Answers
We are asked to determine a polynomial that has the following roots:
\(1+\sqrt[]{2},2-i\)As roots. We will use a polynomial of degree 4 that has the roots:
\(1\pm\sqrt[]{2},2\pm i\)This means that the factors of the polynomials are:
\((x-(1+\sqrt[]{2})(x-(1-\sqrt[]{2}))(x-(2-i))(x-(2+i))\)Now we must expand the given factor in order to get a polynomial of rational coefficients. First, we will take the two first products:
\((x-(1+\sqrt[]{2})(x-(1-\sqrt[]{2}))\)Now we will reassociate terms inside each parenthesis:
\(((x-1)-\sqrt[]{2})((x-1)+\sqrt[]{2}))\)Now we apply the distributive law using the associated terms:
\((x-1)^2+\sqrt[]{2}(x-1)-\sqrt[]{2}(x-1)-(\sqrt[]{2})^2\)Simplifying:
\((x-1)^2-2\)Therefore, the first two products can be replaced by the term we just found:
\(((x-1)^2-2)(x-(2-i))(x-(2+i))\)Now we take the third and fourth products:
\((x-(2-i))(x-(2+i))\)Now we reassociate the terms:
\(((x-2)+i))((x-2)-i))\)Now we apply the distributive law:
\((x-2)^2+i(x-2)-i(x-2)-(i)^2\)Simplifying we get:
\((x-2)^2+1\)Now we can replace this for the third and fourth products:
\(((x-1)^2-2)((x-2)^2+1)\)Now we solve the squares in each parenthesis:
\((x^2-2x+1-2)(x^2-4x+4+1)\)Adding like terms:
\((x^2-2x-1)(x^2-4x+5)\)Now we apply the distributive property:
\(x^4-4x^3+5x^2-2x^3+8x^2-10x-x^2+4x-5\)Adding like terms we get:
\(x^4-6x^3+12x^2-6x-5\)And thus we get the desired polynomial.
Related Questions
Solve.
4 There are 42 tubes of oil paint on trays. Each tray
holds 6 tubes. How many trays of tubes are there?
Show your work.
7
Answers
Answer: 7
Step-by-step explanation:
Since there are 42 tubes and each tray can hold 6 tubes, it will be 42/6 which is 7.
Esther put $400 into a bank account 3 years ago. Now there is $422 in the account. What is the percent increase?
Answers
Answer:
5.50%
Step-by-step explanation:
Answer:
5.5% increase
Step-by-step explanation:
Solution
You subtract value to from value 1 put it in a fraction and x it by 100 and there's your answer.
Calculations
422 - 400=22
Next in fraction 22/400=0.055
0.055 x 100=5.5
And there's you answer.
Hope it helps have a magnificent day
Plssss help me quickly
Answers
Answer:
36
Step-by-step explanation:
First you calculate the area of the rectangle. then you substract the area of the triangle.
The area of a rectangle is equal to the product of its length and breadth. In other words, if the length of a rectangle is ‘l’ and its breadth is ‘b’, then its area ‘A’ can be calculated as A = l x b= 6*8= 48
The area of a triangle can be calculated using the formula A = 0.5 x b x h where ‘b’ is the length of the base of the triangle and ‘h’ is its height. so A =0.5*8*3 = 12
Area of the figure = 48-12=36
You are at a restaurant and your bill comes to $34.78. You need to add the sales tax which
is 6%. You have one $20 bill, two $10 bills, one $5 bill, five $1 bills, and some pennies.
.
.
.
How much is your total bill including tax?
How much should you give the server so you do not get back any pennies?
What denominations will you use for this?
Use the equation editor to show your work.
Answers
In word problem , the Total bill including tax = $34.78+$2.08 = $36.86
and you have to give server one $20 bill , one $10 bill, one $5 bill and two $1 bill, so yo don't get any pennies back.
What is word problem?
Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.
Here the bill = $34.78
Sales tax= 6% of Bill
=> Sales tax = 6% of 34.78
=> Sales tax = \(\frac{6}{100}\times 34.78\)
=> Sales tax = $2.08
Now the Total bill including tax = $34.78+$2.08 = $36.86
Hence you have to give server one $20 bill , one $10 bill, one $5 bill and two $1 bill, so yo don't get any pennies back.
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3 yd 9 yd 6 yd 14 yd 5 yd 9 yd N 5) What is the area of the figure? A) 18 yd2 B) 54 yd2 C) 72 yd2 D) 90 yd2
Answers
Answer:
To figure out the area of the figure, we will divide the shape into two parts as in the image below
Step 1:
The formula to calculate the area of Part A is
\(\begin{gathered} Area_A=l\times b \\ l=9yd,b=3yd \end{gathered}\)By susbstituting the values, we will have
\(\begin{gathered} Area_A=l\times b \\ Area_A=9yd\times3yd \\ Area_A=27yd^2 \end{gathered}\)Step 2:
Calculate the area of part B
\(\begin{gathered} Area_B=l\times b \\ l=9yd,b=5yd \\ \end{gathered}\)By substituting the values, we will have
\(\begin{gathered} Area_B=l\times b \\ Area_B=9yd\times5yd \\ Area_B=45yd^2 \end{gathered}\)Hence,
The area of the figure will be
\(\begin{gathered} A_{figure}=Area_A+Area_B \\ A_{figure}=27yd^2+45yd^2 \\ A_{figure}=72yd^2 \end{gathered}\)Hence,
The final answer is
\(\Rightarrow72yd^2\)OPTION C is the right answer
u/8 = 3/6 solve for u
Answers
Answer:
Step-by-step explanation:
"To solve U/8 = 3/6 for U, you can start by cross-multiplying to get:
6U = 8 x 3
Then, you can simplify by dividing both sides by 6:
U = (8 x 3) / 6
U = 4
Therefore, U = 4. Does that help?"
Please help me please help help me help please
Answers
Answer:
An equation of a line is written in the form y=mx+b. ”m” is the slope and ”b” is the y-intercept. So, substituting the values, the equation is y=-4x+1.
:)
Which choice is equivalent to the quotient below? √14/2√2 A.√7/2 B.√7/√2 C.√7 D.√7/4
Answers
Y and X can both be proportional if:
A. product of Y and X is constant
B. quotient of Y and X is constant
C. increase by x + 2
D. increase by 2x
Answers
Answer: B. quotient of Y and X is constant.
Step-by-step explanation:
If Y and X are proportional, it means that as one variable increases, the other variable also increases or decreases by a constant factor. Mathematically, this can be represented as Y = kX, where k is the constant of proportionality.
If we take the quotient of Y and X, we get:
Y/X = k/X
Here, we can see that the quotient of Y and X is proportional to the constant of proportionality k divided by X. Therefore, if Y and X are proportional, their quotient should be constant.
Answer: B. quotient of Y and X is constant.
Step-by-step explanation:
If Y and X are proportional, it means that as one variable increases, the other variable also increases or decreases by a constant factor. Mathematically, this can be represented as Y = kX, where k is the constant of proportionality.
If we take the quotient of Y and X, we get:
Y/X = k/X
Here, we can see that the quotient of Y and X is proportional to the constant of proportionality k divided by X. Therefore, if Y and X are proportional, their quotient should be constant.
giving 90 points! NEED IN TWO MINS
Answers
Answer:
300
Step-by-step explanation:
A=wl=10·30=300
multiply the length of the rectangle by the width of the rectangle.
The area is measurement of the surface of a shape. To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle or a square. Area, A, is x times y.
Answer:
Area = 378.5 ft²
Step-by-step explanation:
The figure is having two semi circles and one rectangle.
\({ \sf{area = area \: of \: semicircles + area \: of \: rectangle}} \\ \\ { \sf{area = 2( \frac{1}{2} \pi {r}^{2}) + (l \times w) }} \\ \\ { \sf{area = \pi {r}^{2} + (l \times w) }} \\ \\ { \sf{area = 3.14 \times {5}^{2} + (30 \times 10)}} \\ \\ { \sf{area = 378.5 \: {ft}^{2} }}\)
Just a little made up question (20 points). Jack had drunken 120 water bottles in a year. His friend Sam had drunk 98, And Archy had drunk 150. What is the amount of water bottles they drunk altogether?
Answers
Find the midpoint of G and P.
4
5
2
2
Answers
Answer:
2
Step-by-step explanation:
I'm pretty sure it's around 2. P takes 5 jumps to the left (one number per jump) and lands at 2. G takes 5 jumps to the right and ends up around 2.
Answer:
the answer is 2 1/4
Step-by-step explanation:
i had this same question and i came here for help. The other person who answered said 2 and i tried both because on mine the options were
4 1/2
2 1/4
2
and 5.
i had already tried 4 1/2 and 2 so that wasn't it. that would leave 2 1/4 because there was no way it would be 5. 2 1/4 was correct.
P.s i don't know if you still need this answer but here ya go :)
Write the Roman Numeral CXXXIV in standard???
Answers
Answer:
Step-by-step explanation: C is 100 X is 10 IV is 4 since the smaller number is in the front so you subtract instead of add
C=100 3X=30 IV=4
100+30+4=134
CXXXIV=134
The quotient of m and 7.
Answers
Can someone Please help
Answers
Answer:
80
Step-by-step explanation:
20+80+x=180
100+x=180
x=180-100
x=80
plz mark as brainliest
Give the domain and range.
0 2 4 - 2 6 10
a. domain: {0, 2, 4), range: {2, 6, 10}
b. domain: {0}, range: {2}
c. domain: {2, 6, 10), range: {0, 2,4}
d. domain: {2}, range: {0}
Answers
Answer:
The domain: {0, 2, 4}
The range: {2, 6, 10}
Thus, option (a) is correct.
Step-by-step explanation:
From the given diagram
The set X = {0, 2, 4}The set Y = {2, 6, 10}We know that the domain of a relation is the set of all the x-values of the set X. In other words, the domain of relation includes all the input values.
Thus, the domain: {0, 2, 4}
We know that the range of a relation is the set of all the y-values of the set Y. In other words, the range of relation includes all the output values.
Thus, the range: {2, 6, 10}
Therefore, option (a) is correct.
The population of a city was 10,000 in 2010. The population increase at an annual rate of 2.5% per year. Is the growth model function that represents the population of the city linear?
Answers
Answer:
The growth model that represents the population of this city is not linear--it is exponential:
\(f(t) = 10000( {1.025}^{t} )\)
\(t = 0 \: represents \: 2010\)
Si una mujer tiene en su closet 7 camisas,3 pares de zapatos y 4 pantalones ¿de cuántas formas se puede vestir?
Answers
Answer:
14 veces Step-by-step explanation:
The width of a rectangle measures (3.8b-1.5) centimeters, and it's length measures (4.3b-7.2) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle
A.) -17.4+16.2b
B.) -2.9+2.3b
C.) 4.6-5.8
D.) 8.1b-8.7
Answers
Answer:
-17.4+16.2b
Step-by-step explanation:
I just guessed and it was right
What is the range of the conic section?
(yl-3≤y≤3)
Answers
Answer:
1the answer for this is easy it is 4.4
The measure of m < JML is 85* . Select all the true statements.
Answers
The true statements about given angle JML are:
option C. m∠JMK = 50°
option D. m∠KML = 35°
In this question, we have been given the measure of an acute angle ∠JML = 85°
We need to find the true statements.
From given figure, we can clearly see that,
∠JML = ∠JMK + ∠KML ...............(1)
85° = (6x + 2)° + (4x + 3)°
85 = 10x + 5
80 = 10x
x = 8
So, the measure of ∠JMK would be,
⇒ m∠JMK = (6x + 2)°
⇒ m∠JMK = (48 + 2)°
⇒ m∠JMK = 50°
From (1),
m∠JML = m∠JMK + m∠KML
85° = 50° + m∠KML
m∠KML = 35°
Therefore, the true statements about given angle JML are:
option C. m∠JMK = 50°
option D. m∠KML = 35°
Learn more about an angle here:
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How does the slope of g(x) compare to the slope of f(x)? f(x) g(x) O The slope of g(x) is the opposite of the slope of f(x). O The slope of g(x) is less than the slope of f(x). The slope of g(x) is greater than the slope of f(x). O The slope of g(x) is equal to the slope of f(x). 43_-2-14 5 X -2
Answers
Answer: Tell me if i am wrong
The answer is 'The slope of g(x) is less than the slope of f(x)'
Step-by-step explanation:
Given the graphs of f(x) and g(x). we have to compare the slops of these two.
The graph of f(x) passes through the points (1,0) and (2,2)
∴ The slope of \(f(x) = \frac{y2-y1}{x2-x1}=\frac{2-0}{2-1} = 2\)
The graph of g(x) passes through the points (0,2) and (2,3)
∴ The slope of \(g(x)=\frac{y2-y1}{x2-x1} =\frac{3-0}{2-0} =\frac{1}{2}\)
As \(\frac{1}{2} <2\)
This shows that the
The slope of g(x) is less than the slope of f(x).
Solve
-12 + 23
A. -35
B. -11
C. 11
D. 35
Answers
Answer:
C. 11
Step-by-step explanation:
This can be rewritten as
23 - 12
This is equal to 11.
Answer:
11
Step-by-step explanation:
-12 + 23 = 11
since the 12 is negative subtract it from 23 and you get 11 as your answer
If a triangle has a height of 13 and a base of 6, what is the area in square units?
Answers
Answer:
39 square units
Explanation:
\(\text{The area of a triangle}=\frac{1}{2}\times\text{Base}\times\text{Height}\)Given:
• Height=13 units
,• Base = 6 units
Therefore, the area of the triangle is:
\(\begin{gathered} =\frac{1}{2}\times6\times13 \\ =39\text{ square units} \end{gathered}\)the Missing Angles (plus angle review)<8 of 16Whats the measure of each of the angle in degrees? Label the angles, then answer,Subm104056°
Answers
A is angle opposite by the vertex with the angle of 104 degrees, that is why it also measure 104 degrees
The three inner angles of any triangle add 180 degrees, then 56 + A + B = 180
Solving for B: B = 180 - 56 - A = 180 - 56 - 104 = 20
write an equation for the line through the point (-7,-4) and parallel to the line y=8x-4 in point-slope form
Answers
The equation for the line through the point (-7,-4) and parallel to the line y = 8x - 4 in point-slope form is y = 8x + 52
How to determine the equation of the second line?The first equation is given as
y = 8x - 4
The slope of the above equation is
m = 8
Parallel lines have equal slope
So, the slope of the other line is
m = 8
The equation is then calculated as
y = m(x - x1) + y1
Where
m = 8
(x1, y1) = (-7, -4)
So, we have
y = 8(x + 7) - 4
Expand
y = 8x + 56 - 4
Evaluate the difference
y = 8x + 52
Hence, the equation for the line through the point (-7,-4) and parallel to the line y = 8x - 4 in point-slope form is y = 8x + 52
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Find the missing term in the following pattern.
320, 160, 80 blank space then, 20, 10
Answers
40
Step-by-step explanation:
Each number is followed by a number that is half its value, so the sequence goes like
320, 160, 80, 40, 20, 10.
Paul can type 40 words per minute. If he types at the same rate, how many words can Paul type in 30 minutes?
Answers
Answer:
1200
Step-by-step explanation:
since he can type 40 words per minute just times 40 by 30
Autism and Maternal Antidepressant Use A recent study41 compared 298 children with Autism Spectrum Disorder to 1507 randomly selected con- trol children without the disorder. Of the children with autism, 20 of the mothers had used antidepres- sant drugs during the year before pregnancy or the first trimester of pregnancy. Of the control children, 50 of the mothers had used the drugs.
(a) Is there a significant association between prena- tal exposure to antidepressant medicine and the risk of autism? Test whether the results are sig- nificant at the 5% level.
(b) Can we conclude that prenatal exposure to antidepressant medicine increases the risk of autism in the child? Why or why not?
Answers
Answer:
(a) We conclude that there is a significant association between prenatal exposure to antidepressant medicine and the risk of autism at 5% significance level.
(b) Yes, we can conclude that prenatal exposure to antidepressant medicine increases the risk of autism in the child.
Step-by-step explanation:
We are given that Autism and Maternal Antidepressant Use A recent study 41 compared 298 children with Autism Spectrum Disorder to 1507 randomly selected control children without the disorder.
Of the children with autism, 20 of the mothers had used antidepressant drugs. Of the control children, 50 of the mothers had used the drugs.
Let \(p_1\) = proportion of mothers who had used drugs having Autism Spectrum Disorder in their children.
\(p_2\) = proportion of mothers who had used drugs not having Autism Spectrum Disorder in their children.
(a) Null Hypothesis, \(H_0\) : \(p_1=p_2\) {means that there is no significant association between prenatal exposure to antidepressant medicine and the risk of autism}
Alternate Hypothesis, \(H_A\) : \(p_1\neq p_2\) {means that there is a significant association between prenatal exposure to antidepressant medicine and the risk of autism}
The test statistics that would be used here Two-sample z test for proportions;
T.S. = \(\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }\) ~ N(0,1)
where, \(\hat p_1\) = sample proportion of mothers who had used drugs having Autism Spectrum Disorder in their children = \(\frac{20}{298}\) = 0.067
\(\hat p_2\) = sample proportion of mothers who had used drugs not having Autism Spectrum Disorder in their children = \(\frac{50}{1507}\) = 0.033
\(n_1\) = sample of children with Autism Spectrum Disorder = 298
\(n_2\) = sample of children without Autism Spectrum Disorder = 1507
So, the test statistics = \(\frac{(0.067-0.033)-(0)}{\sqrt{\frac{0.067(1-0.067)}{298}+\frac{0.033(1-0.033)}{1507} } }\)
= 2.281
The value of z test statistics is 2.281.
Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.
Since our test statistic doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that there is a significant association between prenatal exposure to antidepressant medicine and the risk of autism.
(b) Yes, we can conclude that prenatal exposure to antidepressant medicine increases the risk of autism in the child because if we reconsider our hypothesis for one-tailed test in which the null hypothesis states that the prenatal exposure to antidepressant medicine does not increases the risk of autism in the child.
For this hypothesis also, our test statistics will be more than the critical value of z and due to which we reject our null hypothesis and conclude that prenatal exposure to antidepressant medicine increases the risk of autism.
you have decided to give your best friend a bag of
red and green marbles for his birthday. your friend
likes green marbles better than red ones, so the
bag has twice as many green marbles as red. The
label on the bag says it lcontains a total of 84 marbles.
How many green marbles are in the bag? Write a
System of equations for this problem. Then solve the
problem using any method you like. Be sure to check
your solutions
Answers
Answer:
There are 28 red marbles and 56 green marbles in the bag.
Step-by-step explanation:
Let's define:
R = number of red marbles in the bag.
G = number of green marbles in the bag.
We know that:
"There is a total of 84 marbles in the bag"
Then we can write this as:
R + G = 84
"The bag has twice as many green marbles as red marbles"
Then:
G = 2*R
So we have two equations:
R + G = 84
G = 2*R
This is the system of equations we need to solve.
To solve this, we usually start by isolating one of the variables in one of the equations, here we can see that G is already isolated in the second equation, then we can ignore the first step.
Now that we have an isolated variable, we can replace it in the other equation, then we can replace the second equation in the first one to get:
R + G = 84
R + (2*R) = 84
3*R = 84
R = 84/3 = 28
This means that there are 28 red marbles in the bag.
Now we can use the equation:
G = 2*R
To find the number of green marbles, where we need to replace R y 28, then we get:
G = 2*28 = 56
Which means that there are 56 green marbles.