If [tex]k\in\mathbb{Z}[/tex] than [tex]k+1\in\mathbb{Z}[/tex] however any [tex]\mathbb{Z}[/tex] divided by 2 is in [tex]\mathbb{Q}[/tex].
But it is not so simple.
If [tex]k[/tex] is odd then [tex]k+1[/tex] is even but when even number is divided by 2, you get an odd number which is in [tex]\mathbb{Z}[/tex].
However if [tex]k[/tex] is even then [tex]k+1[/tex] is odd and when we divide that by 2, you get a number like for example [tex]\frac{5}{2}[/tex] which is not in [tex]\mathbb{Z}[/tex] but rather inside [tex]\mathbb{Q}[/tex]. There are fortunately no irrational numbers.
There is also a problem with zero, zero is neither odd nor even but still an integer. If your [tex]k[/tex] happens to be -1, [tex]k+1=0[/tex], and zero divided by 2 is still just 0 which is in [tex]\mathbb{Z}[/tex].
So to sum up,
If [tex]k[/tex] is odd and not -1, then [tex]\frac{k+1}{2}\in\mathbb{Z}[/tex].
Or to put it in math [tex]\forall k\in\mathrm{odd}-\{-1\}\cup\{0\}\implies\frac{k+1}{2}\in\mathbb{Z}[/tex].
If [tex]k[/tex] is even or -1, then [tex]\frac{k+1}{2}\in\mathbb{Q}[/tex].
Or to put it in math [tex]\forall k\in\mathrm{even}\cup \{-1\}\implies\frac{k+1}{2}\in\mathbb{Q}[/tex].
Notes:
[tex]\mathbb{Z}[/tex] is a set of integers.
[tex]\mathbb{Q}[/tex] is a set of rational numbers.
[tex]\mathbb{Z}\subset\mathbb{Q}[/tex] means integers are a subset of rational numbers, that is, every integer is a also a fraction, however not every fraction is an integer.
Hope this helps :)
Critical Thinking Point M is the midpoint of AB. The coordinates of point A are
(-8, 3) and the coordinates of Mare (–2, 1). What are the coordinates of point B?
Answer:-1,4
Step-by-step explanation:
6 tables or 8 chair cost Rs 2400.What will 24 tables and 12 chairs cost?
Step-by-step explanation:
cost of 1 table=2400/6=rs.400
or ,cost of 1 chair=2400/8=rs.300
now,
cost of 24 tables=24×400=9600
or,cost of 12 chairs=12×300=3600
or,
may be the question is,
6tables + 8 chairs= 2400
24 tables + 12 chairs=?
solution,
cost of 1 tables=rs.200
cost of 1 chair=rs.150
now,
cost of 24 tables=200×24=4800
cost of 12 chairs=150×12=1800
so, ans= 4800+1800=6600
Answer:
Rs.13200
Step-by-step explanation:
cost of 6 tables=Rs.2400
or,
cost of 8 chair=Rs.2400
cost of 1 table=2400/6
=Rs.400
cost of 1 chair=2400/8
=Rs.300
cost of 24 tables=24*400
=Rs.9600
cost of 12 chairs=12*300
=Rs.3600
total cost of 24 tables and 12 chairs=9600+3600
=Rs.13200
(20 points) please help
Answer: The antonym of multiply is divide.
Answer:
Divide
Step-by-step explanation:
Antonym simply means the opposite of the given word.
So the opposite of multiplication is division thus division is the answer.
HOPE THIS HELPED
what is the following sum in simplest form? /8+3/2+/32
Answer:
C
Step-by-step explanation:
Devaughn is 6 years younger than Sydney. The sum of their ages is 46 . What is Sydney's age?
52
if im wrong, sorry
if im right, yay
The maxwell family goes out for dinner and the price of the meal is $60 the sales tax on the meal is 7% and they also want to leave a 15% tip what is the total cost of the meal
Answer: $ 73.20
Step-by-step explanation:
60+(60*0.07)+(60*0.15)=73.2
Use the ÷10 pattern to fill in blanks 400 and 0.4
Answer:
400÷10=0.4
stay safe and healthy
If the statement if I'm hungry, then I am not happy is assumed to be true is it's inverse of I am not hungry then I must be happy also always true
Answer:
yes!
Step-by-step explanation:
"i am not happy when hungry" is the inverse of "i am not hungry, i am happy."
Answer:
No
Step-by-step explanation:
Find the HCF of the following by long divosiin method 102,68,136
Answer:
102=2*3*17
68=2*2*17
136=2*2*2*2*17
The common prime factors are 2 and 17
Highest common factor (HCF)=2*17=34
Hope it helps you.Factor 2x² + 13x + 20
Answer:
(2x+5)(x+4)
Step-by-step explanation:
9514 1404 393
Answer:
(x +4)(2x +5)
Step-by-step explanation:
To factor this, you look for factors of 2·20 = 40 that have a sum of 13.
The factor pairs of 40 are ...
40 = 1·40 = 2·20 = 4·10 = 5·8
The sums of these factor pairs are 41, 22, 14, 13. The last one is the one we want.
There are several ways to use this factor pair. One of the more straightforward methods is to rewrite the middle term as a sum using these numbers:
2x² +5x +8x +20
= x(2x +5) +4(2x +5) . . . . . factor pairs of terms
= (x +4)(2x +5) . . . . . . . . . factor out the common factor
BRAINIEST TO WHOEVER RIGHT
Answer:
(-6,6)
Step-by-step explanation:
−
2
5
y=
\,\,-11
−11
gbaijwghwugaggaufgwhhsuhwkhsiw
The product of 2 more than 5 times a number and 4 less than three times a number
Sorry I'm not sure if I'm right just my thinking...
set the number to be x so that (5x+2)(3x-4)??
Will give brainliest answer
Answer:
a
Step-by-step explanation:
plz gimme brainliest
How can you rewrite simple rational expressions in different forms using long division?
(50 POINTS)PLEASE!!!!!
Find the value of x 3(4x+3)
3(4x+3)=12x+9
i don't know what do you need,
if roots, let 12x+9=0
the root is x=-3/4
Which statement about the function is true?
The graph of the function f(x) = -(x + 3)(x - 1) is shown
below.
6
NA
O The function is positive for all real values of x where
x < -1.
The function is negative for all real values of x
where
x < -3 and where x > 1
The function is positive for all real values of x where
x>0
The function is negative for all real values of x
where
X<-3 or x>-11
+
6
4
2
4
6
x
-2
-2
4
-6-
-
Mark this and retum
Save and Exit
Next
Submit
9514 1404 393
Answer:
(b) The function is negative for all real values of x where x < -3 and where x > 1
Step-by-step explanation:
It is pretty easy to tell from the graph that the function is negative for x < -3 and for x > 1.
1. View The Truth Behind the Golden Ratio video (https://youtu.be/92ZiDsOf2z0)
for additional examples of
the Golden Ratio. Select your favorite example from the video (or your own
research) and explain why this specific example is so interesting to you.
(Possible keywords: the golden ratio + in nature, + in art, + in the human
body, + in geometry).
2. Now that you know more about the Golden Ratio, do you believe its
common presence shows evidence of a grand design within the universe or
is it simply a coincidence? Explain why you feel that way.
3. How does this topic reinforce or change your belief about the application of
math to your daily life?
According to the the video, the Golden Ratio is a figure in mathematics theorized by mathematicians as a value that indicates natures beauty symmetry
[tex]\mathbf{The \ value\ of \ the \ Golden \ ratio \ is \ \phi} = \mathbf{\dfrac{1 + \sqrt{5} }{2} }[/tex]
Good examples of the Golden Ratio in art and architecture is the Great Pyramid of Giza, constructed in 2570 B.C. and the temple of Parthenon for which construction began in 447 BC and the decoration completed in 432 BC
The reason the temple of Parthenon is so interesting is that the temple just like the pyramid were meant to last indefinitely, such that they can only be made to last so long by the deities, as such by building using the Golden Ratio found in nature including the spiral galaxies, is in recognition of nature's beauty which is aesthetically pleasing to the eyes, harmonious, and maybe preservative
2. The common presence of the Golden Ratio in the universe can be seen as both a grand design and a coincidence, however, due to the higher prevalence than random occurrence, it can be taken as a design that can be observed in nature
3. The topic helps reinforce the belief in the application of math to daily life, because it is a good portrayal of how math can contribute to all aspect of human life
Learn more about the Golden Ratio here:
https://brainly.com/question/20730582
https://brainly.com/question/22904993
https://brainly.com/question/15895546
Answer:
Step-by-step explanation:
for additional examples of the Golden Ratio. Select your favorite example from the video (or your own research) and explain
why this specific example is so interesting to you. (Possible keywords: the golden ratio + in nature, + in art, + in the human body, + in geometry).
Find the equation of the parabola that has a vertex at (2,0) and a y-intercept of (0,12).
Question 19 options:
A)
y = 3(x + 2)2
B)
y = (x – 2)2
C)
y = (x + 2)2
D)
y = 3(x – 2)2
Answer:
D
Step-by-step explanation:
standard form would be 3x^2-12x+12
vertex form y=3(x-2)^2
Answer:
y = 3(x + 2)2
Step-by-step explanation:
The solution to an inequality is represented by the number line
Is a measure of 24 inches "far away from a mean of 16 inches? As someone with knowledge of statistics, you answer it depends" and request the standard deviation of the underlying
data
(a) Suppose the data come from a sample whose standard deviation is 2 inches. How many standard deviations is 24 inches from 16 inches?
(b) Is 24 inches far away from a mean of 16 inches?
(c) Suppose the standard deviation of the underlying data is 5 inches. Is 24 inches far away from a mean of 16 inches?
(a) 24 inches is
standard deviation(s) away from 16 inches.
ne doimal olan
nondad)
Answer:
I really need points plsss
Step-by-step explanation:
a trapezoid is shown in the grid
Answer:
To prove that it is a trapezoid, remember that the definition of a trapezoid is a quadrilateral with exactly one pair of parallel sides. Therefore, to prove it is a trapezoid you must verify that one pair of sides is parallel. From algebra, remember that two lines are parallel if they have the same slope.
How do I answer this?
Answer:
Step-by-step explanation:
43 + 39 + <1 = 180 Three angles make up a triangle of 180 degrees.
82 + <1 = 180 Subtract 82 from both sides
<1 = 98
<2 = <1 They are vertically opposite
<2 = 98
4. If
A. 35
B.180
C.125
D.55
Answer:
C
Step-by-step explanation:
z=x as they are alternate angles and x=o as they are alternate exterior angles
If a set S has a total of 6 subsets that consist of 2 members each, then S consists of how many members
A set S has four members if there are six subsets of it, each with two members.
The combination formula, which is given by: can be used to determine the total amount of subsets with two members each.
[tex]^nC_k= \dfrac{n!}{(k!(n-k)!)}[/tex]
There are 6 subsets in this situation, each with 2 members.
So, [tex]^nC_2[/tex] = 6
Simplifying the equation:
n! / (2!(n-2)!) = 6
n(n-1) / (2 x 1) = 6
n(n-1) / 2 = 6
n(n-1) = 12
Expanding the equation:
[tex]n^2 - n = 12[/tex]
[tex]n^2 - n - 12 = 0[/tex]
Factoring the quadratic equation:
(n - 4)(n + 3) = 0
When all factors are set to zero and n is calculated:
n - 4 = 0 or n + 3 = 0
n = 4 or n = -3
Since n must be a positive integer.
So, n = 4 is the valid solution.
Thus, set S consists of 4 members.
Learn more about Combination here:
https://brainly.com/question/28720645
#SPJ12
Find the missing value.
Hint: Use the number line to find the missing value.
-4=
-9
-15
-10
-5
0
5
10
15
Stuck? Review related articles/videos or use a hint.
Manuela bought 11/12 yard of polka dot fabric and 7/9 yard of flowered fabric which fabric did she buy more of
Answer:
She bought more polka dot fabric
Step-by-step explanation:
you can cross multiply so 9x11=99 and 12x7=84. Since 99>84, 11/12>7/9
Which of the following relations represents a function?
{ (-2, 1), (0, 5), (1, -3), (-2, 0)}
{ (-3, 1), (1, 4), (-2, 1), (0, 3)}
{(-1, 3) (-2, 3) (-1, 5) (-2, 5)}
{ (4, 2), (4, 3), (4, 5), (4, 7)}
Answer:
Option A because functions only point to 1 output.
Referring to the figure, find the volume of the solid
shown. Round to the nearest whole number.
First find the area of the triangle using the formula 1/2 x base x height:
1/2 x 22 x 13 = 143 square cm
Now for volume multiply the area by the depth of the figure:
143 x 30 = 4,290 cubic cm
Answer:
780
Step-by-step explanation:
First use pythagorean theorem to find the triangle, then multiply by 30
how many numbers of four different digits can be formed from the integers 0,2,4,5,6.
Answer:
420 even numbers
Step-by-step explanation:
Answer
Total 4 digit even numbers = (Total even numbers) - (Total 3 digit even numbers)
Total even numbers: 4⋅6⋅5⋅4=480
Total 3-digit even numbers: 3⋅5⋅4⋅1=60
Total 4-digit even numbers: 480−60=420 ??
Step-by-step explanation: