Answers
The polynomial in factor form is y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3).
How to derive the equation of the polynomial
In this problem we find a representation of polynomial set on Cartesian plane, whose expression is described by the following formula in factor form:
y(x) = a · (x - r₁) · (x - r₂) · (x - r₃) · (x - r₄)
Where:
x - Independent variable.r₁, r₂, r₃, r₄ - Roots of the polynomial.a - Lead coefficient.y(x) - Dependent variable.Then, by direct inspection we get the following information:
y(0) = - 3, r₁ = - 3, r₂ = - 1, r₃ = 2, r₄ = 3
First, determine the lead coefficient:
- 3 = a · (0 + 3) · (0 + 1) · (0 - 2) · (0 - 3)
- 3 = a · 3 · 1 · (- 2) · (- 3)
- 3 = 18 · a
a = - 1 / 6
Second, write the complete expression:
y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3)
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Related Questions
If f(x)={x+4 if x≤−2
-x if x>−2,
what is f(−4)?
A. -2
B. 4
C. -4
D. 0
Answers
Since -4 is less than or equal to -2, we use the first part of the definition of f(x) which is f(x) = x + 4 if x ≤ -2. Therefore,
f(-4) = (-4) + 4 = 0.
So, the answer is D. 0.
Four family members attended a
family reunion. The table below
shows the distance each person
drove and the amount of time each
person traveled.
Answers
If each person drove at a constant rate,than Laura drove the fastest
What is the distance ?Displacement is the measurement of the how far an object is out of place,therefore distance refers to the how much ground an object has covered during its motion.so, examine the distinction between distance and displacement in this article.
What is the speed?The means of Speed is :he speed at which an object of location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. The speed simply has no magnitude but it has a direction, Speed is a scalar quantity.
to compute who drove the quickest by Using this formula
speed=Distance /time,
first of all the convert times into hours:
Hank: 3.2 hours x 3 hours and 12 minutes.
Laura: 2.5 hours is 2 hours and 30 minutes.
Nathan: 2.25 hours is 2 hours and 15 minutes.
Raquel: 4 hours plus 24 minutes equals 4.4 hours.
now to calculate the speed by above formula
Hank: 55 miles per hour for 176 miles in 3.2 hours.
Laura: 60 miles per hour equals 150 miles in 2.5 hours.
Nathan: 50 miles per houris equal to 112.5 miles in 2.25 hours.
Raquel: 65 miles for 286 miles in 4.4 hours.
As a result, Laura moved the fastest, clocking in at 60 miles. The solution, Laura, is B.
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Please help with this math question!
Answers
The exponential function of the population is P(x) = 15000 * 1.046^x
Calculating the exponential function of the populationFrom the question, we have the following parameters that can be used in our computation:
Initial, a = 15000
Rate, r = 4.6%
The equation of the function is represented as
P(x) = a * (1 + r)^x
Substitute the known values in the above equation, so, we have the following representation
P(x) = 15000 * (1 + 4.6%)^x
Evaluate
P(x) = 15000 * 1.046^x
Hence, the function is P(x) = 15000 * 1.046^x
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How long did Lizzie practice on Thursday and Friday altogether?
J
P
D
Lizzie's Drum Practice
P
S
P
D
P
S
S
Monday Tuesday Wednesday Thursday Friday
= 5 minutes
DONE
0
minutes
7 8
4
00
5
1 2
0
9
6
3
Answers
Answer:
Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.
On Thursday, she practiced for 5 minutes according to the table.
On Friday, she practiced for 9 minutes according to the table.
Adding these two times together, we get:
5 minutes + 9 minutes = 14 minutes
Therefore, Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.
8. You and 4 friends are going to an event, and you want to keep the cost below $100 per person. Write and solve an inequality to find the total cost, x.
Answers
Show that by the uniqueness theorem the linear transformation,
Y = aX + b, is also a normal random variable.
Answers
We can show by the uniqueness theorem that the linear transformation, Y = aX + b, is also a normal random variable because the resultant probaility density fnction of Y equals: f(y) = (1/√(2πa^2σX^2)) * exp(-(y-aμX-b)^2/(2a^2σX^2)).
How to prove a normal random variableTo show that the linear transformation, Y = aX + b is a normal random variable, we need to demonstrate that it satisfies the properties of a normal distribution. This means that it should have a bell-shaped probability density function, mean, and variance.
We can prove that it meets the mean condition this way:
E(Y) = E(aX + b) = aE(X) + b = aμX + b
Next, we can prove that it meets the variance condition thus:
Var(Y) = Var(aX + b) = a^2Var(X) = a^2σX^2
Lastly, the probability density function is given as f(y) = (1/√(2πa^2σX^2)) * exp(-(y-aμX-b)^2/(2a^2σX^2)). This proves that the conditions for a normal random variable is met.
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The height distributions of two different classes at Dover elementary school are shown below both groups, have the same interquartile range how many times the third quartile range is the difference between the median height of the third grade class in the fourth grade class 1/4 1/2 two or four
Answers
The third quartile range is the difference between the median height of the third grade class and the fourth grade class, so the answer is two times.
Write an Algebraic Equation for each problem (include a let statement) and use it to solve the world problem
On number is eight less than five times another. If the the sum of the two numbers is 28, find the two numbers.
The smaller number is __.
The larger number is __.
Answers
The smaller number is 6 .
The larger number is 22
To solve this problem
Let's let x be the smaller number and y be the larger number.
From the problem, we know that one number is eight less than five times the other, so we can write:
y = 5x - 8
We also know that the sum of the two numbers is 28, so we can write:
x + y = 28
Now we have two equations in two variables. We can solve for one of the variables in terms of the other, and substitute that expression into the other equation to eliminate one variable.
Let's solve the first equation for x
x = (y + 8)/5
Now we can substitute this expression for x into the second equation:
(y + 8)/5 + y = 28
Multiplying both sides by 5 to eliminate the fraction, we get:
y + 8 + 5y = 140
Combining like terms, we get:
6y + 8 = 140
Subtracting 8 from both sides, we get:
6y = 132
Dividing both sides by 6, we get:
y = 22
Now we can use the equation y = 5x - 8 to solve for x:
22 = 5x - 8
Adding 8 to both sides, we get:
30 = 5x
Dividing both sides by 5, we get:
x = 6
Therefore, the smaller number is 6 and the larger number is 22.
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In triangle BC, point D is on AC such that AD = 12 and CD = 12. If angle ABC = angle BDC = 90 degrees, then what is BD?
Answers
Answer:
Step-by-step explanation:
BD is craxking treys and cracking treys is gd dissing bd you can look it up i ffrom o block and bd is the opps im telling so you wont lose yo life so please play right if you gdk be gdk if u gd be gd we aint bd ofn
Write the absolute value equation that has the following solutions.
One solution: x = 15
Answers
The absolute value equation is:
|x - 15| = 0
How to write the absolute value equation?We want an absolute value equation that only has the solution x = 15.
So we must have something equal to zero (so we avoid the problem with the signs that we can have with other numbers)
So the equation will be something like:
|x - a| = 0
And the solution is 15, so:
|15 - a | = 0
then a = 15
The equation is:
|x - 15| = 0
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Which of the numbers 0, 1, 2, 3 or 4 make the equation 8/y2 + 2 true?
Answers
None of the given numbers make the equation 8/y² + 2 true.
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
To solve this problem, we can substitute each of the given numbers (0, 1, 2, 3, 4) for y in the equation 8/y² + 2 and see if the equation is true.
Substituting y=0 would make the denominator of the fraction zero, which is undefined, so y=0 is not a valid choice.
Substituting y=1 would give us:
8/1² + 2 = 8 + 2 = 10
So, 1 is not the answer.
Substituting y=2 would give us:
8/2² + 2 = 8/4 + 2 = 2 + 2 = 4
So, 2 is not the answer.
Substituting y=3 would give us:
8/3² + 2 = 8/9 + 2 = 0.888 + 2 = 2.888
So, 3 is not the answer.
Substituting y=4 would give us:
8/4² + 2 = 8/16 + 2 = 0.5 + 2 = 2.5
So, 4 is not the answer.
Therefore, none of the given numbers make the equation 8/y² + 2 true.
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The salaries of six bank employees are $37,000, $38,500, $35,000, $37,000, $45,000, $40,000, and $75,000.
Which statement is true?
Question 1 options:
Both the median and mode are appropriate measures of center.
The mean, median, and mode are all appropriate measures of center.
Both the mean and median are appropriate measures of center.
The median is the only appropriate measure of center.
Answers
The correct answer is: Both the mean and median are appropriate measures of center.
What is statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of mathematical and computational tools to summarize and analyze large sets of data, with the goal of extracting meaningful insights and identifying patterns or trends.
Here,
The mean is the sum of all salaries divided by the number of salaries. In this case, the sum is:
37,000 + 38,500 + 35,000 + 37,000 + 45,000 + 40,000 + 75,000 = 307,500
And there are seven salaries. Therefore, the mean is:
307,500 / 7 = 43,928.57
The median is the middle value when the salaries are arranged in order from lowest to highest. First, we need to arrange the salaries in order:
35,000, 37,000, 37,000, 38,500, 40,000, 45,000, 75,000
The median is the middle value, which is 40,000.
The mode is the value that appears most frequently in the set of salaries. In this case, both 37,000 and 40,000 appear twice, so there is no unique mode.
Since the salaries are not symmetrically distributed, the mean is not a perfect measure of central tendency. However, it can still provide useful information about the "average" salary. On the other hand, the median is resistant to extreme values and may be a better measure of central tendency for this dataset. Therefore, both the mean and median are appropriate measures of center for this dataset.
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^4√p7
in exponential form.
Answers
Answer:1111
Step-by-step explanation:
k^2+6k=0 solve the quadratic equation by factoring
Answers
Answer:
K = √-6k
i did the math and got this answer and it was right
Can someone help me to answer these questions pleases
Listen to Kerry Washington perform Sojourner Truth's speech Ain't I a Woman. Then go to ST's version at the Sojourner Truth Project's website. Compare the differences between Frances Gage's (the one Washington read) and Marius Robinson's earlier version (the one ST read). You can read them here.
Answer the following questions:
1. List 3 differences between the Robinson version and the Gage version of the speech.
2. Why do you think it is important to hear both versions of the speech?
3. How do you think the differences changed the way people (in the north and the south) understood the context of her speech? How about now?
4. How does hearing the differences in dialect change the way you think about the speech?
answer them in at least 10 sentences.
When women’s rights activists spoke out, who were they advocating for, white women or African-American women?
What are the distinct arguments that Truth makes in her speech?
What is Truth saying about women’s rights?
Who is going to give them these rights?
How does Truth’s speech reflect intersectionality?
What passages in the speech reflect this?
Answers
1. In the Robinson version, Truth asks "And ain't I a woman?" four times, while in the Gage version she only asks it three times. 2. It is important to hear both versions of the speech because they highlight the ways in which historical documents can be altered and manipulated over time. 3. The differences between the two versions of the speech likely changed the way people in the north and south understood the context of her speech in significant ways. 4. Hearing the differences in dialect changes the way we think about the speech by highlighting the unique voice and perspective of the speaker.
What is speech?Speech is the act of expressing thoughts, ideas, or emotions through spoken words. It is a form of communication that allows individuals to convey information, share opinions, ask questions, and express feelings to others.
According to question:1. Three differences between the Robinson version and the Gage version of the speech are:
In the Robinson version, Truth says "I have as much muscle as any man" while in the Gage version she says "I have ploughed and planted, and gathered into barns, and no man could head me!".
In the Robinson version, Truth asks "And ain't I a woman?" four times, while in the Gage version she only asks it three times.
In the Robinson version, Truth refers to herself as a "colored woman" while in the Gage version she uses the term "African American".
2. It is important to hear both versions of the speech because they highlight the ways in which historical documents can be altered and manipulated over time. The differences between the two versions show how editors and publishers can change the meaning and impact of a text by making small modifications to it. Additionally, hearing both versions allows us to appreciate the nuances of language and dialect, and how different speakers can bring their own interpretations and emphasis to a text.
3. The differences between the two versions of the speech likely changed the way people in the north and south understood the context of her speech in significant ways. For example, the reference to "colored women" in the Robinson version would have been seen as more confrontational and controversial in certain regions. Today, the differences may help us appreciate the diversity and complexity of language, and how it reflects the cultural and historical contexts in which it is spoken.
4. Hearing the differences in dialect changes the way we think about the speech by highlighting the unique voice and perspective of the speaker. The dialect used in each version reflects the cultural and historical context of the time, and the different audiences that the speeches were intended for. By hearing the dialect of each version, we can better appreciate the ways in which language shapes our understanding of history and identity.
As for the next set of questions:
When women's rights activists spoke out, they were advocating for both white women and African-American women, although the experiences and struggles of African-American women were often ignored or marginalized within the movement.
Truth makes several distinct arguments in her speech, including that women deserve the same rights and respect as men, that the stereotype of women as weak and dependent is unjust, and that the experiences of African-American women are often overlooked in discussions of women's rights.
Truth is saying that women deserve equal rights and respect as men, and that the societal norms that limit women's opportunities and autonomy are unjust and unfounded.
Truth is arguing that women need to fight for their own rights, rather than waiting for men to give them these rights. She also emphasizes the importance of solidarity and mutual support among women.
Truth's speech reflects intersectionality by recognizing the ways in which race and gender intersect to create unique experiences of oppression and marginalization. She argues that the struggles of African-American women cannot be separated from the struggles of all women, and that a truly equitable society must address the needs and concerns of all marginalized groups. One passage that reflects this is when she says, "I have borne thirteen children, and seen most all sold off to slavery, and when I cried out with my mother's grief, none but Jesus heard me! And ain't I a woman?" This passage highlights the intersection of race, gender, and motherhood in Truth's experience.
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(a) What is the value of x? Show your work.
(b) What is the measure of angle C? Show your work.
Answers
In triangle ABC
a) The value of x = 29⁰
b) The angle c equal to 93⁰
What is a triangle?A triangle is a closed plane figure that is formed by connecting three line segments, also known as sides, at their endpoints. The three endpoints, or vertices, where the sides of the triangle meet are not collinear. Triangles are important in mathematics and geometry because they are the simplest polygon that can exist in two-dimensional space.
According to the given informationIn a triangle, the sum of all interior angles is always 180 degrees. Therefore, we can use this fact to find the value of x and angle c.
We know that:
angle a = 35⁰
angle b = 52⁰
angle c = 3(x+2)⁰
Using the fact that the sum of all interior angles in a triangle is 180 degrees, we can write:
angle a + angle b + angle c = 180
Substituting the values we know, we get:
35 + 52 + 3(x+2) = 180
Simplifying the equation, we get:
87 + 3x + 6 = 180
3x + 93 = 180
3x = 87
x = 29
Therefore, x = 29⁰
To find angle c, we can substitute the value of x into the equation we were given for angle c:
angle c = 3(x+2)
angle c = 3(29+2)
angle c = 3(31)
angle c = 93
Therefore, angle c is equal to 93⁰.
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3. How many ways can you line up 7 books on a shelf?
Answers
Answer:
There are 5040 different ways to arrange the 7 books on a shelf.------------------------------
Use the formula for permutations:
n! = n × (n - 1) × (n - 2) × ... × 1, where n is the number of objects and ! denotes a factorial.The number of objects is n = 7 books.
Calculate the factorial:
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040A farmer is building a fence to enclose a rectangular area against an existing wall, shown in the figure below. Three of the sides will require fencing and the fourth wall already exists. If the farmer has 176 feet of fencing,
what is the largest area the farmer can enclose?
Answers
Answer: 46 ft by 92 ft
Step-by-step explanation:
The largest area is enclosed when half the fence is used parallel to the wall and the other half is used for the two ends of the fenced area perpendicular to the wall. Half the fence is 184 ft/2 = 92 ft. Half that is used for each end of the enclosure.
Find the area? For this shape pleae
Answers
please help me in this question is math,solve just d, e&f
Answers
Step-by-step explanation:
a) factorize A
A = (2x-1)²+2(3-6x)(4x-7)-4x²+1
expand the terms
(2x-1)²-52x²+108x-41
factorize
(2x-1)²-(26x-41)(2x-1)
factor out the common factor 2x-1
-(2x-1)(24x-40)
A = -8(2x-1)(3x-5)
b) show that B = (3x-11)(2x-1)
6x²-25x+11
6x²-3x-22x+11
3x(2x-1)-11(2x-1)
(2x-1)(3x-11)
c) Expand and reduce A
(2x-1)²+2(3-6x)(4x-7)-4x²+1
-48x²+108x-40
d) Calculate A for x=0 and x=-1
when x=0 -48(0)²+108(0)-40
A=0
x=-1 -48(-1)²+108(-1)-40
A=-196
e) Reduce 2A-3B
A=-48x²+108x-40 B=6x²-25x+11
2(-48x²+108x-40)-3(6x²-25x+11)
-96x²+216x-80-18x²+75x-33
-144x²+291x-113
f) Factorize 2A-B
A=-48x²+108x-40 B=6x²-25x+11
2(-48x²+108x-40)-(6x²-25x+11)
-96x²+216x-80-6x²+25x-11
-102x²+241x-91
x=(241 + sqrt(20953))/204
x=(241 - sqrt(20953))/204
Please Mark Me Brainliest!
Find the volume of this sphere.
Use 3 for TT.
-d=6in
V ≈ [?] in ³
V = πr³
Enter
Answers
Answer: Spheres aren’t three-dimensional—they are two-dimensional. This is evident from the fact that in order to specify a point on a sphere, you only need two pieces of information, such as latitude and longitude.
If you include the interior of the sphere, this is instead called a closed ball, and that is three-dimensional. You can specify a point in the closed ball in all sorts of different ways; one of the most convenient would be latitude, longitude, and distance from the center. However, other than convenience, there is no reason to prefer one coordinate system over any other.
(This fact has nothing to do with spheres or closed balls—that is just a statement that is generally true. People who insist that “the three dimensions” are length, width, and height don’t know what they are talking about.)
Step-by-step explanation: