Find a polynomial function of least degree having only real coefficients, a leading coefficient of 1, and roots of 1-√6 , 1+ √6 , and 7-i

Answers

Answer 1

Step-by-step explanation:

Use this algebra 2 theorem:

If r and q are roots of a polynomial function then

the polynomial function can be expressed as

[tex](x - r)(x - q)[/tex]

Here the roots are

1- root of 6, 1+ root 6, and. 7-i so our. function can be expressed as

[tex](x - (1 - \sqrt{6} ))(x - (1 + \sqrt{6} ))(x - (7 - i))[/tex]

The first two binomials are difference off squares so the we have

[tex] {x}^{2} + x( - 1 + \sqrt{6} ) + x( - 1 - \sqrt{6} ) + ( - 5)[/tex]

[tex] {x}^{2} - 2x - 5[/tex]

The other root is (7-i).

Also note since (7-i) is a root, then (7+I) is also a root.

So

[tex](x - (7 - i)(x - (7 + i)( {x}^{2} - 2x - 5)[/tex]

[tex]( {x}^{2} - 14x + 50)( {x}^{2} - 2x - 5)[/tex]

Simplify and it gives us

[tex] {x}^{4} - 16 {x}^{3} + 73 {x}^{2} - 30x - 250[/tex]


Related Questions

The function f represents the marketing team's expected number of user profiles after x months, when the domain is restricted to all real or hole

Answers

The standard equation of user will be y = 625x²+1250x+5000

A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

A connection or statement involving one or more variables is called a function.

From the graph we can find following equation:

(0,5000) ----------- 5000 = [tex]\frac{1}{4(f-k)}(0-h)^2 +k[/tex]

(2,10000) ---------- 10000 = [tex]\frac{1}{4(f-k)}(2-h)^2 +k[/tex]

(4,20000) --------- 20000 = [tex]\frac{1}{4(f-k)}(4-h)^2 +k[/tex]

Solving the above three equations we will get following values:

h = -1

k = 4375

f = 10937501/2500

Hence the standard equation of user will be y = 625x²+1250x+5000

Learn more about functions here:

https://brainly.com/question/4025726

#SPJ10

This is confusing please help

Answers

Step-by-step explanation:

Since we have a right triangle, we use the Pythagorean Theorem

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

or

[tex]c = \sqrt{ {a}^{2} + {b}^{2} } [/tex]

where a and b are the legs and c is the hypotenuse

Remember the legs are the sides that form that right angle, and the hypotenuse is the side opposite of the right angle.

So here the hypotenuse is 8, and one of the legs is 4. So we plug those values into the formula

[tex] 8 = \sqrt{ {b}^{2} + {4}^{2} } [/tex]

In testing for differences between the means of two dependent populations where the variance of the differences is unknown, the degrees of freedom are:

Answers

The degrees of freedom in testing for differences between the means of two dependent populations where the variance of the differences is unknown are: df = n - 1

What is the degree of freedom for dependent variables?

In statistics, degrees of freedom refers to the number of distinct values that can change in an evaluation without exceeding any constraints.

The degree of freedom is crucial and necessary when attempting to comprehend the significance of a test statistic and the validity of the null hypothesis.

In testing for differences between the means of two dependent populations where the variance of the differences is unknown, the degrees of freedom are: df = n - 1

Learn more about calculating degrees of freedom for dependent variables here:

https://brainly.com/question/14311814

#SPJ12

You are asked to create a new computer password made up of 4 digits followed
by 3 letters.
Determine how many different computer passwords are possible if digits and
letters cannot be repeated.

Answers

Answer:if we start with 26 letters in the English/Latin alphabet: 26*25*24*23*

and modern Arabic numerals 0–9,

10*9 do the math by multiplying all

Number of dispositions of 4 letters without repetitions of the alphabet (26 letters): 26*25*24*23=358800. 2-digit numbers without repetitions:10*9=90. Number of passwords with 4 letters and 2-digit number without repetitions:

a) if the 2-digit numbers must be in one single position (examples:….XB73DY……..GZ57FE): 358800*90 = 32,292,000.

b) if the 2-digit numbers can be in each of the 5 possible positions (ex.:…73XBDY…X73BDY..XB73DY..XBD73Y..XBDY73…) 5*358800*90=161,460,000.

c) if both digits can be in (C6;2) = 6*5/2= 15 positions (ex.: 7XB3DY…X73BDY…..) 15*358800*90=484,380,000.26*25*24*23*10*9 = 32,292,000

Step-by-step explanation:

I need help with this: -1/4 x (-7/9)

Answers

Multiply -1/4 by -7/9 ((To do this, multiply the numerator by the numerator and the denominator by the denominator.)

[tex]\bf{\dfrac{-1(-7)}{4\times9)} \ \ \to \ \ \ Multiply }[/tex]

Do the multiplications in the fraction -1(-7) / 4 x 9.

[tex]\bf{\dfrac{7}{36} \ \ \Rightarrow \ \ \ Answer }[/tex]

{ Pisces04 }

A group of fitness club members lose a combined total of 28 kilograms in 1 week. There are approximately 2.2 pounds in 1 kilogram. Assuming the weight loss happened at a constant rate, about how many pounds did the group lose each day?

Answers

Answer:8.8 pounds a day

Step-by-step explanation:

7 days in a week

28/7=4 kg a day

2.2*4=8.8

8.8 pounds

The table shows the age of some participants in a quiz competition and the number of questions they could answer correctly:
Age (years) (x)
15 21
17 22 16 19 18
Number of questions they could answer (y) 17 17 17 17 17 17 17
What is the correlation coefficient for the data, and what does it represent?
O0; it represents no correlation between x and y
O1; it represents a linear positive correlation between x and y
O-1; it represents a linear negative correlation between x and y
O1; it represents a linear negative correlation between x and y

Answers

Option first "0; it represents no correlation between x and y" is correct there is no relation between x and y.

What is correlation?

It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.

[tex]\rm r = \dfrac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{{[n\sum x^2- (\sum x)^2]}}\sqrt{[n\sum y^2- (\sum y)^2]}}[/tex]

 

We have:

Age (years) (x)                                                     15  21   17  22  16  19  18

Number of questions  they could answer(y)    17  17   17  17    17  17  17

As we can see all y values are the same.

n∑y² = 7(2023) = 14161

(∑y)² = 119² = 14161

If we put the value of the above data the value will become undefined.

Thus, option first "0; it represents no correlation between x and y" is correct there is no relation between x and y.

Learn more about the correlation here:

brainly.com/question/11705632

#SPJ1

Given the figure below solve for X

Answers

Answer:

x = 37

Step-by-step explanation:

Suppose ∠A and ∠B are complements, while ∠B and ∠C are supplements. If m∠A=3x+17, m∠B=55−x, and m∠C=67(x/3−1), then m∠A=44, m∠B=46, and m∠C=134. TRUE OR FALSE? Please show your work.

Answers

Answer:

TRUE

Step-by-step explanation:

Angle <A and angle <B are complementary, which means their sum must be = 90

Angle <B and angle <C are supplementary which means their sum must be = 180

Now let's see

m∠A=3x+17, m∠B=55−x, and m∠C=67(x/3−1)

first find the sum of A and B

3x + 17 + 55 - x = 90 add like terms

2x + 72 = 90 subtract 72 from both sides

2x = 18 divide both sides by 2

x = 9

TRUE OR FALSE is asked for

m∠A=44, m∠B=46, and m∠C=134

to find that we just replace c with 9 with every expression given for angles

m<A = 3x + 17

m<A = 3*9 + 17 = 44

m<B =  55 - x

m<B = 55 - 9 = 46

m<C = 134, we don't really need to calculate one by one since the angle are complementary and supplementary.

The answer is TRUE

The statement is true if A and ∠B are complements, while ∠B and ∠C are supplements.

What is an angle?

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have:

∠A and ∠B are complements, while ∠B and ∠C are supplements.

∠A + ∠B = 90 degree

3x + 17 + 55 - x = 90

2x = 18

x = 9

Angle ∠B and angle ∠C are supplementary:

∠B + ∠C = 180

55 -x + 67(x/3  - 1) = 180

x = 9

Put the value of x and find angles A, B, and C.

m∠A = 44

m∠B = 46

m∠C = 134

∠A + ∠B = 90

∠B + ∠C = 180

The above statement is true.

Thus, the statement is true if A and ∠B are complements, while ∠B and ∠C are supplements.

Learn more about the angle here:

brainly.com/question/7116550

#SPJ


This probability distribution shows the
typical grade distribution for a Geometry
course with 35 students.
Grade
A B
C
D F
Frequency 5 10 15 3 2
Find the probability that a student earns a

Answers

Answer:

14.3%

Step-by-step explanation:

5 students got an A out of 35 total students. This means that the probability of students getting an A is 5/35 = 0.1428

helppppp pleaseee tap or click picture if needed​

Answers

Answer:

A

Step-by-step explanation:

He saves allowance for 5 months     5 months * $6 = 30 dollars

  30 ÷ 3      would be the # of rides he can go on

Which of the following values can be found by using the formula √1+tan^2 0?

Answers

√1+tan²Ø√1+sin²Ø/cos²Ø√cos²Ø+sin²Ø/cos²Ø√1/cos²Ø1/cosØsecØ

cos and sec can be found

The requried simplified expression is 1 / cosØ, which is equivalent to secØ. The correct option is secØ.

Let's simplify the given expression and see which of the provided options match:

We are given the expression √(1 + tan²Ø).

Now, recall the trigonometric identity: tan²Ø = sin²Ø / cos²Ø.

Substitute this identity into the expression:

√(1 + sin²Ø / cos²Ø)

Next, find a common denominator for the fraction inside the square root:

√((cos²Ø + sin²Ø) / cos²Ø)

Since cos²Ø + sin²Ø = 1 (as per the Pythagorean trigonometric identity), the expression becomes:

√(1 / cos²Ø)

Now, we can take the square root of 1 and cos²Ø separately:

√1 / √cos²Ø

Simplify:

1 / cosØ

The simplified expression is 1 / cosØ, which is equivalent to secØ.

Therefore, the correct option is: secØ.

Learn more about trigonometry here:

https://brainly.com/question/20885025

#SPJ4

Please help answer needed asap

Answers

Answer:

A

Step-by-step explanation:

a = 3n-30       solve for 'n'

a + 30 = 3n

n = (a+30)/3

n(a) = (a+30)/3

What function is shown in the graph above?

Answers

By definition of linear functions and the comparison with the attached figure, the function that represents the graph is y = (7/15) · x + 4, - 6 ≤ x ≤ 9.

What kind of function represents the graph?

Graphically speaking, linear functions represent lines and we see that the line seen in the figure presents two bounds, the points (- 6, 0) and (9, 7). Linear functions are characterized by slope and intercept:

y = m · x + b     (1)

Slope

m = (7 - 0)/[9 - (- 6)]

m = 7/15

Intercept

b = 4

By definition of linear functions and the comparison with the attached figure, the function that represents the graph is y = (7/15) · x + 4, - 6 ≤ x ≤ 9.

To learn more on linear functions: https://brainly.com/question/14695009

#SPJ1

Which function is shown in the graph below?

Answers

Answer: c

Step-by-step explanation:

It has been given that the point (3,1) is on the graph.

And in order for the point (3,1) to lie on the graph, of all the given options the closest we can get is when we have Option C

NEED HELP ASAP! ITS IN THE IMAGE BELOW.
i’ve done the graph which is part a and b but i need help in part c and d, help will be appreciated!

Answers

Answer:

(a)  see below

(b)  see attached

(c)  (15, 180) is not on the line

(d)  a = -40

Step-by-step explanation:

Given equation:

[tex]y = 10x+20[/tex]

Part (a)

To complete the table of values, simply substitute each value of x into the given equation:

[tex]x=-3 \implies y=10(-3)+20=-10[/tex]

[tex]x=-1 \implies y=10(-1)+20=10[/tex]

[tex]x=0 \implies y=10(0)+20=20[/tex]

[tex]x=1 \implies y=10(1)+20=30[/tex]

[tex]x=3 \implies y=10(3)+20=50[/tex]

[tex]\large \begin{array}{| c | c | c | c | c | c | c | c |}\cline{1-8} x & -3 & -2 & -1 & 0 & 1 & 2 & 3\\\cline{1-8} y & -10 & 0 & 10 & 20 & 30 & 40 & 50\\ \cline{1-8} \end{array}[/tex]

Part (b)

Plot 2 points from the table and draw a straight line through them.

Part (c)

To determine if (15, 180) is on the line, substitute x = 15 into the given equation of the line:

[tex]\begin{aligned} x=15 \implies y & =10(15)+20\\& = 150 + 20\\& = 170\end{aligned}[/tex]

Therefore (15, 180) is not on the line

Part (d)

If (-6, a) is on the line, substitute x = -6 and y = a into the equation and solve for a:

[tex]\begin{aligned} y & = 10x+20\\\implies a & = 10(-6)+20\\a & = -60 + 20\\a & = -40\end{aligned}[/tex]

Therefore, a = -40

I need help asp. Identifying Geometric Figures.

Answers

Answer:

The angle created by OX and OZ is angle XOZ

The two rays that create YOX are ray OX and ray OY

The center of the circle is point O

Step-by-step explanation:

The image attached below shows a circle with a center at point O at which several rays meet to form the following angles, namely:

ray OX and ray OZ meet at center O to form angle XOZ.

ray OX and ray OY meet at the center O to form angel YOX.

Therefore:

The angle created by rays OX and OZ is <XOZ

The two rays that created <YOX are: OX and OY

The center of the circle is point O.

I hope this is helpful.

Kaye bought 7 mangoes for $49, 4 apples for $24, and 3 oranges for $15. Which fruit is very cheap in price?

Answers

Answer:

oranges

Step-by-step explanation:

Answer: The oranges.

Step-by-step explanation: I'll set up my work below.

Mangoes: $[tex]49/7=7[/tex] =$7 per mango

Apples: $[tex]24/4=6[/tex]=$6 per apple

Oranges: $[tex]15/3=5[/tex]=$5 per orange

Given this, the cheapest fruit is the orange.

I hope this helps!! Pls mark brainliest :)


A pound of chocolate costs 6 dollars. John buys p pounds. Write an equation to represent the total cost c that John pays.
0-0 2
Question 29
XS ?

Answers

Answer:

c=6p

Step-by-step explanation:

you multiply

6 dollars per pound by p pounds

pounds cancel out and you are left with dollars

that is the cost

How can properties of logarithms be used to change bases into equivalent bases? (to any other flvs students, this is an essential question for 05.02 of alg 2)

Answers

Answer:

We can use change of base rule

What is the solution to this system of equations? x + y = 2 and y - z = -3 and x + y - z = 0

Answers

Answer:

x = 3

y = -1

z = 2

Step-by-step explanation:

if x+y = 2, and x+y-z = 0, then we can substitute 2 for x+y. this means 2-z=0, meaning z=2.  if y-z=-3, then y-2=-3, and y=-1. x+y=2 which means x-1=2 so x=3. plug in the values to check your answer.

Adam traveled out of town for a regional basketball tournament. He drove at a steady speed of 72.4 miles per hour for 4.62 hours

Answers

Step-by-step explanation:

im sorry but im not sure about this question

Answer:

334.488 miles

Step-by-step explanation:

You don't have a specific request on what I should answer, if it was distance then here's your answer

Table I contains outputs of the function f(x)=b^xf(x)=b
x

I need help

Answers

Answer: Table 1: Answer = 1. 404

Table 3 Answer = 1.66

Step-by-step explanation: i hope it's right if not, tell me

What is the solution for x in the equation?
5
3x + 4 =
2
OA. * = -4
OB. * = 4
12
O C.
OD.
X
x =
-1/7/20

Answers

Equations are separated by an equal sign. The value of x is given as -6/5

Equations and values

Given the equations below;

5(3x + 4) = 2

Expand

5(3x) + 5(4) = 2

15x +20 = 2

Subtract 2 from both sides

15x = 2 - 20

15x = -18

x = -18/15

x = -6/5

Hence the value of x is given as -6/5

Learn more on equation here: https://brainly.com/question/13763238

#SPJ1

PLS HELP ME

Mike invested $29,000 at 7.24% compounded daily.
What will Mike's account balance be in 21 years?

Answers

Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. Mike's account balance after 21 years is $69,131.44.

What is compound interest?

Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out so that interest is received on the principal plus previously collected interest in the next quarter.,

[tex]A = P(1+ \dfrac{r}{n})^{nt}[/tex]

where A is the final amount

P is the principal amount

r is the rate of interest

n is the number of times interest is charged in a year

t is the number of years

The principal amount that Mike invested is $29,000. The rate of interest is 7.24% compounded daily, for 21 years. Therefore, the account balance after 21 years is

[tex]\text{Account Balance after 21 years} = 29,000(1+\dfrac{0.0724}{365})^{(365 \times 21)}[/tex]

                                                     = $69,131.44

Hence, Mike's account balance after 21 years is $69,131.44.

Learn more about Compound Interest:

https://brainly.com/question/25857212

#SPJ1

Jill has c comic books. Tonya has 4 more than twice Jill's comic books. What variable expressions represents the total number of comic books Jill & Tony have all together?

Answers

Answer:

3c + 4

Step-by-step explanation:

Forming an expression

Number of books with Jill = c

To find the number of books with Tonya, multiply 'c' by 2 and then add 4 to it.

Number of books with Tonya = 2*c + 4

                                                 = 2c + 4

Total books all together = c + 2c + 4   {Combine like terms}

                                        = 3c + 4

Use graphing to determine the solution to the system of linear equations x=-1 y=3x+1

Answers

At x = -1 the value of y will be equal to -2 for the equation y = 3x + 1.

What is an equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Given that:-

The system of linear equations x=-1 and y=3x+1.

The equation will be solved as:-

Y = 3x + 1

Y = 3 ( -1 ) + 1

Y = -3 + 1

Y = -2

I have also plotted the graph of the two equations in the graph the two equations intersect at the point x = 1 and y = -2 so the solution of the equations will be ( -1, -2 ).

Therefore At x = -1 the value of y will be equal to -2 for the equation y = 3x + 1.

To know more about equations follow

https://brainly.com/question/2972832

#SPJ1

A, B, C, D got stuck with this problem

Answers

The third option. The translation would move it down, and the reflection would make the shape flip and move to the desired shape.

Two students created a list of steps for the following construction. Which student has steps in the correct order, and which does not? Explain.

Answers

The steps of student B are in the correct order but the steps of student A are in the incorrect order.

What is a perpendicular and parallel line?

Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines and the lines that never intersect are known as parallel lines.

We have:

You are given AB and point C. Construct a line parallel to AB that passes through point C

The correct way to draw a parallel line to AB that passes through point C is:

1. Draw a line that intersects points B and C.2. Place the compass on point B, and swing an arc that crosses line AB and line BC. Label the points D and E.3. Keep the compass at the same width, and place it on point C.4. Swing an arc that crosses line BC, and label the point F.5. Open the compass to the width between points D and E.6. Keeping the compass at the same width, place it on point F.7. Swing an arc that intersects the arc created from line BC at point C.8. Mark the intersection of the two arcs as point G.9. Draw a line through point C and point G.

The steps of student B are in the correct order but the steps of student A are in the incorrect order.

Thus, the steps of student B are in the correct order but the steps of student A are in the incorrect order.

Learn more about the perpendicular and parallel lines here:

brainly.com/question/18271653

#SPJ1

Which is the best estimate to the nearest one percent of startfraction 7 over 15 endfraction?

Answers

The best estimate to the nearest one percent of the fraction; 7/15 is; 47%.

What is the best estimate of the fraction to the nearest percent?

From the task content, it follows that the fraction given whose estimate is to be determined is; 7/15.

The fraction expressed as a percentage is;

(7/15) × 100 %

= 46.667%.

Hence, when rounded to the nearest one percent; = 47%.

Read more on percentage;

https://brainly.com/question/843074

#SPJ1

Other Questions
suppose the equilibrium price of oranges is $2.00 per pound. if the actual price is above the equilibrium price a: The graphs of the functions f (x) = 2x+ 7 and g(x) = x2 -1 intersect in txy-coordinate plane. What are the points of intersection? From 1820 to 1850, the largest group of immigrants came to the United States fromO France.O Germany. Great Britain.O Ireland I need help!!!!True OR False------------------------m - 63 = 37, m = 100? When a range of values is used to estimate a population parameter, it is called a. A point estiamte b. A range estimate c. A statistical parameter d. An interval estimate. A(n) _________ Web page displays customized content in response to keyboard or mouse actions or based on information supplied directly or indirectly by the person viewing the page. write the structure of root URGENT + 20 Points! The regression equation for water being poured into a large, cone-shaped cistern is In(volume) = -1.327 +2.993 In(Time). What is the predicted volume for a time of 12 seconds?- There is a line above "(volume)" 1.810 cm36.110 cm334.589 cm3450.485 cm3 the price of an mp3 player is increased by 8%to 52.92what was the original price? Researchers designing studies to be conducted in host countries outside the u. S. Should: PLEASE HELP ILL GIVE BRAINLIEST PLEASE PLEASE PLEEEEEEEAAAAASEWrite the recursive formula for the arithmetic sequence.A(n)=(-1)+(n-1)(-5) A snowboarder on a slope starts from rest and reaches a speed of 4.2 m/s after 7.3 s Select the correct answer.Consider function f.f(x) = 2xWhat is the value of ()(x)O A.8x4OB. 16x4OC. 4x44x2D. In my country, we make so much waste-we buy and throw away, buy and throw away, buy and throw away-and yet northern countries will not share with the needy. Even when we have more than enough, we are afraid to share, we are afraid to let go of some of our wealth.The Girl Who Silenced the World for Five Minutes,Severn Cullis-SuzukiBased on the passage, why are the people in Suzukis country wasteful?because they do not have enoughbecause they are afraid of people in the southern countriesbecause they share too much with othersbecause they are afraid to lose wealth What two houses of Congress were created by the Great Compromise? Symptoms of malaria appears when In a train timetable, in order to estimatearrival and departure time, read thetimes from Which word is the best antonym for invincible. a. often victoriousb. quickly forgottenc. easily defeatedd. not athletic Want to earn 20 points for correct answer CLICK ME A firm operating in a perfectly competitive market is a price taker because: