The statement "the integers and the natural numbers have the same cardinality" is false.
To understand why, let's first define what we mean by "cardinality." Cardinality refers to the size or quantity of a set, often represented by a number called its cardinal number.
Natural numbers are a set of counting numbers starting from 1, and they go on infinitely. So, the cardinality of natural numbers is infinite.
On the other hand, integers include both positive and negative numbers, including 0. The integers also go on infinitely in both directions. Thus, the cardinality of the integers is also infinite, but it is a different type of infinity than the natural numbers.
We can prove that the cardinality of the integers is greater than the cardinality of the natural numbers using a technique called Cantor's diagonal argument. This argument shows that we can always construct a new integer that is not included in the set of natural numbers, and therefore, the two sets have different cardinalities.
In summary, while both the integers and natural numbers are infinite sets, they do not have the same cardinality. The cardinality of the integers is greater than the cardinality of the natural numbers.
Learn more about Cantor's diagonal argument here:
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Lana and Andrew gather data by surveying their classmates. Lana asked them about the longest time they had ever run. Andrew asked them about their favorite color.
How could Lana and Andrew represent their data?
Would they represent them in the same way?
Why or why not?
Answer:
No because Andrew aske them being different to Lana an far over.
Find the slope- intercept from for the line Perpendicular to y-1/5x+5 passing through the point (3,-4)
find the equation of a line passing through the point(-3,0) and (2,-3)
Answer (assuming the question allows it to be written in slope-intercept form):
[tex]y = -\frac{3}{5} x-\frac{9}{5}[/tex]
Step-by-step explanation:
1) First, find the slope of the equation. Use the slope formula [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex], substitute the given points' x and y values, and simplify:
[tex]m = \frac{(-3)-(0)}{(2)-(-3)} \\m =\frac{-3-0}{2+3}\\m = -\frac{3}{5}[/tex]
Thus, the slope is [tex]-\frac{3}{5}[/tex].
2) Now, use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] and substitute real values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex].
Since [tex]m[/tex] represents the slope, substitute [tex]-\frac{3}{5}[/tex] in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line crosses, use the x and y values of any one of the given points to substitute into the formula. (Either one is fine. I chose (2,-3).) Then, isolate y to put it into slope-intercept form and find the answer:
[tex]y-(-3) = -\frac{3}{5} (x-(2))\\y + 3 = -\frac{3}{5} x + \frac{6}{5} \\y = -\frac{3}{5} x - \frac{9}{5}[/tex]
Answer:
y = -3
Step-by-step explanation:
Teddy is writing a proof about the figure shown on the coordinate plane below. He wants to show that quadrilateral WXYZ is a parallelogram.
Which statement proves that WXYZ is a parallelogram?
A. Show that segments WX and YZ have equal slopes.
B. Show that segments WX and YZ have equal lengths.
C. Show that the midpoints of segments WY and XZ are the same point.
D. Show that segments WX and XY have slopes that are opposite reciprocals of each other.
The statements are -
A. Show that segments WX and YZ have equal slopes.
B. Show that segments WX and YZ have equal lengths.
C. Show that the midpoints of segments WY and XZ are the same point.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Teddy is writing a proof about the figure shown on the coordinate plane below. He wants to show that quadrilateral WXYZ is a parallelogram.
The statements that prove WXYZ as a parallelogram are -
A. Show that segments WX and YZ have equal slopes.
B. Show that segments WX and YZ have equal lengths.
C. Show that the midpoints of segments WY and XZ are the same point.
Therefore, the statements are -
A. Show that segments WX and YZ have equal slopes.
B. Show that segments WX and YZ have equal lengths.
C. Show that the midpoints of segments WY and XZ are the same point.
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Martina bought 4 CDs that were each the same price. Including sales tax, she paid a total of $70.40 . Each CD had a tax of $ 1.10 . What was the price of each CD before tax?
[tex]1.10 \times 4 = 4.40[/tex]
[tex]70.40 - 4.40 = 66[/tex]
[tex]66 \div 4 = 16.5[/tex]
Each CD was $16.50 before tax
Proof
[tex]total \: cost = 16.5(4) + 1.10(4)[/tex]
[tex]total \: cost = 66 + 4.40[/tex]
[tex]total \: cost = 70.40[/tex]
Can someone please help me with this ASAP
Answer:
24.84
Step-by-step explanation:
Hopefully this helps! let me know if it doesn't
I NEED HELP ASAP!!!!!!!!
Answer: b
Step-by-step explanation:
Which statement describes the congruent triangles
Answer:
it is the first answer
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
you have to line the angles up so the congruent sides lay on each other.
Bir sayının 2 bölü 5 'sinin 3 eksiği, bu sayının çeyreğine eşittir.
Buna göre bu sayı kaçtır?
Answer:
si cardo bahyanbayansusb
What is the value of x?
Answer:
x=16
Step-by-step explanation:
according to the geometric mean for altitude
8 squared = 4x
64=4x
x=16
if my answer helped please mark as brainliest.
Step-by-step explanation:
X = 16 .
16 is the correct answer of this question .
plz mark my answer as brainlist if you find it useful.
What is the square root of 7.29 ?
Answer:
2.7
Step-by-step explanation:
Answer:
2.7
Step-by-step explanation:
determine if JK and LM parallel, perpendicular, or neither .
Answer:
3 - Perpendicular.
4 - Parallel.
Step-by-step explanation:
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
[tex]JK = \frac{1-(-7)}{-4-(-10)} = \frac{8}{6} = \frac{4}{3}[/tex]
[tex]LM = \frac{-2-2}{-6-(-3)} = \frac{-4}{3}[/tex]
Perpendicular, because two lines are considered perpendicular if their slopes are opposite reciprocals.
[tex]JK = \frac{-2-(-2)}{3-11} = \frac{0}{-8} = 0[/tex]
[tex]LM = \frac{-2-(-7)}{1-1} = \frac{5}{0} = 0[/tex]
Help me out?!?! tysmmmm
Answer:
1 is isoscele
2 is scalene
3 is equalateral
4 is scalene
BCDE is a rhombus. Find the missing measures.
BC = 28 and BD = 32
CD =
FD =
EF =
EC =
Answer: CD=28
FD= 16
Step-by-step explanation:
I need help answering this question:
-9 ÷ +3
Answer:
-3
Step-by-step explanation:
-9 divided by +3 can be written as -9 divided by 3, because when you have a positive number, you don't have to write a plus sign in front of it. Next, we can just do 9/3 and then add the negative sign to the result to get our answer. 9 divided by 3 is equal to 3, and when you add the negative sign, you get -3.
Solve for x in the following figure and choose the appropriate result.
Answer:
2x is equal to 45
e is equal to x and 2
Step-by-step explanation:
give answer please.............................fast
Answer:
120
Step-by-step explanation:
Find out the answer for 78^ - 42^.
78^ - 42^ = 4320
36 x = 4320
1 x = 4320 ÷ 36 = 120
Una pirámide de base cuadrada se corta con un plano paralelo a la base por la mitad de la altura de la pirámide, obteniendo una pirámide más pequeña y un tronco de pirámide. ¿Cuántas veces es más grande el volumen del tronco con respecto al volumen de la pirámide pequeña?
Answer: what does this say?
Step-by-step explanation:
Solve for x to the nearest tenth.
please help i’m failing
Answer:
x≈ 8.3
Step-by-step explanation:
ok first you have to find the hypotenuse of the smaller triangle
a²+b²=c²
2²+4²=c²
4+16=20
√20≈ 4.5
4.5²+7²=c²
20.25+49≈ 69.25
√69.25≈ 8.3
Answer:
x = [tex]\sqrt{69}[/tex]
Step-by-step explanation:
Pythagorean theorem: A^2 + B^2 = C^2
first, find the length of the line cutting through the shape:
let's call this line L.
plug the numbers into the theorem.
4^2 + 2^2 = L^2
16 + 4 = L^2
20 = L^2
next, plug 7 and L into the theorem again to find x
L^2 + 7^2 = x^2
20 + 49 = x^2
69 = x ^2
x = [tex]\sqrt{69}[/tex]
Write an equivalent expression by factoring for 6a + 15
HURRYYYY FASTTT
There are 16 fluid Ounces of juice in 2 bottles of your favorite juice. How many fluid Ounces are there in 10 bottles?
80 fluid Ounces
72 fluid Ounces
160 fluid Ounces
96 fluid Ounces
Answer:
80 fluid ounces
Step-by-step explanation:
16*5=80
Answer:
80 fluid Ounces
Step-by-step explanation:
I majored in Mathematics
pls help with this math question !
thx !
Answer:
h^4
Step-by-step explanation:
Please let me know if you want me to write an explanation for my answer :)
HCF of 10,100,1000.
Answer:
So the greatest common factor 10 and 1000 is 10.
plz mark me as brainliest
find the slope of the line y = 4/3x - 2/3
Answer:
4/3
Step-by-step explanation:
Line equations are of the format:
y = m*x + b
((m is slope; b is y-intercept))
So this line has a slope of 4/3 and a y-intercept of -2/3.
hi anyone tell me the answer
Answer:
x= 136 degree ( being vertically opposite angle)
Answer:
x = 136
Step-by-step explanation:
x and 136 are vertical angles and congruent, then
x = 136
Describe the graph of x > 2 and x < 5. ( i think its a number line for compund inequalitites)
It would have hollow circles on 2 and 5 and you would connect them
Hello! It would help a lot if I had assistance with this question:
Answer:
numerator
Step-by-step explanation:
Answer:
Numerator
Step-by-step explanation:
Numerator is at the top while on the bottom is the denominator.
If $30,000 then is equivalent to $900,000;
then, what is $1 then equivalent to in today's
dollars?
Answer:
$30
Step-by-step explanation:
You need to figure out how the money changes between then and now. To do that, take now and divide it by then; 900,000/30,000 = 30, the amount now is 30 times that of then. To figure out what any amount then is worth now, multiply it by 30 and you'll get you answer. (In this case: 1*30 = 30)
Think of a favorite dance move, such as the Running Man. Determine whether there is periodicity associated with this dance move.
Answer:
I don't remember if Alan Walker can dance :/
Step-by-step explanation:
Dream did it better than me, you should see his answer.
Answer:
I don't know
Step-by-step explanation:
x^2y+y^2-30x+221=0 find the radius
Answer:
2
Step-by-step explanation
Let's complete the square. We get:
(x^2-30x)+y^2+221=0
(x^2-30x+225)+y^2+221-225=0
(x-15)^2+y^2-4=0
(x-15)^2+y^2=4
By analyzing this, we see that the radius is just :[tex]\sqrt{4}[/tex]=2