Prove Statement 5.38: Let T be the relation on Z defined by (m,n) ∈T iff m−n is divisible by 3 . Prove T is an equivalence relation.
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If n is devisible by 3 then n^2 is devisible by 3 it easy.
n=3k so n^2=9k so 9 is devisible by 3.
In the other way, if n^2 is devisible by 3we have n^2=3k wher k is integer number which has to be devisible by 3. If k is not devisible by 3, then n=/sqrt3*r , r^2=k. So n is not integer, contradiction.
This proof show us that iff doesnt work.
If n is devisile by 4 then n^2 is also devisible by 4. But if we have that n^2 is devisibke by 4 then n hasn’t be devisible by 4. Example: n^2=36 is dev by 4 but n=6 is not dev by4.
Its allow because /sqrt 4 is 2.
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Related Questions
Jessica plans to watch 3 movies each month. Write an equation to represent the total number of movies n that she will watch in m months.
Answers
Number of movies = n and if Months = m
Then 3 per month = 3m
i.e. n = 3m
Hope this helps!
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Find the height of the tower using the information given in the illustration.
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using SOH CAH TOA
Tan 85.144 =h/130
h=tan 85.144*130
h=1530.19 fr
In KLM,Q is the intersection of the three medians. If QN = 18, find MN
Answers
MN=32 i believe is the correct answer
Answer:
MN=54
Step-by-step explanation:
Q is the centroid center of the the triangle which means QM = QN×2
Sense we know QN = 18, then QM= 18×2 which equals 36. To find MN we add these 2 lengths together and we will get 18+36=54.
MN=54
wanza sold a bag of potatoes for sh.420 and made a profit.if she sold it at sh.320 ,she could have made a loss .Given that the profit is thrice the loss ,how much did she pay for the bag of potatoes
Answers
Answer:
sh.345
Step-by-step explanation:
The difference between the price selling with profit and price selling at a loss is 420-320 = 100
Profit is thrice the loss says we can take the difference in prices and divide it into 4 parts, x and 3x, representing the loss and thrice the loss, or profit margin.
x + 3x = 100
4x = 100
x = 25
loss would be 25,
profit would be 75
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sold at a profit: 420 -75 = sh.345
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Does this exercise seem similar to what you're doing in class?
Sanjay has £356.54 in his bank account. He spends £595.99 on a new mountain bike. What is his new bank balance?
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your answer would be -239.45.
356.54
-595.99
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-239.45
For the question of total area of the cuboid is 200cm^.
I understand where we divide 150 by 4.
But why do I need to multiply by 5, when there are 6 faces.
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You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.
When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.
A cuboid has six faces, but each face has a pair that is identical in size and shape.
Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.
To find the surface area of a cuboid, you can add up the areas of all its faces.
However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:
(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.
By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.
Essentially, you are considering one face from each pair and then summing their areas.
Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.
When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.
Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.
Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.
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The administration at a high school wants to conduct a survey of student opinion. Administrators want to begin with a simple random sample of 100 students. Which of the following survey methods will produce a simple random sample? (4 points)
A-Survey the first 100 students to arrive at school in the morning
B-Survey every 10th student entering the school gym until 100 students are surveyed
C-Use random numbers to choose 25 each of freshmen, sophomores, juniors, and seniors Number the gym seats. Use a table of random numbers to choose seats and interview the students until 100 have been interviewed.
D- Number the students on the school roster.
E-Use a table of random numbers to choose 100 students from this roster for the survey.
Answers
Answer:
C
Step-by-step explanation:
Each year will have 25 student
8. Choose all decimals that are equivalent to (7 x 100) + (5 × 1) + (8 × 7) + X 10 (1 × 100). 75.081 705.810 705.801 75.810 705.81 705.081
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Answer:
705.81 and 705.810
Step-by-step explanation:
700 + 5 + 0.8 + 0.01 = 705.81
Answers:
705.810
705.81
22/7 - 4/7
A)2
B)2 4/7
C)2 5/7
D)3
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Answer:
None of the option is correct.
The right answer is 18/7 or 2.57
Step-by-step explanation:
Plz help ASAP I’ll give lots of points
Answers
Answer:
8
Step-by-step explanation:
Because it is equal to the 4 side
Jill Janzen's gross weekly pay is $298. Her earnings to date for the year total $14,900. What amount is deducted from her pay each week for Social Security, which is taxed at 6.2%?
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Jill's annual earnings can be calculated by multiplying her weekly pay by the number of weeks in a year: $298/week x 52 weeks/year = $15,496/year. Her earnings to date are $14,900, so she has earned an additional $596 in the current week.
Social Security is taxed at 6.2%, so the amount deducted from her pay each week is 6.2% of her gross weekly pay. That's 0.062 x $298 = $18.48.
Why is FOQZ the odd one out in
these sets of letters?
BCDEGPTV AJK FOQZ IY
Answers
The odd one out in the set is "FOQZ." It deviates from the pattern by the other sets, where the letters are arranged in Alphabetical order.
The set of letters "BCDEGPTV AJK FOQZ IY" seems to follow a specific pattern. If we examine the letters in each group, we can identify a difference that sets "FOQZ" apart from the others.
In the first group "BCDEGPTV," the letters are arranged in alphabetical order. Similarly, in the second group "AJK," the letters are also in alphabetical order. However, when we look at the third group "FOQZ," the letters do not follow alphabetical order.
Based on this pattern, we can conclude that the odd one out in the set is "FOQZ." It deviates from the pattern followed by the other sets, where the letters are arranged in alphabetical order.
It's worth noting that the pattern could be based on different criteria, such as the position of the letters in the alphabet or some other sequence. Without additional information or context, it is difficult to determine the exact pattern or reason for the deviation.
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Find the value of a in the triangle shown below.
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Answer: Where is the triangle? There is no picture.
Let A= {1 , 2 , 3 , ... ... ...... , 10} and R = {(a, b): a ∈ A , b ∈ A and a + 2b = 10} Find the domain and range of R.
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In domain and range of a relation, if R be a relation from set A to set B, then
• The set of all first components of the ordered pairs belonging to R is called the domain of R.
Thus, Dom(R) = {a ∈ A: (a, b) ∈ R for some b ∈ B}.
• The set of all second components of the ordered pairs belonging to R is called the range of R.
Thus, range of R = {b ∈ B: (a, b) ∈R for some a ∈ A}.
Therefore, Domain (R) = {a : (a, b) ∈ R} and Range (R) = {b : (a, b) ∈ R}
if is a repeated # wich is the mode?
Answers
5 ten thousands 8 thousands 3 hundreds 7 tens 4 ones in standard
Answers
Step-by-step explanation:
Just : 5,8374
-x+3y=11 pls sove by elimation and step by step
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Answer:
Therefore, the solution to the equation -x + 3y = 11 is x = -34/11 and y = 29/11.
Step-by-step explanation:
The given equation is:
-x + 3y = 11
To solve this equation by elimination, we need to add or subtract one or both equations to eliminate one of the variables. In this case, we can eliminate the variable x by adding the equation with another equation that has x with the same coefficient, but opposite sign.
Let's suppose we have another equation with x, for example:
2x + 5y = 7
We can eliminate x by multiplying the first equation by 2 and the second equation by 1, so that the coefficients of x are opposite:
-2x + 6y = 22 (multiply the first equation by -2)
2x + 5y = 7 (the second equation)
Now we can add the two equations to eliminate x:
-2x + 2x + 6y + 5y = 22 + 7
Simplifying the equation, we get:
11y = 29
Dividing both sides by 11, we get:
y = 29/11
Now that we know the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:
-x + 3y = 11
Substituting y = 29/11, we get:
-x + 3(29/11) = 11
Simplifying the equation, we get:
-x + 87/11 = 11
Subtracting 87/11 from both sides, we get:
-x = 11 - 87/11
Multiplying both sides by -1, we get:
x = 87/11 - 11
Simplifying the equation, we get:
x = (87 - 121)/11
x = -34/11
Clara looked at the clock on her way to band practice.
Answers
Answer:
3:45 pm
Step-by-step explanation:
Seventy percent of the children went on the excursion. If 27 stayed at school, how many went?
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By using the Unitary Method we get the number of children who went on an excursion was 63. Thus, the total number of children at school is 90.
We are given that,
No. of children who stayed at school is 27,
Also, 70% of the children went on an excursion.
Suppose, the total number of children in percentage is 100%
Out of which 70% went on an excursion
Thus, the children who stayed at school is 100% - 70% = 30%
By using the Unitary method, we can find out the number of 70% of children.
If 30% of the children are 27
Then 70% of the children are = 27 × 100
30
= 63
∴ the total no. of children in the school = 27 + 63
= 90
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Juan spins two different fair spinners. One spinner has numbers 1 through 8. The other has letters A through F. What is the probaility that one spinner will land on 3 and the other will land on C?
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Answer:
...
Step-by-step explanation:
Help
look at the picture
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\(x7 - 2 \: or \: x \leqslant - 3\)
stimulus check summary please help me please
Answers
Answer: I think it’s great but you should make a stronger opinion and always have back up evidence
Step-by-step explanation:
PLS HELP simplify (2b^3)^2
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Answer: 4b^6
Remember if theres a bracket you multiply the power instead of adding
For example if it was 2b^3 x 2b^2 then the answer would be 4b^5 instead according to indices law, read up on it if you havent yet itll help a bunch! :)
2. center (5, -6), radius 4
Answers
Answer:
(x - 5)² + (y + 6)² = 16
Step-by-step explanation:
assuming you require the equation of the circle
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
here (h, k ) = (5, - 6 ) and r = 4 , then
(x - 5)² + (y - (- 6) )² = 4² , that is
(x - 5)² + (y + 6)² = 16
Given that f(x) = 2x + 5 and g(x) = x − 7, solve for f(g(x)) when x = −3. (1 point) −15 −8 10 25
Answers
Answer:
-15
Step-by-step explanation:
When functions are "nested" like this (nested is not a math word; the mathy word is composed or composition) you need to start all the way on the inside.
f(g(-3))
means find g(-3) first, then put that answer into f.
g(x) = x - 7
g(-3) = -3 - 7
g(-3) = -10
We found g(-3) is -10, so now put -10 into f.
f(x) = 2x + 5
f(-10) = 2(-10) + 5
= -20 + 5
= -15
The function f and g are given by \(f(x)=x^2\) and \(g(x)=-^1_2 x+5\).
Let R be the region bounded by the x-axis and the graphs f and g as shown at the bottom. Also, I only need you to answer part b, I've already finished part a.
a) Describe how you would find the area of R.
\(R=18 \frac{2}{3}\)
b) The region R is the base of a solid. For each y, where
0 < y < 4, the cross-section of the solid taken perpendicular to the y-axis is a rectangle whose base lies in R and whose height is 3y. Explain how you would write an expression that gives the volume of the solid.
![The function f and g are given by [tex]f(x)=x^2[/tex] and [tex]g(x)=-^1_2 x+5[/tex].Let R be the region](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/ggEzoWmKybVU6E5yxmAhM4iPrwjkmIdz.png)
Answers
As you've pointed out, R is a different region that I originally thought. The area of R can be computed using either
\(\displaystyle \int_0^2 x^2 \, dx + \int_2^{10} -\frac x2 + 5 \, dx\)
or
\(\displaystyle \int_0^4 (10-2y)-\sqrt y \, dy\)
Either way, you've gotten the correct area for part (a).
For part (b), we can use part of the integral with respect to \(y\) above. The horizontal distance between the curves \(y=x^2\) and \(y=-\frac x2+5\) is obtained by first solving for \(x\),
\(y=x^2 \implies x=\sqrt y\)
\(y=-\dfrac x2+5 \implies x = 10-2y\)
so the length of each cross section is \(10-2y-\sqrt y\).
The height of each cross section is \(3y\).
Then the volume of the solid is
\(\displaystyle \int_0^4 3y \left(10-2y-\sqrt y\right) \, dy = \boxed{\int_0^4 -6y^2 + 30y - 3y^{3/2} \, dy}\)
The instructions don't say to evaluate, but if you're looking for practice the volume ends up being 368/5, or 73 3/5.
![The function f and g are given by [tex]f(x)=x^2[/tex] and [tex]g(x)=-^1_2 x+5[/tex].Let R be the region](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/M1Nx3qF6H3zIbmOtytCKXpjyebsahFPB.jpeg)
Helppppp pleaseeeeee
Answers
Answer:Godo luck!
Step-by-step explanation:
PLEASE HELP!!! Needed asappp!
Answers
Step-by-step explanation:
Add the corresponding sides of the two equations
1.
2x=6
x=3
substitute for x
3+y=-1
y=-4
4.
5x=10
x=2
substitute for x
2(2)+2y=-2
2y=-6
y=-3
5.
12y=24
y=2
substitute for y
6x+5(2)=4
6x+10=4
x=-6
x=-1
Answer:
Q3. x = 3, y = -4
Q4. x = 2, y = -3
Q5. x = -1, y = 2
Step-by-step explanation:
Since the question is asking us to solve the system using elimination/adding, that's what I'll do.
To solve by adding, we add the like terms of both equations together.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1st question:
x + y = -1
x - y = 7
We add the first term together.
x + x = 2x
Then the second term.
y + -y = y - y = 0
Then the last term.
-1 + 7 = 6
Which becomes:
2x = 6
Then we solve the linear equation.
2x = 6
÷ 2 ÷ 2
x = 3
From the x value, we can then find y.
We can use either equation. In this example, I'll choose the first one.
x + y = -1
Substitute x = 3
3 + y = -1
-3 -3
y = -4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2nd question:
2x + 2y = -2
3x - 2y = 12
We add the first term together.
2x + 3x = 5x
Then the second term.
2y + - 2y = 2y - 2y = 0
Then the last term.
-2 + 12 = 10
Which becomes:
5x = 10
Then we solve the linear equation.
5x = 10
÷5 ÷5
x = 2
From the x value, we can then find y.
We can use either equation. In this example, I'll choose the first one.
2x + 2y = -2
Substitute x = 2
4 + 2y = -2
-4 -4
2y = -6
÷2 ÷2
y = -3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
3rd question:
6x + 5y = 4
-6x + 7y = 20
We add the first term together.
6x + -6x = 6x - 6x = 0
Then the second term.
5y + 7y = 12y
Then the last term.
4 + 20 = 24
Which becomes:
12y = 24
Then we solve the linear equation.
12y = 24
÷12 ÷12
y = 2
From the x value, we can then find y.
We can use either equation. In this example, I'll choose the first one.
6x + 5y = 4
Substitute y = 2
6x + 10 = 4
-10 -10
6x = -6
÷6 ÷6
x = -1
WILL GIVE BRAINLIEST
given: RTSU is a rectangle with vertices R (0,0), S (0, a), T(a,a) and U, (a,0) where a ≠ 0
Prove: RTSU is a square
look at image
Answers
The missing parts of the proof are: A. distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it is a square.
What is a Square?A square is a special type of rectangle whose consecutive sides are congruent. All four sides of a square are congruent.
In the proof given, the distance formula \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\) was used to find ST = a units in step 2.
By the definition of congruence, RS = ST in step 4.
Finally, RSTU is stated to be a square because if two consecutive sides of a rectangle are congruent, then it is a square.
The option that completes the proof in the right order is: A. distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it is a square.
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Answer:
distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it’s a square
Step-by-step explanation:
so its c for me
Write the equation of the line parallel to y=1/2x−6 that passes through (−10,4).
Answers
Answer:
y = 1/2 x + 9
Step-by-step explanation:
y = 1/2 x + b
4 = (1/2)(-10) + b
4 = -5 + b
b = 9