10)=5×10-12=3

g(-2)=5×(-2)-12=-10-12=-22

g(a)=5×a-12=5a-12

g(a+b)=5×(a+b)-12=5a+5b-12

h(10)=(10)^2 +4(10)-7=100+40-7=133

h(-2)=(-2)^2 +4(-2)-7=4-8-7=-11

h(a)=a^2 +4a -7

h(a+b)=(a+b)^2 +4a+4b-7=a^2+2ab+b^2+4b-7

Solve the below:
4x+3y=7 3x-2y=9

Answers

4x+3y=7
3x-2y=9

12x+9y=21
12x-8y=36
^^Multiply top equation by 3 and multiply bottom equation by 4

12x+9y=36
- 12x-8y=36

17y=-15
^^Then subtract those two new equations

17y/17= -15/17

Y= -0.88
^^Next divide both sides by 17

4x+3* -0.88=7

4x + (-2.64) =7
-(-2.64) -(-2.64)

4x = 9.64

4x/4=9.64/4
X=2.41

^^then choose on equation and put your new y in the y spot and solve.


X=2.41

Y=-0.88

Your point/coordinate is (2.41,-.88)

Which graph could represent a car that begins by increasing its speed, then travels at a constant speed, and then decreases its speed, as time increases?

A graph with time (minutes) on the horizontal axis and speed (miles per minute) on the vertical axis. Both axes are unnumbered. The speed begins at 0, goes up at first, is steady for a while, and then goes down over time.
A graph with time (minutes) on the horizontal axis and speed (miles per minute) on the vertical axis. Both axes are unnumbered. The speed begins in the middle of the vertical axis, goes down at first, is steady for a while, and then goes up over time.
A graph with time (minutes) on the horizontal axis and speed (miles per minute) on the vertical axis. Both axes are unnumbered. The speed begins at 0, goes up at first, goes down for a while, and then is steady over time.

Answers

9514 1404 393

Answer:

  A

Step-by-step explanation:

If you read your own question, you find that it answers itself.

The problem statement tells you that speed ...

  ... increasing its speed, constant speed, then decreases

And it tells you the graphs show ...

  (a) begins at 0, goes up, is steady for a while, and then goes down

  (b) begins in the middle, goes down, is steady, and then goes up

  (c) begins at 0, goes up, goes down, and then is steady

___

The first graph has the increasing, steady, decreasing pattern you're looking for.

After writing a $400 check to pay a bill, a student had a balance of $550 in his account. How much did he have in the account before he wrote the check?

a) Let x= his balance before writing the check. Write the equation you would use to solve this problem.

Answers

Answer:

x=950

Step-by-step explanation:

550+400=x

The sum of twice a number and three

Answers

Answer:

i dont get what youre asking

Step-by-step explanation:

Answer:

2n + 3

Step-by-step explanation:

n = number

Sum of twice a number (2n) and (3)

-> 2n + 3

QUESTION 1 11 How does the term quartile relate to how data values are grouped when using a five- number summory?​

Answers

Data from the Bureau of Labor Statistics has been put into order by placing data in the lower and upper quartiles. If data are placed in order, then the lower quartile is central to the lower half of the data and the upper quartile becomes central to its upper half.

Find the midpoint of the segment with the given endpoints. (-7,-4) and (3,7)?

Answers

9514 1404 393

Answer:

  (-2, 1.5)

Step-by-step explanation:

The coordinates of the midpoint are the average of the end point coordinates:

  ((-7, -4) +(3, 7))/2 = (-7+3, -4+7)/2 = (-4, 3)/2 = (-2, 1.5)

The coordinates of the midpoint are (-2, 1.5).

Anyone’s knows how do this and the answer?

Answers

Answer:

12 -16. 19

4. 8. 22

3. -9. -4

Step-by-step explanation:

13-1 = 12

-10-6= -16

12 - -7 = 12+7=19

6-2 = 4

Keep subtracting

19. When the members of a high school club are
arranged in rows of 2, 3, or 4, there is one
person always left over. But when the club
members are arranged in rows of 5, no one is
left over. What is the least number of people
who could be in the club?
À 15 people
C 45 people
B 25 people D 85 people

Answers

9514 1404 393

Answer:

 B.  25 people

Step-by-step explanation:

The remainders tell you the number will be 1 more than some multiple of the least common multiple (LCM) of 2, 3, and 4. The LCM is 3·4 = 12, so we want some multiple (n) of that such that 12n+1 is a multiple of 5. We know this is the case for n=2.

The least number of people who could be in the club is 2·12+1 = 25.

derivative : y=[(1+x^2)arctgx-x]/2

Answers

Answer:

s,-8*2-`±_'682-¥´owhsi

Problem 2
Find the area of each shaded region. Show or explain your reasoning.
A
2 cm
B
2 cm
2cm
6 cm
5 cm
3 cm
6 cm
8 cm
C С
D
15 cm
8 cm
8 cm
15 cm
9 cm
6 cm
10 cm

Answers

Step-by-step explanation:

A

this is the combination of a 4×6 rectangle and a 2×2 square. nothing is excluded.

so, the area is

(6-2)×6 + 2×2 = 4×6 + 4 = 24 + 4 = 28 cm²

B

this is the area of the large 8×5 rectangle minus the area of the small 2×3 rectangle.

so the area is

8×5 - 3×2 = 40 - 6 = 34 cm²

C

Basically the same thing as for B. large rectangle minus smaller rectangle.

so, the area is

15×10 - 9×6 = 150 - 54 = 96 cm²

D

the area of a triangle is

baseline × height / 2

or baseline here is 2×8, and the height is 5

so we get the area

2×8 × 5 / 2 = 8×5 = 40 cm²

Solve for x
ax+bx=10

Answers

Answer:

[tex]ax + bx = 10 \\ \\ x(a + b) = 10 \\ \\ x = \frac{10}{a + b} [/tex]

I hope I helped you^_^

find the value of a and b in (a,2)=(2,b)​

Answers

Answer:

a=2 and b=2...............

3cm and 7cm
please help me find the area and the perimeter of the above figures using the formular ​

Answers

Its must be a rectangle

Length=3cmBreadth=7cm

Perimeter:-

[tex]\\ \sf\longmapsto 2(L+B)[/tex]

[tex]\\ \sf\longmapsto 2(3+7)[/tex]

[tex]\\ \sf\longmapsto 2(10)[/tex]

[tex]\\ \sf\longmapsto 20cm[/tex]

Area:-

[tex]\\ \sf\longmapsto Length\times Breadth[/tex]

[tex]\\ \sf\longmapsto 3(7)[/tex]

[tex]\\ \sf\longmapsto 21cm^2[/tex]

Answer:

Length=3cm

breadth=7cm

Area(A)=?

we know that,

Area of rectangle (A)=l*b

=3cm*7cm

= 21cm^2

Now,

Perimeter (P)= 2(l+b)

=2(3cm+7cm)

=2*10cm

=20cm Ans.

4 adults consumed food costing $60 for 3days. For the same food cost ,what would be the cost of food consumed by 7 adults for 5days?

Answers

Answer:

$175

Step-by-step explanation:

$60÷3÷4 =5

$5 is the cost of one adult's food for one day.

$5×7×5

=$175

$175 is the cost of food consumed by 7 adults for 5 days.

[tex]\lim_{n \to \0}(x/(tan⁡(x))^(cot⁡(x)^2 )[/tex]

Answers

It looks like the limit you want to compute is

[tex]\displaystyle L = \lim_{x\to0}\left(\frac x{\tan(x)}\right)^{\cot^2(x)}[/tex]

Rewrite the limand with an exponential and logarithm:

[tex]\left(\dfrac{x}{\tan(x)}\right)^{\cot^2(x)} = \exp\left(\cot^2(x) \ln\left(\dfrac{x}{\tan(x)}\right)\right) = \exp\left(\dfrac{\ln\left(\dfrac{x}{\tan(x)}\right)}{\tan^2(x)}\right)[/tex]

Now, since the exponential function is continuous at 0, we can write

[tex]\displaystyle L = \lim_{x\to0} \exp\left(\dfrac{\ln\left(\dfrac{x}{\tan(x)}\right)}{\tan^2(x)}\right) = \exp\left(\lim_{x\to0}\dfrac{\ln\left(\dfrac{x}{\tan(x)}\right)}{\tan^2(x)}\right)[/tex]

Let M denote the remaining limit.

We have [tex]\dfrac x{\tan(x)}\to1[/tex] as [tex]x\to0[/tex], so [tex]\ln\left(\dfrac x{\tan(x)}\right)\to0[/tex] and [tex]\tan^2(x)\to0[/tex]. Apply L'Hopital's rule:

[tex]\displaystyle M = \lim_{x\to0}\dfrac{\ln\left(\dfrac{x}{\tan(x)}\right)}{\tan^2(x)} \\\\ M = \lim_{x\to0}\dfrac{\dfrac{\tan(x)-x\sec^2(x)}{\tan^2(x)}\times\dfrac{\tan(x)}{x}}{2\tan(x)\sec^2(x)}[/tex]

Simplify and rewrite this in terms of sin and cos :

[tex]\displaystyle M = \lim_{x\to0} \dfrac{\dfrac{\tan(x)-x\sec^2(x)}{\tan^2(x)}\times\dfrac{\tan(x)}{x}}{2\tan(x)\sec^2(x)} \\\\ M= \lim_{x\to0}\dfrac{\sin(x)\cos^3(x) - x\cos^2(x)}{2x\sin^2(x)}[/tex]

As [tex]x\to0[/tex], we get another 0/0 indeterminate form. Apply L'Hopital's rule again:

[tex]\displaystyle M = \lim_{x\to0} \frac{\sin(x)\cos^3(x) - x\cos^2(x)}{2x\sin^2(x)} \\\\ M = \lim_{x\to0} \frac{\cos^4(x) - 3\sin^2(x)\cos^2(x) - \cos^2(x) + 2x\cos(x)\sin(x)}{2\sin^2(x)+4x\sin(x)\cos(x)}[/tex]

Recall the double angle identity for sin:

sin(2x) = 2 sin(x) cos(x)

Also, in the numerator we have

cos⁴(x) - cos²(x) = cos²(x) (cos²(x) - 1) = - cos²(x) sin²(x) = -1/4 sin²(2x)

So we can simplify M as

[tex]\displaystyle M = \lim_{x\to0} \frac{x\sin(2x) - \sin^2(2x)}{2\sin^2(x)+2x\sin(2x)}[/tex]

This again yields 0/0. Apply L'Hopital's rule again:

[tex]\displaystyle M = \lim_{x\to0} \frac{\sin(2x)+2x\cos(2x)-4\sin(2x)\cos(2x)}{2\sin(2x)+4x\cos(2x)+4\sin(x)\cos(x)} \\\\ M = \lim_{x\to0} \frac{\sin(2x) + 2x\cos(2x) - 2\sin(4x)}{4\sin(2x)+4x\cos(2x)}[/tex]

Once again, this gives 0/0. Apply L'Hopital's rule one last time:

[tex]\displaystyle M = \lim_{x\to0}\frac{2\cos(2x)+2\cos(2x)-4x\sin(2x)-8\cos(4x)}{8\cos(2x)+4\cos(2x)-8x\sin(2x)} \\\\ M = \lim_{x\to0} \frac{4\cos(2x)-4x\sin(2x)-8\cos(4x)}{12\cos(2x)-8x\sin(2x)}[/tex]

Now as [tex]x\to0[/tex], the terms containing x and sin(nx) all go to 0, and we're left with

[tex]M = \dfrac{4-8}{12} = -\dfrac13[/tex]

Then the original limit is

[tex]L = \exp(M) = e^{-1/3} = \boxed{\dfrac1{\sqrt[3]{e}}}[/tex]

express 3x-x^2 as m-(x-n)^2. Ill give brainliest to correct answer!
(Also please see the picture since you might mistake x having a square as a 2x)

Answers

This is simply done by Method of Completing the Square.

3x - x²

Add and subtract half the coefficient of x and square it.

( This is done so there'd be no alterations to the quadractic Expression)

So To start

We'd like x² to be positive...(So factor out a negative).

( - 3x )

Now In this case

You see there's a Negative Outside the the bracket

Instead of adding and Subtracting squared values of half the coefficient of X... We'd Add Twice and do not subtract.

Reason: If you add outside the bracket and subtract the other inside the bracket... This will be wrong because there's a negative patiently waiting outside the bracket to Interact with the negative you subtracted to make it Positive.

See what I mean.

Let's say you added 2² and subtracted 2² in this problem

( - 3x - 2²)

If you decide to open the bracket

You'll have

+ 3x + 2²

NOW THIS IS WRONG BECAUSE WE ALTERED THIS EXPRESSION. WHERE'D 2² + 2² COME FROM?

THIS IS WHY YOU'LL ADD THE SQUARED COEFFICIENT OF X TWICE IN CASES LIKE THESE.

SO GOING BACK TO THE ORIGINAL QUESTION.

(x² - 3x )

Adding the half the coefficient of x twice and squaring them...

Coefficient of x = 3

Half of 3 = 3/2

Squaring it gives (3/2)²

NOW PROCEEDING

(3/2)² [ - 3x + (3/2)²]

If you open this bracket... (3/2)² will cancel out with (3/2)²

Meaning that we haven't altered the expression in any way

Moving On...

Applying basic factorizing principle

9/4 ( x - 3/2)².

Answer = 9/4 ( x - 3/2)² Which is in the Form m ( x - n )²

Therefore m = 9/4 and n = 3/2.

Hope This Helps

Name the two input device​

Answers

Answer:

keyboard and mouse are two examples of input device

Answer:

keyboard and mouse

Step-by-step explanation:

If you like my answer than please mark me brainliest

On solving equation 3*1/5b+5=50, the value of b will be?

Answers

Answer:

Step-by-step explanation:

14 1⁄16

divide write your answer in simplest form 2/3 divided by 1/4

Answers

Answer:

8/3 or 2.6667

Step-by-step explanation:

when you divide fractions you use a technique called KCF

K = keep

C = change

F = flip

You write the equation [tex]\frac{2}{3}[/tex] ÷ [tex]\frac{1}{4}[/tex]

you keep [tex]\frac{2}{3}[/tex]

you change the symbol, so from ÷ you change it to x

and flip the last fraction, so you would have  [tex]\frac{4}{1}[/tex]

then you solve it

[tex]\frac{2}{3}[/tex] x  [tex]\frac{4}{1}[/tex] = [tex]\frac{8}{3}[/tex]

The result of 2/3 divided by 1/4 in simplest form is 8/3 .

Division: It is one of the four basic mathematical operation, the other three being addition, subtraction, multiplication.

Given, division of [tex]\frac{2}{3}[/tex] by [tex]\frac{1}{4}[/tex].

Division of fractional terms:

[tex]=\dfrac{\frac{a}{b}}{\frac{c}{d}}\\= (a)\times(d)/(b)\times(c)[/tex]

Apply, division process of fractional terms.

[tex]=\dfrac{\frac{2}{4}}{\frac{1}{3}}\\ = (2)\times(4)/(1)\times(3)[/tex]

[tex]= \frac{8}{3}[/tex]

Know more about division,

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The Earth scientist most likely to study volcanoes is a (n)

A. Meteorologist

B. Geologist

C. Oceanographer

D. Astronomer

Answers

The answer is B Geologist

Answer:

geologist

Step-by-step explanation:

they work with the earths surface and natural land that changes

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Write a letter to your friend describing how you saved a child who was in danger Multiply the numbers. Round the answers to the nearest cent.21. $4.50 X 30.2522. $8.30 X 3.2523. $14.50 X 32.5 Order 0.5, -1/7, -0.2, and 1/3 from least to greatest. C=(3x-5)^2-36x^2tm x Evaluate814????? HELP A hummingbird can hover like a helicopter (PLEASE HELP) Substitution and Evaluation, Complete the students work by dragging the numbers to the empty spaces How does thelocation of theUnited States affectits landforms?A. Many of the landforms are the same.B. The landforms of the north and the south are thesame.C. The United States has many different landforms.D. The landforms of the south and west are the same. Write anequation that passes through the origin with a rate of change equal to 1 Is the product of a rational number and an irrational number always irrational? WORD FORMATION:If you are (sense), you might hurt someone's feeling How do Curves A and B compare to each other with respect to f and f ?The answer cannot be determined. f: Curve B, f : Curve A f: Curve A, f : Curve B Neither Curve A nor Curve B are derivatives of each other. How do bacteria evolve? Do you think animal testing for cosmetics and household products should be banned? In PQR, sinQ=25, sinR=13, and q=6. Find the side length r.Can someone please help *TIMED LOTS OF POINTS*Read the excerpt from the General Prolgue to the Canterbury Tales. To any kind of man; he was indeed The very pattern of a noble knight. But as for his appearance and outfit, He had good horses, yet was far from smart. Which is the correct translation of the excerpt into Middle English? In listes thryes, and ay slayn his foo. This ilke worthy knight had been also Somtyme with the lord of Palatye, Ageyn another hethen in Turkye: And evermore he hadde a sovereyn prys. And though that he were worthy, he was wys, And of his port as meke as is a mayde. He never yet no vileinye ne sayde In al his lyf, un-to no maner wight. He was a verray parfit gentil knight. But for to tellen yow of his array, His hors were gode, but he was nat gay. Of fustian he wered a gipoun Al bismotered with his habergeoun; For he was late y-come from his viage, And wente for to doon his pilgrimage. halogens can react with metals by accepting a/an____ from a metal atom and forming an ionic compound What are all the steps in a descriptive investigation? The author uses many types of evidence in the passage. Which of the following isan example of statistics?A. In the United States, the Rio Grande and the Colorado River are running dry."B. One obvious solution to this problem is to move the water where it is needed."C. But today, more than 1.1 billion people do not have access to safe drinking water."D. "Recently, researchers created a map of the world's water use and water resources. The control in an experimentGroup of answer choicesminimizes experimental inaccuracy.reduces the experimental errors.allows for comparisons to the experimental group.is an additional replicate for statistical purposes.