Define a relation Ron R by for a,beR (a,b) e Rif and only if a-bez Which of the following properties does have? Reflexive Symmetric Antisymmetric Transitive
Answers
In summary:
The relation R is reflexive. The relation R is not symmetric. The relation R is antisymmetric. The relation R is transitive.
Let's analyze the properties of the relation R:
Reflexive:
A relation R is reflexive if every element in the set is related to itself. In this case, we need to check if (a, a) belongs to R for every a in the set.
For the given relation R: (a, b) belongs to R if and only if a - b = 0.
Since a - a = 0, (a, a) satisfies the condition and is in R for every a in the set. Therefore, the relation R is reflexive.
Symmetric:
A relation R is symmetric if for every (a, b) belongs to R, (b, a) must also be in R.
For the given relation R: (a, b) belongs to R if and only if a - b = 0.
However, if a - b = 0, it does not imply that b - a = 0. Therefore, the relation R is not symmetric.
Antisymmetric:
A relation R is antisymmetric if for every distinct (a, b) belongs to R, (b, a) cannot be in R.
For the given relation R: (a, b) belongs to R if and only if a - b = 0.
Since a - b = 0 implies b - a = 0, it means that if (a, b) and (b, a) are in R, then a must be equal to b. Thus, for distinct elements a and b, it is not possible for both (a, b) and (b, a) to be in R. Therefore, the relation R is antisymmetric.
Transitive:
A relation R is transitive if for every (a, b) and (b, c) belongs to R, (a, c) must also be in R.
For the given relation R: (a, b) belongs to R if and only if a - b = 0.
If a - b = 0 and b - c = 0, it implies that a - c = 0. Therefore, if (a, b) and (b, c) are in R, then (a, c) is also in R. Thus, the relation R is transitive.
In summary:
The relation R is reflexive.
The relation R is not symmetric.
The relation R is antisymmetric.
The relation R is transitive.
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Related Questions
the count in a bacteria culture was 800 after 15 minutes and 1200 after 40 minutes. assuming the count grows exponentially,
Answers
Use the exponential growth formula to find the initial size. The initial size of the bacteria culture was approximately 457.
To determine the initial size of the bacteria culture, we can use the exponential growth formula: \(N(t) = N_0 * (2^{(t/d)})\), where N(t) is the population at time t, N₀ is the initial population, t is the time elapsed, and d is the doubling period.
Given that N(15) = 800 and N(30) = 1700, we can set up two equations:
\(800 = N_0 * (2^{(15/d)})\\1700 = N_0 * (2^{(30/d)})\)
To solve these equations, we can take the ratio of the second equation to the first equation:
\(1700/800 = (2^{(30/d)}) / (2^{(15/d)})\)
Simplifying the equation, we have:
2.125 = 2^(30/d - 15/d)
Taking the logarithm of both sides, we get:
log₂(2.125) = 30/d - 15/d
Simplifying further, we have:
0.0833d = 15
Solving for d, we find that d ≈ 180 minutes.
Substituting d = 180 minutes into one of the original equations, we can solve for N₀:
\(800 = N_0 * (2^{(15/180)})\)
Simplifying, we find that N₀ ≈ 457.
Therefore, the initial size of the bacteria culture was approximately 457.
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The complete question is:
The count in a bacteria culture was 800 after 15 minutes and 1700 after 30 minutes. Assuming the count grows exponentially, what was the initial size of the culture?
What is a perpendicular slope example?
Answers
Examples of perpendicular slope are the sides of a fixed square, a window, and the Red Cross emblem.
Describe perpendicular slope.Lines that are vertical and horizontal are perpendicular to one another. In this instance, the perpendicular line's slope would be equal to a horizontal line's slope, which would be 0. The slope of the perpendicular line is zero, but the slope of the parallel line is unknown. By taking the negative reciprocal of the slope of the provided line, one can determine the slope of a perpendicular line from that line. We obtain m2 = -1/m1 if the slope of the provided line is m1 and the slope of a perpendicular line is m2.
Given
There are a lot of perpendicular lines that we may see in reality. The corners of the chalkboard, the arms of a clock at specific times of the day, the sides of a fixed square, a window, and the Red Cross emblem are a few examples.
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Tell whether the given value is a solution of the inequality.
x + 1 > 10; x = 9
Answers
Answer:
given x+1 > 10,
x > 10 - 1
x > 9
which means x MUST BE more than 9 , which also means 9 isnt included in the inequality therefore x = 9 is not a solution.
Help asaaaaap please
Answers
Answer:
A. 1
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define
-5x - 1 ≤ -9
Step 2: Solve for x
Add 1 to both sides: -5x ≤ -8Divide -5 on both sides: x ≥ 8/5Here we see that any value x greater than or equal to 1.6 would work as a solution.
Therefore, our answer is A. 1, as it doesn't work as a solution.
If \( f(x, y)=e^{3 x} \sin (4 y) \) then: \[ \nabla f(-1,-3)= \]
Answers
The gradient of the function \(\(f\)\) at the point \(\((-1, -3)\)\) is:
\(\[\nabla f(-1, -3) = \left(-3e^{-3} \sin(12), 4e^{-3} \cos(12)\right)\]\)
To find the gradient of the function \(\( f(x, y) = e^{3x} \sin(4y) \)\) at the point \(\((-1, -3)\)\), we need to compute the partial derivatives with respect to \(\(x\) and \(y\)\) and evaluate them at that point.
The gradient of a function is given by:
\(\[\nabla f(x, y) = \left(\frac{{\partial f}}{{\partial x}}, \frac{{\partial f}}{{\partial y}}\right)\]\)
Let's calculate the partial derivatives:
\(\[\frac{{\partial f}}{{\partial x}} = \frac{{\partial}}{{\partial x}}\left(e^{3x} \sin(4y)\right) = 3e^{3x} \sin(4y)\]\)
\(\[\frac{{\partial f}}{{\partial y}} = \frac{{\partial}}{{\partial y}}\left(e^{3x} \sin(4y)\right) = 4e^{3x} \cos(4y)\]\)
Now, we can evaluate these derivatives at the point \(\((-1, -3)\):\)
\(\[\frac{{\partial f}}{{\partial x}}\Bigr|_{(-1, -3)} = 3e^{3(-1)} \sin(4(-3)) = 3e^{-3} \sin(-12)\]\)
\(\[\frac{{\partial f}}{{\partial y}}\Bigr|_{(-1, -3)} = 4e^{3(-1)} \cos(4(-3)) = 4e^{-3} \cos(-12)\]\)
Simplifying further:
\(\[\frac{{\partial f}}{{\partial x}}\Bigr|_{(-1, -3)} = 3e^{-3} \sin(-12) = -3e^{-3} \sin(12)\]\)
\(\[\frac{{\partial f}}{{\partial y}}\Bigr|_{(-1, -3)} = 4e^{-3} \cos(-12) = 4e^{-3} \cos(12)\]\)
Therefore, the gradient of the function \(\(f\)\) at the point \(\((-1, -3)\)\) is:
\(\[\nabla f(-1, -3) = \left(-3e^{-3} \sin(12), 4e^{-3} \cos(12)\right)\]\)
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Solve the initial value problem y"-10y'+50y=0 for y(O)=1 and y'(O)=5. After getting the equation for the particular solution, determine the value of y when x=1.52. Note: SOLVE CONTINUOUSLY. Input numerical values only. Round your answer to two decimal places if the answer is not a whole number. Example: If your answer is 28.3654, input 28.37 If your answer is 28.3641, input 28.36
Answers
The given initial value problem is a second-order linear homogeneous differential equation. To solve it, we first find the characteristic equation by substituting y = e^(rx) into the equation. This leads to the characteristic equation r^2 - 10r + 50 = 0.
The general solution of the differential equation is y(x) = e^(5x)(C₁cos(5x) + C₂sin(5x)), where C₁ and C₂ are constants determined by the initial conditions.
To determine the particular solution, we differentiate y(x) to find y'(x) = e^(5x)(5C₁cos(5x) + 5C₂sin(5x) - C₂cos(5x) + C₁sin(5x)), and then differentiate y'(x) to find y''(x) = e^(5x)(-20C₁sin(5x) - 20C₂cos(5x) - 10C₂cos(5x) + 10C₁sin(5x)).
Substituting the initial conditions y(0) = 1 and y'(0) = 5 into the general solution and its derivative, we obtain the following equations:
1 = C₁,
5 = 5C₁ - C₂.
Solving these equations, we find C₁ = 1 and C₂ = 4.
Therefore, the particular solution to the initial value problem is y(x) = e^(5x)(cos(5x) + 4sin(5x)).
To find the value of y when x = 1.52, we substitute x = 1.52 into the particular solution and evaluate it. The result will depend on the rounding instructions provided.
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is this right?
what is the correct answer if I am wrong.
Answers
Answer:
yes
Step-by-step explanation:
Answer
it looks like your correct but i would go for b or a
Step-by-step explanation:
3. Tara started out with $347.14 in her
bank account. After buying a new
bicycle, she had $58.71 left over.
How much did the bicycle cost?
Answers
Answer:
$288.43
Step-by-step explanation:
$347.14 - $58.71 = $288.43
Hope this helped! Good luck in Math! Also, I also have a question that someone needs to answer to lol. Have a good day!
Hay 323232 delanteros y 808080 defensas en la liga de baloncesto de Leo. Leo debe incluir a todos los jugadores en un equipo y quiere que cada equipo tenga el mismo número de delanteros y el mismo número de defensas. Si Leo crea el mayor número de equipos posible, ¿cuántos defensas habrá en cada equipo?
Answers
Answer:
5 defensores
Step-by-step explanation:
La pregunta correcta es la siguiente;
Hay 32 delanteros y 80 defensas en la liga de baloncesto de Leo. Leo debe incluir a todos los jugadores en un equipo y quiere que cada equipo tenga el mismo número de delanteros y el mismo número de defensas. Si Leo crea el mayor número de equipos posible, ¿cuántos defensas habrá en cada equipo?
Responda como sigue;
Ahora queremos saber el número de defensas que deberíamos tener por equipo.
La respuesta a esta pregunta es simplemente encontrar la relación entre el número de delanteros y el número de defensores.
matemáticamente,
eso sería 32:80 = 2: 5 Entonces esto significa que por cada 2 delanteros en un equipo, debería haber 5 defensores
can the following side lengths form a triangle?
Answers
Answer:
no
Step-by-step explanation:
The triangle inequality requires the sum of the shorter two sides exceed the length of the longest one. Here, we have ...
10 +12 = 22 . . . . does not exceed 22
The lengths will not form a triangle.
_____
Additional comment
Some authors write the triangle inequality as ...
a +b ≥ c
If this is the one your curriculum author uses, then these side lengths will form a triangle.
20 POINTS!! (please help quickk)
15 dance tickets were sold in one half hour. If this rate continues, how many hours would you expect it to take to sell 270 tickets?
Answers
First, you would divided 270 by 15
270 ÷ 15 = 18
Then, you would divide 18 by 2 because it only takes half an hour to sell 15.
18÷2 = 9
Therefore, it would take 9 hours!
-----
Another Way!
First, multiply 15 by 2 because it only takes half an hour to sell 15.
15×2 = 30
Then, divide 270 by 30!
270÷30 = 9
Therefore, it would take 9 hours!
math question need help with it
Answers
Answer:
c- 4 x 10^7
Step-by-step explanation:
for scientific notation, the first number can not be greater than 9
so you have to split your number into a decimal
37,250,000
3.7250000
so the first part of your equation is 4 because the 7 rounds up the 3
then, there are 7 digits after the decimal, so that is your exponent
it is also positive.
so your final answer is
4 x 10^7 :)
Simplify 5a + 5b - 6a + 8b
Answers
Answer:
-1a + 13b
Step-by-step explanation:
combine like terms and just be sure to change signs as needed
Step-by-step explanation:
-a+13b
colect like terms and solve
Write a recursive method that computes the factorial of an input number (0! =
1! = 1, and for n > 1, n! = n ·(n −1)!). Assume that the input argument to the
method is a nonnegative integer less than 11.
Write a Java program called Factorial.java that uses your method to compute the
factorial of an input number. The input is a positive integer read from the standard
input. The output is the factorial of the input number. The output should be a
number appearing on a line by itself. Your method should take an int argument,
and return an int value.
For example, if the input is
10
then the output should be
3628800
by using Java Programming Language.
Answers
The Java program Factorial.java implements a recursive method to compute the factorial of a nonnegative integer less than 11.
The Factorial.java program in Java utilizes a recursive method to calculate the factorial of a given number. The recursive method follows the mathematical definition of factorial, where the factorial of a number n is n multiplied by the factorial of (n-1). The program first checks if the input number is within the valid range (0 to 10). If it is, the program calls the recursive method to calculate the factorial. The base case of the recursive method is when the input number is 0 or 1, where the factorial is defined as 1. For any other number, the method recursively calls itself with the number decreased by 1 until it reaches the base case. The factorial value is calculated by multiplying the current number with the factorial of the decreased number. Finally, the program displays the computed factorial as output.
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open a bank account make a deposit $150
Answers
What is the price per lb of brand X coffee
if 8 lb were mixed with 12 lb of brand Y
coffee which costs $9/Ib to make 20 lb of
Mark's special coffee blend which costs
$13/1b?
Answers
Answer: x = 8/4 = 2
12(2) + 4(6) = 24 + 24 = 48 = 6*8
Step-by-step explanation:
$12X + $6(4) = (X+4)*$8
12X + 24 = 8(x+4)
12x + 24 = 8x + 32
12x + 24 - 8x - 32 = 0
4x - 8 = 0
4x = 8
x = 8/4 = 2
Please help no links
Answers
Answer:
x=11
Step-by-step explanation:
These add up to 180 since a straight line = 180 degrees
Your equation is: 4x+15+11x=180
15x+15=180
15x=165
x=11
Answer:
X=11
HOPE THIS HELPS
- Todo ❤️
Step-by-step explanation:
4x+15+11x=180
15x+15=180
180-15=165
165/15=11
X=11
Which shows the price of a $35 video game after a markup of 27%?
Answers
Answer:
$44.45
Step-by-step explanation:
27% of 35 is 9.45 add that to 35 to get $44.45
Answer:
The answer is $44.45
Step-by-step explanation:
You change the percent into a decimal so it would be .27 then multiply the .27 to the $35 and you will get $9.45. Then you add the $9.45 to the $35 and you will get the answer.
Can someone also explain this.. :)
Answers
Answer: √60
Step-by-step explanation:
For what amount of exit proceeds would these two structures yield the same amount of carried interest?
.20 (Z-250) = .30 (Z-200)
Solve for Z.
Answers
Answer:
Step-by-step explanation:"To solve this equation, you can start by distributing the 0.20 and 0.30 terms. Then, you can simplify the equation by combining like terms. After that, you can isolate the variable Z on one side of the equation by adding or subtracting terms from both sides. Finally, you can solve for Z. The solution is Z = 1000. Does that help?"
!!PLS HELP ASAP!!30 POINTS!!
Divide using synthetic division
\(x^4-3x^3-7x+1\)÷\(x+2\)
Answers
The quotient and remainder are x³ -5x² + 10x - 17 and 55.
What is Synthetic division?
When the divisor is a linear factor, synthetic division is a technique used to carry out the division operation on polynomials.
Here, (x+2) is a linear factor which indicates that synthetic division can be applied.
So, we will divide the x^4 - 3x^3 - 7x + 1 by x+2.
(refer the attached solution)
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![!!PLS HELP ASAP!!30 POINTS!!Divide using synthetic division[tex]x^4-3x^3-7x+1[/tex][tex]x+2[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/8yprsebfa86csj8Wx4vXMSdg67ka61bd.jpeg)
Set up for proportion its not 9 or 6 or 2
Answers
The value of x in the triangle is 2√13.
We have,
There are two similar triangles.
So,
The ratio of the corresponding sides is equal.
Now,
4/x = x/(9 + 4)
4/x = x / 13
4 x 13 = x²
x² = 4 x 13
x = √(4 x 13)
x = 2√13
Thus,
The value of x in the triangle is 2√13.
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Please help!!! For what value of why must LMNP be a parallelogram?
Answers
Answer:
107 degrees
Step-by-step explanation:
The four angles of a parallelogram add up to 360 degrees. Any two adjacent angles of a parallelogram add up to 180 degrees. So y is equal to 180 degrees minus 73 degrees, which is equal to 107 degrees.
Help me with 3 please and thank you
Answers
Answer:
Ray
Step-by-step explanation:
A ray starts at one direction and in the other direction it goes on forever.
Which expression represents a negative number?
Answers
Answer:
The expression is A that is -b
Help pleaseeeee!!!!!!
Answers
Answer:
17
Step-by-step explanation:
Firstly the formula to find the circumference of a circle is 2 * pi * radius
In this case the circumference is 2*pi
However we want the circumference for an angle of 120 which is 1/3 of 360.
This gives us 2/3 * pi for the arc.
Then to find the whole perimeter we add the length of the radius on both sides giving a value of 4.1
Please help!!! I’ll give brainiest
Answers
Answer:
Parker is NOT right when he says that it is a division problem 6 ÷ 3.
In fact, it is a multiplication problem 6 × 3 because 6 × 3 = 18 would give us the correct number of total rectangles which are 18
Step-by-step explanation:
Total number of rectangles = 18
As there are 3 rows with each row containing 6 rectangles.
Now, if we multiply 6 with 3, we get the result 18.
Thus,
6 × 3 = 18
Hence, Parker must have mentioned that this arrow of 18 rectangles shows the multiplication problem 6 × 3.
Thus,
Parker is NOT right when he says that it is a division problem 6 ÷ 3.
In fact, it is a multiplication problem 6 × 3 as 6 × 3 = 18 would give us the correct number of total rectangles which are 18.
2/3(6x-1/6) + 3x simplify the expression
Answers
Answer:
\(21x \: - \frac{1}{3} \\ 3\)
Find the missing value.
Hint: Use the number line to find the missing value.
—9+
--
—3
主
-15
-10
-5
0
5
10
15
Answers
Answer:
-9 + 6 = -3
Step-by-step explanation:
The Number Line
The original number -9 is located as the red dot in the number line as shown in the figure below.
To move to the number -3 (as a blue dot) we must jump right 6 numbers. Thus, this is the number that must be filling the box.
-9 + 6 = -3
given any set of seven integers, must there be at least two that have the same remainder when divided by 6?
Answers
Given any set of seven numbers that should be at least 2 that must have the same remainder when divided by 6
What are the factors?A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product since the product is divisible by them.
How do you find factors?Step 1: factor the provided number into primes, or describe it as the product of primes.
Step 2: Write the prime factorization in exponent form in step three.
Step 3: Increase each exponent by one.
Step 4: Multiply each of the results.
There can only be a maximum of six different remainders when dividing by six: 0, 1, 2, 3, 4, and 5.
In any set of seven integers, two must have the same remainder when divided by seven according to the pigeon hole principle.
b) Consider set of integers 0, 1 ,2, 3, 4, 5 and 66. All these have different remainders upon division by 8 and hence the answer is no.
The interpretation is yes
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