Answers
Step-by-step explanation:
First we recall the relevant definitions and properties:
An even integer is an integer that is a multiple of 2, that is, an integer that can be written as 2k2k where kk is also an integer.
An abelian group is a set with an operation that is closed in that set, is associative, has an identity element, has inverses, and is commutative.
Addition is already associative and commutative over the set of all integers, and has an identity 00 and an inverse −n−n for each integer nn.
Oh, and multiplication of integers distributes over addition (this is important because we’re dealing with multiples of 2 but also with addition. The distributive property is how multiplication relates to addition).
This means we have to show a few things:
Addition is closed over the even integers. This holds due to the distributive property: if you have even integers 2k2k and 2m2m, then 2k+2m=2(k+m)2k+2m=2(k+m) is also an even integer. The odd integers fail this property: for example, 11 is odd but 1+1=21+1=2, which is not odd.
Addition is associative over the even integers. This holds because addition is already associative over the set of all integers: 2k+(2m+2j)=(2k+2m)+2j2k+(2m+2j)=(2k+2m)+2j. The odd integers do satisfy associativity, since they’re also a subset of the integers.
Addition has an identity element over the even integers. Since we already know that 00 is an identity for the set of all integers and 00 is even, this shows that we have an identity for the even integers: 2k+0=2k2k+0=2k. This doesn’t hold for the set of odd integers, because if nn and kk are odd integers and n+k=nn+k=n then k=0k=0, a contradiction since 00 is not odd.
Addition has inverses over the even integers. We already know that integers have inverses, and if 2k2k is an even integer then −k−k is the inverse of kk, so that 2k+2(−k)=2(k+(−k))=2(0)=02k+2(−k)=2(k+(−k))=2(0)=0. This means the even integer 2(−k)2(−k) is the inverse of 2k2k. The odd numbers do satisfy this property, since they’re also a subset of the integers.
Addition is commutative over the even integers. This holds because addition is already commutative over the set of all integers: 2k
Related Questions
4th grade work for my brother help him please
Answers
Answer:
6 x 2 = 12
Step-by-step explanation:
i might be wrong, i hope this helps!
...
Sebastian opened a bank account with
$125. He purchased groceries for $87.
Then he went to the movies and spent
$43. How much money does he have in
his bank account?
Answers
Answer:-5
Step-by-step explanation:
i could be wrong i used my calculator
(b) determine the ratio of the volume of a paraboloid (a parabola rotated about the y axis) to the volume of a cylinder with the same height and base radius: vparaboloid vcylinder with the same height and base radius . Vcone/Vcyl=_______
Answers
The volume of a paraboloid is therefore 1/3 of the volume of a cylinder with the same height and base radius.
The volume of a paraboloid can be expressed as:
The formula for a paraboloid's volume is Vparaboloid = (π/3) x (r²) x h, where r is the base's radius and h is the object's height.
A cylinder's volume can be expressed as follows with the same height and base radius:
Vcylinder = π x (r²) x h.
A paraboloid's volume to a cylinder's volume with the same height and base radius is calculated as follows:
Vparaboloid / Vcylinder = (π/3) x (r²) x h / (π x (r²) x h) = (π/3) / π = 1/3.
The volume of a paraboloid is therefore 1/3 of the volume of a cylinder with the same height and base radius.
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Suppose that $7500 is placed in an account that pays 6% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
(b) Find the amount in the account at the end of 2 years
Answers
a) The compounded amount in the account at the end of 1 year is $7,950.
b) The compounded amount in the account at the end of 2 years is $8,427.
What is compound interest?Compound interest is the interest added to the principal amount after each period in order to compute the period's interest.
By compounding, we mean that accumulated interest is added to the principal to compute the subsequent interest.
Compound interest is unlike simple interest, which does not compound interest.
The compound interest formula is:
A = P(1 + r/n)^nt
A = Final amount
P = initial principal balance
r = interest rate
n = number of times interest is applied per time period
t = number of time periods elapsed
Since this investment is compounding annually, we can find the final amount at the end of each year using the common formula as follows:
A = P(1 + r)ⁿ
Principal = $7,500
Compound interest rate = 6%
Compounding period = Annually
Amount at the end of Year 1 = $7,950 ($7,500 x 1.06¹)
Amount at the end of Year 2 = $8,427 ($7,500 x 1.06²)
Thus, the compounded amount at the end of year 1 is $7,950 and $8,427 at the end of year 2.
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what is (x+5)……………
……….:…………
Answers
Answer:
x+5
Step-by-step explanation:
there are no like terms
Quadrilateral ABCD is graphed on a coordinate plane with the vertices A(-9,6), 3(-4,-6), C(-3,2), and D(-8,-2)
A. Quadrilateral ABCD is translated to the left 2 units and up 6 units. Write the translation in terms of x and y using ordered pair notation.
B. Determine the coordinates of the vertices of the image. Be sure to name each of the vertices of the image with the correct notation.
Answers
Answer:
Answer is part A.
Step-by-step explanation:
Select all of the following statements that are true.
- + 0 = -
- - = -
- = +
- + = -
- + = +
- + = 0
Answers
Answer:
-+=- is true
Step-by-step explanation:
because - and+ are equal to -
but - and- are eqial to +
After running a mile a day over a period of two weeks, the average amount of weight loss is 2.5 pounds. A dietitian, who publishes health articles in a newspaper, states their new diet program helps with additional weight loss when combining their special diet with running a mile a day over a period of two weeks. Interested in studying the dietitian's article further, you ask friends who have tried the dietitian's new program and you determine their weight loss to be 3.0 pounds in a two week period, on average. As you set up a hypothesis test to determine if the dietitian's article is correct, what is the dietitian's claim?
a. Adults should run every day to lose weight.
b. The average amount of weight loss is less than 2.52.5 pounds.
c. The average amount of weight loss is greater than 3.03.0 pounds.
d. The average amount of weight loss is greater than 2.52.5 pounds.
Answers
Answer:
d. The average amount of weight loss is greater than 2.5 pounds.
Step-by-step explanation:
After running a mile a day over a period of two weeks, the average amount of weight loss is 2.5 pounds.
At the null hypothesis, we test if this mean is of 2.5, that is:
\(H_0: \mu = 2.5\)
A dietitian, who publishes health articles in a newspaper, states their new diet program helps with additional weight loss.
With the additional weight loss, the dietitian claims that the mean is more than the value presented at the null hypothesis, that is, more than 2.5, and thus, the correct answer is:
\(H_1: \mu > 2.5\)
And thus, the correct option is given by option d.
Find the area of the trapezoid 6.5 cm 9 cm 18.5 cm
Answers
Answer:
if the 'a base' is 6.5 & the height is 9 & 'b base' is 18.5, the answer is a = 112.5 cm^3
Two othice desks that are
5 1/4 feet long are to be placed together on a wall that is 10 3/4 feet long Will they fit on the wall?
Select the correct choice below and if necessary, fill in the answer box to complete your choice.
A Yes, it no more than a total of foot is needed for spacing between desks.
(Type an integer or a simplified fraction)
OB. No, they do not all fit along the wall
Answers
Answer:
Yes, they fit along the wall. The space between desks is 1/4 of a foot.
Step-by-step explanation:
(2)*(5 1/4)
(2) * (21/4 = 42/4
10 3/4 = 43/4
43/4 - 42/4 = 1/4
This is due today, please help me out and show me how you did it!!
Answers
The area of the rectangular figure with two semicircles on the opposite side is 36.56 sq cm.
What are the circumference and diameter of a circle?The circumference of a circle is the distance around the circle which is 2πr.
The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.
Given, A rectangle with two semicircles on two opposite sides.
The length of the rectangle is 6cm and the width of the rectangle is 4cm.
The two given semicircles have a diameter of 4cm seems obvious.
∴ The area of the total figure is an area of the rectangle added to the area of 2 semicircles which makes up to a circle with a radius 2 cm.
∴ (4×6) + π(2)² sq cm.
= 24 + 4π sq cm.
= 24 + 12.56 sq cm.
= 36.56 sq cm.
The area which is not taken up in the rectangle and two circle questions are
(area of the rectangle - 2 times the area of a circle).
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Determine the domain of functions
What is the domain of h?
Answers
Answer:
What is the domain of h?
See attached!
Step-by-step explanation:
Situation 1. ROCKET RIDE.
The Rocket Coaster has 10 cars, some that
hold 4 people and some that hold 8 people.
There is room for 56 people altogether.
How many 4-passenger cars are there?
How many 8-passenger cars are there?
Let x= number of 4-passenger cars
Let y = number of 8-passenger cars
equation #1:
equation #2:
Solution:
Answers
Place the indicated product in the proper location on the grid. (y - x)(y - x)
Answers
Answer:
\(y^2-2xy+x^2\)
Step-by-step explanation:
\((y-x)(y-x)\\=(y)(y)+y(-x)+(-x)(y)+(-x)(-x)\\=y^2-xy-xy+x^2\\=y^2-2xy+x^2\)
7. A floor is covered by 800 tiles measuring 10 squared cm. How many square tiles of side 8 cm would be needed to cover the same floor?
Answers
Answer:
1000 tiles
Step-by-step explanation:
Determine total floor space
800 x 10 = 8000 squared cm total floor space.
Divide floor space by size of tile
8000 / 8 = 1000 tiles now required to cover the floor.
Yesterday, between noon and midnight, the temperature decreased by 29.2°F. If the temperature was -0.7°F at midnight, what was it at noon?
Answers
The temperature at noon, based on the equation, is 28.5°F.
What is an equation?An equation is a mathematical expression that shows that two values are equal.
Equations are represented by the equation mark (=).
Data and Calculations:Let the temperature drop, d = 29.2°F
Let the temperature at midnight after the drop, f = -0.7°F
Let the starting temperature = x
Final temp (at midnight) = starting temp (at noon) - drop in temp
Starting temp (at noon) - drop in temp = final temp (at midnight)
Therefore, x - d = f
x - 29.2 = -0.7
Adding 29.2 on both sides of the equation:
x - 29.2 + 29.2 = -0.7 + 29.2
x = 28.5°F
Thus, the temperature at noon, based on the equation, is 28.5°F.
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In trapezoid ABCD, line AC is a diagonal and angle ABC is congruent to angle ACD. Find AC if the lengths of the bases line BC and line AD are 12m and 27m, respectively
Answers
Since ΔABC and ΔACD are similar triangles, therefore the length of AC is 18 m.
What are Similar Triangles?Similar triangles are triangles with corresponding sides that have the same ratio.
Thus:
AD is parallel to BC (bases of a trapezoid are parallel)
Therefore:
∠ACB = ∠CAD (alternate interior angles)
This implies that, ΔABC ~ ΔACD by AA similarity theorem.
Thus:
AC/DA = CB/AC
Substitute
AC² = 12 × 27
AC = √324
AC = 18 m
Therefore, since ΔABC and ΔACD are similar triangles, therefore the length of AC is 18 m.
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through: (5,-1) and (-3,-5)
Answers
Answer:
If you are trying to find slope the answer is 1/2
Step-by-step explanation:
I'm sorry if im wrong but thats if you're trying to find slope if you're not my bad.
(
5
,
−
1
)
(
5
,
-
1
)
with vertex
(
−
3
,
5
)
(
-
3
,
5
)
using the vertex form
y
=
a
(
x
−
h
)
2
+
k
y
=
a
(
x
-
h
)
2
+
k
.
Standard Form:
y
=
−
3
32
x
2
−
9
16
x
+
133
32
y
=
-
3
32
x
2
-
9
16
x
+
133
32
Vertex Form:
y
=
−
3
32
(
x
+
3
)
2
+
5
y
=
-
3
32
(
x
+
3
)
2
+
5
Is 3.275 rational number
Answers
Answer:
yes it is rational number examples
3.275/5
3.275/10
hope.it helps
plz mark a brainliest
the two rectangular plots of land have properties side lengths what is the perimeter of the smaller rectangle A. 28 B. 32 C. 36 D. 76
Answers
Answer:
I think that it would be b 32
For a tiger, there are approximately 4.2 lbs, of muscle for every 7.4 lbs. of body weight. How much of the weight is muscle on a 563 lb. tiger?
Answers
Answer:
320
Step-by-step explanation:
563/7.4=76
76*4.2=320
Given circle V with diameter TU and radius VR. RS is tangent to V at R. If RU =15 and VT=13, solve for RT . Round your answer to the nearest tenth if necessary. If the answer cannot be determined click cannot be determined
Answers
In this problem, we have that
the triangle URT is a right triangle
because
m by inscribed angle
arc UT=180 degrees ----> because the diameter TU divide the circle into two equal parts
so
mmIn the right triangle URT
we know
RU=15 -----> given
VT=13----> given ----> is the radius
TU=13(2)=26 ----> the diameter is two times the radius
solve for RT
Applying the Pythagorean theorem
TU^2=RT^2+RU^2
26^2=RT^2+15^2
RT^2=26^2-15^2
RT^2=451
RT=21.2 unitsLet m and n be non-zero rational numbers, and x and y be irrational numbers,
Consider the operations below and select all answers that will make each
statement true.
Answers
Answer:
(a) Irrational
(b) Irrational
Step-by-step explanation:
Given (Missing Operations):
\(m * x\)
\(n * y\)
The options are:
Rational Irrational
(a) \(m * x\)
m is a rational number while x is an irrational number.
And we know that:
\(rational * irrational = irrational\)
Hence:
\(m * x = Irrational\)
(b) \(n * y\)
n is a rational number while y is an irrational number.
And we know that:
\(rational * irrational = irrational\)
Hence:
\(n * y = Irrational\)
PLEASEE HELP IM BEGGING YOU
Answers
Answer: god it's hard, but i will try
Right to explain how this digit 6 changes value in number 666, 666, 666
Answers
Answer:
devil!!!!!!!!!!!!!!!!
Step-by-step explanation:
Write the expression without using exponents.
(−9x)4
Answers
The expression (-9x)^4 can be represented as -6561x^3 without using exponents.
To express the expression (-9x)^4 without using exponents, we can expand it by multiplying the base (-9x) four times using the multiplication property.
(-9x)^4 = (-9x) * (-9x) * (-9x) * (-9x)
To simplify this expression, we can multiply the terms together, taking care to apply the rules of multiplication:
(-9x) * (-9x) = (-9 * -9) * (x * x) = 81 * x^2 = 81x^2
So, by substituting this result back into the original expression, we get:
(-9x)^4 = 81x^2 * (-9x) = -6561 x^3
Therefore, the expression (-9x)^4 can be represented as -6561x^3 without using exponents.
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Find the degree of each polynomial and indicate whether the
polynomial is a monomial, binomial, trinomial, or none of these.
Answers
Answer:
1. Degree = 1, monomial
2. Degree = 2, monomial
3. degree = 2, trinomial
4. Degree = 2, binomial
5. Degree = 2, binomial
Step-by-step explanation:
Aşağıda verilen balik kılçığı diyagramını tamamlayalım.
Answers
Answer:
Let's complete the fishbone diagram given below
thats what they said
Step-by-step explanation:
does the table represent a proportional relationship?
x 3 6 9 12
y 7 13 19 25
Answers
Answer:
x does y does not
Step-by-step explanation:
The top tree broke and fell over.the remaining tree teunk is 3 feet tall.the tip of the tree rests on the ground 14 feet from the base of the trunk.what is the lenght of the broken part of the tree to the nearest tenth of a foot
Answers
Answer:
14.3 feet.
14.3 feet
Step-by-step explanation:
The problem forms a right triangle in which:
The Vertical Leg of the Right Triangle = 3 feet
The Horizontal Leg of the Right Triangle =14 feet
We are to determine the length of the broken part of the tree. This is the Hypotenuse of the Right Triangle,
Using Pythagoras Theorem
\(Hypotenuse^2=Opposite^2+Adjacent^2\\Hypotenuse^2=14^2+3^2\\Hypotenuse^2=205\\Hypotenuse=\sqrt{205}\\Hypotenuse=14.32\\ \approx 14.3 feet $(to the nearest tenth of a foot).\\Therefore, the lenght of the broken part of the tree to the nearest tenth of a foot is 14.3 feet.\)
