A polynomial function P(x) with rational coefficients has the roots sqrt 2 and - sqrt 13. Find two additional roots.

Answers

Answer 1

Answer:

[tex]-\sqrt{2}[/tex] and [tex]\sqrt{13}[/tex]

Step-by-step explanation:

Given a polynomial with rational coefficients, its irrational and complex roots would occur in conjugate pairs.

For example, if the roots of a polynomial are 2 + [tex]\sqrt{3}[/tex], 3 and 4 - 3i, then 2 - [tex]\sqrt{3}[/tex], and 4 + 3i are also roots of the polynomial.

Therefore, since the given polynomial has rational coefficients and some of its roots are , [tex]\sqrt{2}[/tex] and  - [tex]\sqrt{13}[/tex], then -[tex]\sqrt{2}[/tex] and [tex]\sqrt{13}[/tex] are also roots of the polynomial.


Related Questions

ILL GIVE BRAINLIEST PLS HELP IMMEDIATELY -- The ages of trees in a forest are normally distributed with a mean of 25 years and a standard deviation of 4. Approximately what percent of the trees are between 20 and 30 years old? (2 points)

Answers

Answer:

79%

Step-by-step explanation:

Most of today's student calculators have built-in statistical functions.  I will use my old TI-83 Plus here:

normalcdf(20, 30, 25, 4)

The calculator returns 0.789.

Approximately 79% of the trees are between 20 and 30 years old

Answer:

68%.

Step-by-step explanation:

The mean is 25 and the standard deviation is 5. So 20 is one standard deviation below the mean and 30 is one standard deviation above the mean.

According to the Empirical Rule, 68% of the normal curve is between ±1 standard deviations. So the answer is 68%.

Please help
VX is a midsegment of UWY
IF UY=13p-1 and VX=20p-95 what is UY

Answers

The length UY of the triangle is 90 units

How to determine the length UY

From the question, we have the following parameters that can be used in our computation:

VX is a midsegment of triangle UWYUY = 13p - 1 and VX = 20p - 95

This means that

UY = 2 * VX

Substitute the known values in the above equation, so, we have the following representation

13p - 1 = 2 * (20p - 95)

Evaluate the products

13p - 1 = 40p - 190

So, we have

40p - 13p = 190 - 1

So, we have

27p = 189

Divide by 27

p = 7

Substitute p = 7 in UY = 13p - 1

UY = 13 * 7 - 1

So, we have

UY = 90

Hence, the length is 90 units

Read more about midsegment at

https://brainly.com/question/25886396

#SPJ1

HELP DUE IN 15 MINS!


Quadrilateral DAVE has vertices D(2, 2), A(4, 2), and V(5, -3). Plot a point E to make DAVE an isosceles trapezoid.


1. What are the coordinates of E ( , )??

Answers

Answer:

i believe it's (1, -3)

hope it helps!

Can the sine ratio of an acute angle be greater than 1?

Answers

No, the sine ratio of an acute angle cannot be greater than 1.

What is an acute angle?

Each angle in an acute triangle must be less than 90 degrees. A triangle is not an acute triangle even if one of its angles is 90 degrees. Because all angles (60°) are less than 90°, an equilateral triangle, for instance, is always sharp.

Here,

We have to determine whether the sine ratio of an acute angle can be greater than 1 or not.

We concluded that the value of the Sine ratio will always be between zero and one.

The Sine ratio is related to one of the acute angles of a right triangle such that the sine of the acute angle is the ratio of the side opposite the specific acute angle (the reference angle) to the hypotenuse.

Hence, the sine ratio of an acute angle cannot be greater than 1.

To learn more about the acute angle from the given link

https://brainly.com/question/6979153

#SPJ4

Please help, I’ll give brainliest UwU

Answers

Answer:

uwu your answer is c because jake did not like lily during the performance.

Step-by-step explanation:

Answer:

The UWU answer UwU is UwU C UwU owa owa

what are the nouns in this sentence?

Answers

Answer:

A noun is most commonly taught a person, place, or thing and sometimes idea. In this sentence, it would be Magazine, Americans, and carbohydrates. And if smith is also part of the sentence, he is a person, so its also a noun. :) Happy learning friend

2) Jenny has a water tank that needs to be
filled up. The water tank can hold 500 gallons
of water. She adds 20 gallons of water every
hour. How many hours does it take for Jenny
to be able to fill up the tank?

Answers

It will take 25 hours for Jenny to fill up the tank.

To solve this problem, we divide the capacity of the tank by the rate at which it is being filled:

500 gallons / 20 gallons/hour = <<500/20=25>>25 hours

*PLEASE PLEASE HELP I WILL MARK THE BRAINLIEST*

Write an expression equivalent to 3n2 + 12n that is a product of two expressions.
Enter numbers, variables, or expressions in the boxes.

Answers

Answer:

3n(n + 4) = 0

n = 0, -4

Step-by-step explanation:

3n(n + 4) = 0

3n = 0

n = 0

n + 4 = 0

n = -4

Answer:

Step-by-step explanation:

3n2 + 12n factors into (3n)(n + 4n).

A scooter shop is offering a 30% discount on all of its scooters. Shirley buys a scooter that had an original price of $840. What was the discounted price of the scooter?

Answers

Answer:

$588

Step-by-step explanation:

Original price = $840

Discount = 30%

Discounted price is:

$840 - 30% of $840 =$840*0.7 = $588

A bakery sells yesterday's bagels for a discounted rate of $2.64/dozen. What is the price per bagel?​

Answers

Answer:

$0.22 per bagel

Step-by-step explanation:

A dozen is 12:

2.64/12 = 0.22

Dylan opened a credit card account with $575.00 of available credit. Now that he has made some purchases, Dylan's account only has $465.75 of available credit. What is the percentage decrease of the amount of available credit in Dylan's account?

Answers

Answer:

19%

Step-by-step explanation:

First, we have to find how much did he spend by taking

$575.00 - $465.75 = $109.25

Then we find the percentage decrease by taking

109.25 divided by 575, then times 100% = 19%

So,  the percentage decrease of the amount of available credit in Dylan's account is 19%

Shelley drew a scale drawing of a neighborhood park. The volleyball court, which is 8 meters wide in real life, is 4 millimeters wide in the drawing. What is the scale factor of the drawing?

Simplify your answer and write it as a fraction.
I need IXL answer's PLEASE

Answers

The scale factor of the drawing of the neighborhood park would be = 2000.

What is a scale factor?

The scale factor is defined as the ratio between the scale of the original object and the new object, which represents it but in a different size (larger or smaller).

The width of the neighborhood park. in real life = 8 meters

To convert 8 meters to millimetres is to multiply by 1000

= 8 × 1000 = 8000 mm

The scale factor = 4 × X = 8000

make X the subject of formula;

X = 8000/4

X = 2000.

Learn more about scale factor here:

https://brainly.com/question/28339205

#SPJ1

Which equation represents a linear function?
y – 2 = –5(x – 2)
x + 7 = –4(x + 8)
y – 3 = y(x + 4)
y + 9 = x(x – 1)

Answers

Correct Answer: y-2= -5(x-2)

Why is Avogadro's number 6.02 x10 23?

Answers

The value of  Avogadro's number is 6.02214076 × 10²³. The ratio of the actual mass of an element to its atomic mass is always constant which is known as  Avogadro's number.

What is one mole?

One mole consists of an Avogadro number of atoms. If you are aware of the mole quantity, you can convert a mole into grams.

The mole (symbol: mol) is the unit of material quantity used by the International System of Units. The amount of a substance determines how many elementary entities of that substance are present in an object or sample. The mole must contain precisely 6.02214076×10²³ elementary entities.

The proportionality factor that connects the number of constituent particles (often molecules, atoms, or ions) in a sample with the amount of material in that sample is called the Avogadro constant, also known as NA or L. It has a precise value of  6.02214076 × 10²³ reciprocal moles and serves as a SI defining constant.

It shows how many atoms or molecules make up one gram of an element's or compound's molecular weight. The value is "6.022 × 10²³" when the atomic mass of an element is divided by the actual mass of its atom.

To learn more about Avogadro's number, click on the below link:

https://brainly.com/question/24175158

#SPJ4

Work out 37% of 4618.57
Give your answer to 1 decimal place.

Answers

Answer:

37/100(4618.57)

170887.09/100

1708.9

The solution of the given expression is 1708.9.

What is percentage?

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

The given expression is as below,

37% of 4618.57

It can be simplified as follows,

37% of 4618.57

= 37/100 × 4618.57

= 1708.87

It can be approximated as 1708.9.

Hence, the given expression can be worked out up to one decimal place as 1708.9.

To know more about percentage click on,

brainly.com/question/29306119

#SPJ2

Please does anyone know the answer to c & d

Answers

Answer:

c = 8^5

d = 7^2

Step-by-step explanation:

Answer:

c) =8^5

d) =7^2

Step-by-step explanation:

i hope this helps :)

5 3/4 as a fraction greater then one

Answers

Answer:

23/4

Step-by-step explanation:

 

Answer: yes

Step-by-step explanation:

A glass is 2/3 full. Then 40cm^3 of orange juice is poured in. The glass is now 4/5 full What is the total volume of the glass?

Answers

Answer:

The total volume of the glass is 300 cm^3.

Step-by-step explanation:

Let V represent the total glass volume.

Then (4/5)V - (2/3)V = 40 cm^3.  The LCD here is 15, so we rewrite this equation as

(12/15)V - (10/15)V = 40 cm^3, or

(2/15)V = 40 cm^3.

Solve for V by multiplying both sides of this equation by (15/2):

(15/2)(2/15)V = (15/2)(40  = 300 cm^3

The total volume of the glass is 300 cm^3.

what is the answer for -40= -50 + x ?

Answers

Answer:10

Step-by-step explanation: Because negative 40 equals -50 + x equals 10

How do you find the missing side of a triangle?

Answers

The missing sides of the triangle can be found by applying the Pythagoras Theorem .

What is Pythagoras Theorem ?

The Pythagoras Theorem states that square of  hypotnuse (that is longest side) is equal to sum of the square of perpendicular and base .

that means : [tex]Hypotnuse^{2} = Perpendicular^{2} +Base^{2}[/tex]  ;

let missing side of the Right triangle be hypotnuse ;

So , missing side is written as : [tex]Hypotnuse = \sqrt{Perpendicular^{2} +Base^{2}}[/tex] .

For Example : Let a right triangle has sides lengths of perpendicular = 6 and hypotnuse = 10 .

let , the length of side "base" be unknown.

So ,  in order to find length of side b  (base) , we substitute the  known values into Pythagoras theorem:

[tex]10^{2} =6^{2} +Base^{2}[/tex] ;

[tex]Base = 100-36[/tex] ;

So , missing side "base" is = 8 ;

Therefore , the missing side can be found by using  the Pythagoras Theorem .

Learn more about Triangles here

https://brainly.com/question/30104289

#SPJ4

A regular square pyramid has base edge b, height h, and slant height l. Three expressions give the surface area, A, of this pyramid. Which expression does NOT?

Answers

Answer:

1/3 . Abase . height

Step-by-step explanation:

Please find attached the complete question

a square pyramid is a pyramid that has a square base.

total surface area measures the total area of the surfaces of an object

the formula 1/3 x Area of the base x height is used to calculate the volume of the pyramid and not the surface area

can someone help me with this I'll give a crown thing please hurry!​

Answers

Answer:

1) 1: 107

  2: 73

  3: 107

  4: 73

  5: 107

  6: 73

  7: 107

  8: 73

3) 1: 128

  2: 52

  3: 128

  4: 52

  5: 128

  6: 52

  7: 128

  8: 52

Step-by-step explanation:

Vertical, corresponding, alternate exterior, and alternate interior angles are all congruent (equal). Angles such as same side exterior and same-side interior are supplementary; meaning these angles add up to 180°.

When a positive number is multiplied by the sum of twice the number and half the number, the result is the original number. What is the number

Answers

By setting up the equation and solving we get the positive number is 2/5.

What is positive number?

A positive number is a number greater than zero. In mathematical terms, it is a number that is greater than zero on the number line. Positive numbers are often represented with a "+" sign in front of them, but this is not always necessary as the positive sign is the default and is usually omitted.

What is equations?

An equation is a mathematical statement that asserts the equality of two expressions. It is a statement that asserts that the two expressions on either side of the "=" sign are equal and have the same value. The expressions on either side of the "=" sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation.

For example:

2x + 3 = 7

x(2x+x/2)=x

2x^2+x^2/2=x

5x^2/2=x

5x^2=2x

5x=2

x=2/5

To know more about numbers visit:

https://brainly.com/question/17429689

#SPJ1

Select the correct answer. which equation combines with the given equation to form a system of equations with the solution x = 3 and y = 9? x 2y = 21
a. 4x 6y = 64
b. 2x y = 36
c. 4x y = 21
d. -3x 4y = 33
e. 3x 2y = 28

Answers

An equation that combines with the given equation  x + 2y = 21 to form a system of equations with the solution x = 3 and y = 9 is 4x + y = 21.

The correct answer is an option (c)

As x = 3 and y = 9 are the solution of system of equations, the required equation must be true for x = 3 and y = 9.

Given equation is: x + 2y = 21

For x = 3 and y = 9 given equation is 3.

In order to find the required equation, we substitute the values of x and y in each equation and check whether the equation is true for x = 3 and y = 9.

a. For equation, 4x + 6y = 64

LHS = 4(3) + 6(9)

LHS = 12 + 54

LHS = 66

LHS ≠ RHS

So, this is not a required equation.

b. 2x + y = 36

LHS = 2(3) + 9

LHS = 6 + 9

LHS = 15

LHS ≠ RHS

So, this is not a required equation.

c. 4x + y = 21

LHS = 4(3) + 9

LHS = 12 + 9

LHS = 21

LHS = RHS

this is the required equation.

d. -3x + 4y = 33

LHS = -3(3) + 4(9)

LHS = -9 + 36

LHS = 27

LHS ≠ RHS

So, this is not a required equation.

e. 3x + 2y = 28

LHS = 3(3) + 2(9)

LHS = 9 + 18

LHS = 27

LHS ≠ RHS

So, this is not a required equation.

Therefore, the reuired equation is 4x + y = 21

Learn more about an equation here:

https://brainly.com/question/649785

#SPJ4

A 140 meter rope is cut into two pieces. One piece is four time as long as the other. How long is each piece? Solve using substitution or elimination.

Answers

Answer:

28 m,  112 m

Step-by-step explanation:

x = length of short piece

4x = length of long piece

x + 4x = 140

5x = 140

x = 140/5 = 28

4x = 4(28) = 112

Which negative angle is equivalent to a 75° angle?
O A. An angle measuring -105°
B. An angle measuring -275°
C. An angle measuring -75°
D. An angle measuring -285°

Answers

Answer:

maybe c?... I'm sorry that's just my educated guess..

The school surveillance camera was able to capture an image of the suspect. The image
shows the thief standing next to the gym door. In real life the door measures 84 inches but
is 14 cm in the image. If your suspect is 10.83 cm in the photo. How many inches tall are
they in real life? (Round to nearest whole inch.) Report the height in feet and inches. Ex.
"2 feet 5 inches"

Answers

Answer:

77.4 inches

6 feet 4 inches

Step-by-step explanation:

what persent of 14 is 10.83 is 77.35

what persent of 84 is 77.3571428571 is 92.08

what is 92.08% of 84 is 77.34

77.34 inches to feet is 6 feet and 4 inches

Write the equation of the line that passes through the point (-9, 5) and is parallel to the line y = -1/3x - 4.

Answers

Answer:

i just found the link ill post it under your question hold up

Step-by-step explanation:

What 3 numbers make a right triangle?

Answers

Answer:

A right triangle equals to 90 degress, and has 2 equal angles.

Example: 20 degress, 20 degrees and 50 degress could make a right triangle.

I hope this helps you!

1. Write 7 example of mathematical expreion. 2. Larry had 5 3/6 yard of fabric. He ued 2 2/3 to make a bag for hi computer. Write an expreion that will how how much of the fabric Larry will have left. PLEASE HURRY UPPPPP!!! I HAVE 1 HOUR LEFT UNTIL SUBMISSION!!!

Answers

a) 7 examples are:

[tex]2x + 3y\\(4a - 5b) / 2c\\(5 + 8) * 3\\8^2 - 6\\√(64)\\(1/3) * π * r^2\\2(3x + 4y) - 5z[/tex]

b) Fabric Larry will have left after using [tex]2\frac{2}{3}[/tex] yard out of [tex]5\frac{5}{6}[/tex] yard to make a bag for his computer is: [tex]3\frac{3}{6} yard[/tex]

What kinds of expressions are examples?

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

7 examples of mathematical expression are:

[tex]2x + 3y\\(4a - 5b) / 2c\\(5 + 8) * 3\\8^2 - 6\\√(64)\\(1/3) * π * r^2\\2(3x + 4y) - 5z[/tex]

For the second part of the question:

Larry had 5 3/6 yards of fabric. He used 2 2/3 yards to make a bag for his computer. Write an expression that will show how much of the fabric Larry will have left.

The mathematical expression that represents the amount of fabric Larry has left is:

5 3/6 - 2 2/3 = 2 7/18

You can simplify this further:

2 7/18 = 2 1/6

The amount of fabric Larry will have left is 2 1/6 yards.

Learn more about mathematical expression visit:

brainly.com/question/723406

#SPJ4

Other Questions
ANSWER CORRECTLY FOR BRAINLY questions IN PIC Which substance is considered a building block for all living things?hydrogenglucosecarbonprotein Pls help !! AS SOON AS POSSIBLE I WILL GIVE BRAINLIEST ( and pls no random link) A change in relative interest rates causes investment expenditures to decrease within an economy resulting in a decrease of real GDP from $38,000 to $35,000. What is the percent change in real GDP Think about how ocean surface currents couldaffect floating garbage. Record your evidence. HELPPP What do Lannis and Isa do as a resultof their disagreement? which is an example of species diversity?A. Variation in a flock of pigeonsB. Fire ant colony C. Giraffes,earth worms,algaeD. A savanna and a tropical rain forest Read the following excerpt from The Jungle Book by Rudyard Kipling. A wolf accustomed to moving his own cubs can, if necessary, mouth an egg without breaking it, and though Father Wolf's jaws closed right on the child's back not a tooth even scratched the skin, as he laid it down among the cubs. What is the most important purpose of the narrator in this excerpt? to show that the wolves can be very tender and caring to show that the wolves want to eat the man cub to show that the wolves can carry eggs in their mouths to show that the wolves carry their young in their mouths What is the length of AB? Would Adam Smith be considered an industrial capitalist, or a mercantile capitalist? I NEED HELP ASAPPPP PLSSSSSSSS Write an exponential function to describe the given sequence of numbers, 10, 60, 360, 2160, 12960,. A sanitation department is interested in estimating the mean amount of garbage per bin for all bins in the city. In a random sample of 46 bins, the sample mean amount was 49.41 pounds and the sample standard deviation was 3.99 pounds. Construct a 92.7% confidence interval for the expected amount of garbage per bin for all bins in the city. Answer to 3 decimals (a) What is the lower limit of the 92.7% interval help me please anyone -25-2x=3xI know the answer to the problem but im not sure how to move the constant (-25) to the other side. When you move the constant to the right side the equation should be -2x=3x+25. How do you move a constant to the other side? How is local humidity influenced by a flow of energy and the movement of matter in the form of water? What are examples of environmental variations? economics-- multiple choice! Let's say the federal government decides to establish and run national parks in four states, and one U.S. territory with, struggling economies. What is the most likely reason for the government embarking on this large-scale project?Control inflationExpand MedicaidCombat unemploymentLimit spillover costp.s. i have more questions like this on my profile-- please help me with other questions if you can :) In a far-off galaxy, an astronomer observes a moon orbiting a planet. The moon stays in orbit because of the planets gravity.Which scenario would increase the gravity of the planet? True or False: Death was not to be spoken of as it was considered a curse that one could bring on their families and homes. *