Answer:
[tex](x + 2)(5x + 2)[/tex]
Step-by-step explanation:
What we would normally do when factoring a polynomial is find the greatest factor, but in this case, there is none. What we do then is multiply the coefficient of the first term by the last term.
So in this case, that expression would be...
[tex]5 * 4 = 20[/tex]
Then, we have to find two factors of 20 that, when added together, equal the second term's coefficient (12).
These factors would be 2 and 10.
[tex]2 * 10 = 20\\\\2 + 10 = 12[/tex]
We then replace the second term in the polynomial with [tex]10x + 2x[/tex]. This ends up looking like this:
[tex]5x^2 +10x + 2x +4[/tex]
Keep in mind that this did not change the value of the polynomial, as 10x + 2x still equals 12x.
This new expression lets us use a technique called group factoring. To start group factoring, we need to take out the greatest common factor (GCF) of the first two terms. That ends up looking like this:
[tex]5x(x + 2)[/tex]
Then, we do the same thing with the last two terms.
[tex]2(x + 2)[/tex]
We know we're on the right track at this point, because the expressions inside the parenthesis in both GCFs are the same.
The last step is combining the terms on the outside of the parenthesis, and multiplying it with what's inside the parenthesis. The final answer looks like this.
[tex](x + 2)(5x + 2)[/tex]
HELP PLEASE!!!!!! Find the speed of an athlete who makes 4and3/4 laps in 3mins45 seconds on a 400m field in m/s
Given:
An athlete who makes [tex]4\dfrac{3}{4}[/tex] laps in 3 mins 45 seconds on a 400m field.
To find:
The speed of the athlete in m/s.
Solution:
We know that,
Distance covered in 1 lap = 400 m
Distance covered in [tex]4\dfrac{3}{4}[/tex] laps = [tex]4\dfrac{3}{4}\times 400[/tex] m
= [tex]\dfrac{19}{4}\times 400[/tex] m
= [tex]1900[/tex] m
We know that,
1 minute = 60 seconds
3 minutes = 180 seconds
3 minutes 45 second = 180 + 45 seconds
= 225 second
The speed of the athlete is:
[tex]Speed=\dfrac{Distance}{Time}[/tex]
[tex]Speed=\dfrac{1900}{225}[/tex]
[tex]Speed\approx 8.44[/tex]
Therefore, the speed of the athlete is about 8.44 m/s.
Please help me I will give u points whenever u wanna only Percy answers pleaseee ❤️
And don’t forget about explain
Answer:
this point is 72 digri ok
please help quickly!
Answer:
answer I have no clue sorry dude
The simple interest on $600 saved for 3 years at an interest rate of 6 percent. Find the interest
Answer:
interest = $108
Step-by-step explanation:
interest = p * r * t
interest = 600*0.06*3
interest = $108
An isosceles triangle has a base of 20cm and legs measuring 36cm. How long are the legs of a similar triangle with a base measuring 50cm?
Answer:
90 cm
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, then
50 ÷ 20 = 2.5
The legs of the similar triangle are 2.5 times the original legs, that is
legs of similar triangle = 2.5 × 36 cm = 90 cm
Mrs. DeRossett's sister goes to the bank to get a loan to purchase a new home. The bank advises that she make sure her mortgage payment does not exceed 30% of her monthly take home pay. If Mrs. DeRossett's sister makes roughly $5,000 per month, then what would be her recommended maximum monthly mortgage?
Answer:
1,500
Step-by-step explanation:
The volume of a cube is reduced by how much if all sides are halved?
Let the side of a cube be "a". The volume of the cube is "a³".
If all sides of the cube are halved, each side will now measure "a/2".Therefore, the new volume will be (a/2)³ cubic units. That is:a³ / 8 cubic units. The new volume of the cube will be reduced to 1/8 of its original volume.
A block is a three-layered strong item limited by six square faces, features or sides, with three gathering at every vertex. It looks like a hexagon from the corner, and its net usually looks like a cross. The block is the main customary hexahedron and is one of the five Non-romantic solids.
The volume of any three-dimensional solid is simply defined as the amount of space it occupies. A cube, cuboid, cone, cylinder, or sphere are all examples of these solids. The volumes of different shapes vary.
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Picture is included please help
Answer:
B cannot be factored into a perfect square
1)
If A is an m x n matrix and B is an n x r matrix, then the product C = AB is:
Group of answer choices
a) Undefined
b) An m x r matrix
c) An m x m matrix
d) An n x n matrix
2) A sequence {Xn} of state matrices that are related by the equation Xk+1 = PXk where P is a stochastic (probability) matrix is called a _______.
3) In Hypothesis testing, each level of significance α has a critical value C that determines the __________ for H0.
The answer to given statements are
1. the correct answer is b) An m x r matrix.
2. Markov chain
3. rejection region
1. The product C = AB of an m x n matrix A and an n x r matrix B will result in an m x r matrix.
Therefore, the correct answer is b) An m x r matrix.
2. A sequence {Xₙ} of state matrices that are related by the equation Xk+1 = PXk, where P is a stochastic (probability) matrix, is called a Markov chain.
3. In hypothesis testing, each level of significance α has a critical value C that determines the rejection region for H0.
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What is the probability that a randomly selected bottle is correctly placed and a Plastic #4 bottle?
A. 1/2
B. 1/3
C. 1/4
D. 1/6
Answer:
1/4
Step-by-step explanation:
Use the following information for the next two questions: • A portfolio consists of 16 independent risks. • For each risk, losses follow a Gamma distribution, with parameters 0 = 250 and a = 1. The Central Limit Theorem: Suppose that X is a random variable with mean u and standard deviation and suppose that X, X2...., Xy are independent random variables with the same distribution as X (i.e. Independent and Identically Distributed or IID assumption). Let Y = X2, X2..... X... Then E[Y] = nu and Var(Y) = ng2. As n increases, the distribution of Y approaches a normal distribution Nínu, no4). This is also known as normal approximation. (a) Without using the Central Limit Theorem, determine the probability that the aggregate losses for the entire portfolio will exceed 6,000. (b) Using the Central Limit Theorem, determine the approximate probability that the aggregate losses for the entire portfolio will exceed 6,000.
The probability that the aggregate losses for the entire portfolio will exceed 6,000 can be determined by calculating the cumulative distribution function (CDF) of the Gamma distribution without using the Central Limit Theorem. Alternatively, using the Central Limit Theorem, the approximate probability can be estimated by treating the sum of 16 independent risks as a normal distribution with a mean of 4000 and a standard deviation of 4.
(a) Without using the Central Limit Theorem, the probability that the aggregate losses for the entire portfolio will exceed 6,000 can be determined by calculating the cumulative distribution function (CDF) of the Gamma distribution for the sum of 16 independent risks. Since each risk follows a Gamma distribution with parameters θ = 250 and α = 1, the sum of 16 risks will follow a Gamma distribution with parameters θ' = 16 * 250 = 4000 and α' = 16 * 1 = 16. By evaluating the CDF at the value of 6,000, we can find the probability that the aggregate losses exceed 6,000.
(b) Using the Central Limit Theorem, we can approximate the distribution of the sum of 16 independent risks as a normal distribution. According to the theorem, as the number of independent and identically distributed (IID) risks increases, the distribution of their sum approaches a normal distribution with mean μ' = n * μ and standard deviation σ' = √(n * σ^2), where n is the number of risks, μ is the mean of each risk, and σ is the standard deviation of each risk.
In this case, with 16 independent risks, the approximate distribution of the aggregate losses will be a normal distribution with mean μ' = 16 * 250 = 4000 and standard deviation σ' = [tex]\sqrt{ (16 * 1^2)}[/tex] = 4. By calculating the probability that the normal distribution exceeds 6,000, we can estimate the approximate probability of the aggregate losses exceeding 6,000.
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PLS HELP ME PLS ACTUALLY PUT AN ANSWER
Answer:
Hi
Step-by-step explanation:
The answer is B and D.
Hope it's correct.
A time series graph is useful for which of the following purposes?
Representing relative frequencies of categories in a specific year
Representing the cumulative frequencies of the data in a specific year
Representing the frequencies of the data, sorted from largest to smallest
Representing the frequencies of a data category over a period of several years
Answer: A time series graph is useful for representing the frequencies of a data category over a period of several years.
Explanation: Time series graphs are usually employed when it is critical to examine data values and trends over time. A time series graph displays changes in data over time. It is usually used to depict economic, social, or physical characteristics that are measurable over time. A time series is a collection of observations or data taken at regular intervals over time and used to track and analyze changes in data over time.
Time series graphs display data over time on a graph with time on the x-axis and a measured value, such as temperature or height, on the y-axis. The graph can display change trends over time as well as seasonal or other patterns, in addition to providing insight into how data values are changing over time.
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complete the square to rewrite the following equation in standard form
By completing the square, the equation in standard form is (x - 2)² + (y + 4)² = 4².
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represent the coordinates at the center of a circle.r represent the radius of a circle.From the information provided below, we have the following equation of a circle:
x² - 4x + y² + 8y = -4
x² - 4x + (-4/2)² + y² + 8y + (8/2)² = -4 + (-4/2)² + (8/2)²
x² - 4x + 4 + y² + 8y + 16 = -4 + 4 + 16
(x - 2)² + (y + 4)² = 16
(x - 2)² + (y + 4)² = 4²
Therefore, the center (h, k) is (2, -4) and the radius is equal to 4 units.
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Complete Question:
Complete the square to rewrite the following equation in standard form. x² - 4x + y² + 8y = -4.
Which expression is evaluated first in the following statement?
if (a > b && c == d || a == 10 && b > a * b)?
a. a * b
b. b && c
c. d || a
d. a > b
e. none of the above
The expression "a > b" is evaluated before the other expressions.
How to evaluate an expression?
Follow the order of operations (PEMDAS/BODMAS). Evaluate the expression following the order of operations or the rules of precedence.
Let's break down the given statement and determine the order of evaluation for each expression:
if (a > b && c == d || a == 10 && b > a * b)
The statement consists of two logical expressions connected by the "&&" and "||" operators. To determine the order of evaluation, we need to consider operator precedence and associativity.
1. Parentheses: As there are no parentheses in the statement, we move on to the next step.
2. "&&" Operator: The "&&" operator has higher precedence than the "||" operator, so expressions connected by "&&" are evaluated before those connected by "||".
The first expression connected by "&&" is "a > b". Let's call this Expression 1.
The second expression connected by "&&" is "c == d". Let's call this Expression 2.
3. "||" Operator: The "||" operator has lower precedence than the "&&" operator.
The first expression connected by "||" is Expression 1 (a > b) && (c == d).
The second expression connected by "||" is "a == 10" && "b > a * b". Let's call this Expression 3.
Now, let's evaluate each expression in the given order:
Expression 1: a > b
Expression 2: c == d
Expression 3: a == 10 && b > a * b
Therefore, the expression evaluated first in the given statement is Expression 1: a > b.
To summarize, in the statement "if (a > b && c == d || a == 10 && b > a * b)", the expression "a > b" is evaluated first.
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A recent study focused on the method of payment used by college students for their cell phone bills. Of the 1,220 students surveyed, 600 stated that their parents pay their cell phone bills. Use a 0.01 significance level to test the claim that the majority of college students' cell phone bills are paid by their parents.
Identify the null and alternative hypotheses for this scenario.
Test the claim that the majority of college students' cell phone bills are paid by their parents.
The significance level of 0.01 indicates that we want to use a 1% level of significance to evaluate the evidence against the null hypothesis.
The null and alternative hypotheses for testing the claim that the majority of college students' cell phone bills are paid by their parents can be stated as follows:
Null hypothesis (H0): The majority of college students' cell phone bills are not paid by their parents.
Alternative hypothesis (Ha): The majority of college students' cell phone bills are paid by their parents.
In this scenario, the null hypothesis assumes that the proportion of college students whose parents pay their cell phone bills is less than 50% (not a majority), while the alternative hypothesis suggests that the proportion is greater than or equal to 50% (a majority). The significance level of 0.01 indicates that we want to use a 1% level of significance to evaluate the evidence against the null hypothesis.
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SKETCH the area D between the lines x = 0, y = 3 – 37, and y = 3.x – 3. Set up and integrate the iterated double integral for D∫∫xdA.
The area D is bounded by the lines x = 0, y = 3 – 37, and y = 3x – 3. To calculate the iterated double integral for ∫∫xdA over D, the value of the iterated double integral ∫∫xdA over the area D is 0.
To set up the iterated double integral for ∫∫xdA over D, we first need to determine the limits of integration for x and y. Looking at the given lines, x = 0 indicates that x varies from 0 to some upper limit. The line y = 3 – 37 represents a horizontal line, indicating that y has a constant value of 3 – 37, which simplifies to -34. The line y = 3x – 3 represents a slanted line with a slope of 3, indicating that y varies linearly with x.
To find the limits of integration for x, we need to determine the x-values where the slanted line and the vertical line intersect. Setting 3x – 3 equal to 0, we find x = 1. Substituting this value back into the slanted line equation, we get y = 3(1) – 3 = 0. Therefore, x varies from 0 to 1.
For y, since it has a constant value of -34, the limits of integration for y are -34 to -34.
Setting up the iterated double integral, we have ∫∫xdA = ∫[0 to 1]∫[-34 to -34] x dy dx. Integrating with respect to y first, we have ∫[0 to 1] x(-34 - (-34)) dx, which simplifies to ∫[0 to 1] 0 dx. Finally, integrating with respect to x, we get 0. Therefore, the value of the iterated double integral ∫∫xdA over the area D is 0.
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Please help another one
Please no joke :)
Have a good day gelp me please
Answer:
1) [tex]x^{2}\cdot y[/tex] - It is a monomial with two variables: [tex]x[/tex], [tex]y[/tex]
2) [tex]3\cdot x^{3}+x^{3}[/tex] - It is binomial reductible to a monomial due to like terms. Number of variables: [tex]x[/tex]
3) [tex]a^{2}\cdot b^{3}\cdot c^{4}[/tex] - It is a monomial with three variables: [tex]a[/tex], [tex]b[/tex], [tex]c[/tex]
4) [tex]2\cdot x^{2}-3=n[/tex] - It is binomial equivalent to a monomial. Number of variables: [tex]x[/tex], [tex]n[/tex].
5) [tex]x^{2}-y+2\cdot x^{2} = 3[/tex] - It is trinomial reductible to a binomial due to like terms. And equivalent to a constant. Number of variables: [tex]x[/tex], [tex]y[/tex]
Step-by-step explanation:
We proceed to explain the context on each case and answer appropriately:
1) [tex]x^{2}\cdot y[/tex] - It is a monomial with two variables: [tex]x[/tex], [tex]y[/tex]
2) [tex]3\cdot x^{3}+x^{3}[/tex] - It is binomial reductible to a monomial due to like terms. Number of variables: [tex]x[/tex]
3) [tex]a^{2}\cdot b^{3}\cdot c^{4}[/tex] - It is a monomial with three variables: [tex]a[/tex], [tex]b[/tex], [tex]c[/tex]
4) [tex]2\cdot x^{2}-3=n[/tex] - It is binomial equivalent to a monomial. Number of variables: [tex]x[/tex], [tex]n[/tex].
5) [tex]x^{2}-y+2\cdot x^{2} = 3[/tex] - It is trinomial reductible to a binomial due to like terms. And equivalent to a constant. Number of variables: [tex]x[/tex], [tex]y[/tex]
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
Answer:
2/11
Step-by-step explanation:
Let's say x = 0.18181818..
Then, 100x = 18.1818181....
so, if you put x in the repeating decimal in 18.1818,
you get the equation,
100x = 18+x
so, 99x = 18
x = 18/99 = 2/11
Answer:
18/100 = 9/50
Answer is 9/50
Do you really think you’re going to give me brainliest lol
can somebody help me
[tex](15f + 37f + 53 + 55)[/tex]
Answer:
(15f + 37f + 52 + 55) = ?
15f + 37f = 52f
52 + 55 = 107
So, (15f + 37f + 52 + 55) = 52f + 107.
Step-by-step explanation:
Hope that this helps! :)
Have a great rest of your day/night!
Emily buys some of her clothes second
hand. If 75% of her shirts are second hand
and she owns 24 shirts, how many of
Emily's shirts are second hand?
Answer:
18 shirts
Step-by-step explanation:
75% of 24
convert 75% to decimal number
75% is 0.75
0.75 x 24 = 18
The ages of the winners of a cycling tournament are approximately bell-shaped. The mean age is 27.6 years, with a standard deviation of 3.5 years. The winner in one recent year was 30 years old. (a) Transform the age to a z-score. (b) Interpret the results.
(a) The z-score for an age of 30 years is approximately 0.6857.
(b) The winner's age of 30 years is roughly 0.6857 standard deviations above the mean age of the winners (27.6 years), indicating they were slightly older than the average age.
(a) To transform the age of 30 years to a z-score, we use the formula:
z = (x - μ) / σ
where:
x = individual value (age of the winner) = 30 years
μ = mean age = 27.6 years
σ = standard deviation = 3.5 years
Plugging in the values, we get:
z = (30 - 27.6) / 3.5
Calculating this expression, we find:
z ≈ 0.6857
Therefore, the z-score for an age of 30 years is approximately 0.6857.
(b) Interpretation of the results:
The z-score indicates the number of standard deviations an individual value (in this case, the age of the winner) deviates from the mean. A positive z-score suggests that the individual value is above the mean.
In this context, the z-score of approximately 0.6857 means that the age of the winner (30 years) is roughly 0.6857 standard deviations above the mean age of the winners (27.6 years). This suggests that the winner in that recent year was slightly older than the average age of the tournament winners.
By using z-scores, we can compare and interpret individual values within the context of a distribution, such as the bell-shaped distribution of ages in the cycling tournament winners.
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A reporter surveyed 300 randomly selected people of all ages about their opinion of a new song. The results are shown in the table. Which of the following is a valid conclusion about data? select all that apply.
Answer:
the answers is A and E <3
Step-by-step explanation:
i took this test
A right cylinder has a radius of 5 and a height of 9. What is its surface area? A. 457 units2 B. 1407 units2 C. 907 units? D. 700 units2
Answer: B
The surface area of the right cylinder is 140π cubic units or 439.60 cubic units.
Step-by-step explanation:
We have formula to find the surface area of a right cylinder.
Surface area = 2πr(h + r)
Given: r = 5 and h = 9,
Now plug in the value of r and h in the above formula, we get
Surface area = 2π.5 (9 + 5)
= 10π(14)
Surface area = 140π
The value of π = 3.14, when we plug in the value of π, we get
The surface area = 140 × 3.14
= 439.60 cubic units.
Therefore, the surface area of the right cylinder is 140π cubic units or 439.60 cubic units.
Hope this helped!!!
the scatterplot shows the number of hours that 12 people spent learning to type on a keyboard and each persons average typing speed. Based on the scatterplot, what is the best prediction of a persons average typing speed in words per min. if the person has spent 70 hours learning to type?
Answer:
85 wpm
Step-by-step explanation:
From the scatter plot, we can see the following;
At 20 hours, average typing speed = 34 wpm
At 30 hours, the average typing speed = 40 wpm
At 40 hours, the average typing speed = 51 wpm
At 50 hours, the average typing speed = 65 wpm
Average differences = ((40 - 34) + (51 - 40) + (65 - 51))/3 = 10.3
Approximating to a whole number = 10
Now, we can approximate that at 60 hours, average typing speed = 65 + 10 = 75 wpm
At 70 hours, the average typing speed = 75 + 10 = 85 wpm
Answer:
85 wpm
Step-by-step explanation:
I took this test!
The following data set shows the bank account balance for a random sample of 17 IRSC students. 343 45 340 SN 105 343 29 340 101 343 alelse 1 340 343 101 312 142 340 36 Round solutions to two decimal places, if necessary. What is the mean of this data set? mean What is the median of this data set? median What is the mode of this data set? If no mode exists type DNE. If multiple modes existenter the values in a comma-separated list. Round solutions to two decimal places, if necessary. What is the mean of this data set? mean What is the median of this data set? median- What is the mode of this data set? If no mode exists, type DNE. If multiple modes exist, enter the values in a comma-separated list. mode =
The mean of the data set is approximately 210.94. The median of the data set is 101. The mode of the data set is 343.
To determine the mean, median, and mode of the data set:
Data set: 343, 45, 340, SN, 105, 343, 29, 340, 101, 343, alelse, 1, 340, 343, 101, 312, 142, 340, 36
To calculate the mean, we need to find the average of all the values in the data set. However, it seems that there are some non-numeric entries like "SN" and "alelse." We need to remove these non-numeric entries before calculating the mean.
After removing the non-numeric entries, the data set becomes: 343, 45, 340, 105, 343, 29, 340, 101, 343, 1, 340, 343, 101, 312, 142, 340, 36.
Mean: Sum all the values and divide by the number of values.
Mean = (343 + 45 + 340 + 105 + 343 + 29 + 340 + 101 + 343 + 1 + 340 + 343 + 101 + 312 + 142 + 340 + 36) / 17
Mean ≈ 210.94 (rounded to two decimal places)
To calculate the median, we need to find the middle value of the data set when it is arranged in ascending order. If the number of values is odd, the median is the middle value. If the number of values is even, the median is the average of the two middle values.
Arranging the data set in ascending order: 1, 29, 36, 45, 101, 101, 105, 142, 312, 340, 340, 340, 343, 343, 343, 343, 340.
Median: Since the number of values is odd (17), the median is the middle value.
Median = 101
To calculate the mode, we need to find the value(s) that appear(s) most frequently in the data set.
Mode: In this data set, the value 343 appears most frequently, so the mode is 343.
In summary:
Mean ≈ 210.94
Median = 101
Mode = 343
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Can someone help me solve these equations?
1. 2y^2+5Y+2 |
2. 5x^2-18x+9 |
3. 16b^2+60b-100 | 4.-6a^2-25a-25 |
5. 49x^2-14x+1 |
6. 81x^2-49
HELP ASAP PLEASE!!!!
Answer:
q=(1,5) t=(-2,3)r=(3,-1)s=(0,0)
Step-by-step explanation:
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
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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What substitution should be used to rewrite 16(x^3 +1)^2 – 22(x^3+1) – 3 = 0 as a quadratic equation? a. u = (x3) b. u = (x3+1) c. u = (x3+1)2 d. u = (x3+1)3
The correct substitution to rewrite the equation 16(x^3 + 1)^2 - 22(x^3 + 1) - 3 = 0 as a quadratic equation is:
c. u = (x^3 + 1)^2
By substituting u = (x^3 + 1)^2, the equation can be rewritten as 16u - 22u - 3 = 0, which is a quadratic equation in terms of u.
To solve the quadratic equation for u, you can use factoring, completing the square, or the quadratic formula. Once you find the solutions for u, you can substitute back (x^3 + 1)^2 for u to obtain the solutions for the original equation.
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