Show that the equation x^4/2021 − 2021x^2 − x − 3 = 0 has at least two real roots.

Answers

Answer 1

The roots of an equation are simply the x-intercepts of the equation.

See below for the proof that [tex]\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}[/tex] has at least two real roots

The equation is given as: [tex]\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}[/tex]

There are several ways to show that an equation has real roots, one of these ways is by using graphs.

See attachment for the graph of [tex]\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}[/tex]

Next, we count the x-intercepts of the graph (i.e. the points where the equation crosses the x-axis)

From the attached graph, we can see that [tex]\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}[/tex] crosses the x-axis at approximately -2000 and 2000 between the domain -2500 and 2500

This means that [tex]\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}[/tex] has at least two real roots

Read more about roots of an equation at:

https://brainly.com/question/12912962

Show That The Equation X^4/2021 2021x^2 X 3 = 0 Has At Least Two Real Roots.

Related Questions

Kevin walked 5 miles in 3 hours. What was his walking rate in miles per hour?
But use the / as your answer like 5/8

Answers

9514 1404 393

Answer:

  5/3 mi/h

Step-by-step explanation:

To find rate in miles per hour, divide miles by hours:

  (5 mi)/(3 h) = 5/3 mi/h

Part c Katie started with $40. How much money did she have left after purchasing the supplies? Enter your answer in the box provided.​

Answers

Answer:

gotta give me more details here Katie

Pls Help! Put a proper answer! And do not put a link or I will report you!
Two times the sum of a number, x, and 9 is at most four times the number. Write and solve an inequality to find the value of the number.

Answers

Answer:

2(x+9)≤4x

Step-by-step explanation:

2x+18≤4x

-18       -18

2x≤4x-18

-4x  -4x

-2x≤18

/-2  /-2

x≥9

A small town has 2,500 residents. In a random sample of 125 residents, 2 have the flu. Predict the number of residents of the town who have the flu.
A. 400
B. 20
C. 200
D. 40

Answers

Answer:

20

Step-by-step explanation:

40 is  the number of residents of the town who have the flu.

What is  multiplication?

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

A small town has 2,500 residents.

In a random sample of 125 residents, 2 have the flu.

i.e. in 2500 residents have flu = 2500*2/125

                                                  =5000/125

                                                  =40

Hence, 40 is  the number of residents of the town who have the flu.

To learn more on multiplication click:

brainly.com/question/5992872

#SPJ2

there are between 24 and 40 students in a class. give the ratio of boys to girls

I will give you 50 points!!!!!!!

Answers

Answer:

1:1.66

Step-by-step explanation:

you can round it up to 1:1.7 if that's what your teacher says

Answer:

33 students

If you divided the class into groups with 4 boys and 7 girls in each group, there will be 11 students in each group.

The total number of students in the class therefore must be a multiple of 11.

The only multiple of 11 between 24 and 40 is 33.

There are therefore 33 students.

4/11×33=12 are boys and 7/11×33=21are girls.

12:21= 4:7

hope it helps you

please mark me as brainlist

What are the first 100 digits of pi?

Answers

Answer:

3.1415926585979323846264338327952884197967987511582097414459230781546262862089910825342117067?

I did this from memory of a song I didn't use goo gle so all might not be right

Step-by-step explanation:

A circle has a radius of 5 centimeters. What is its area?

Answers

Answer:

[tex] \bf \huge 78.5 \: c.m.[/tex]

Step-by-step explanation:

Given that :

A circle has a radius of 5 centimeters.

to find :

What is its area?

formulas used :

A = πr²

where,

A = areaπ = 22/7 r = radius

explanation :

finding the area of circle

⟼ A = πr²

⟼ A = 22/7 × 5²

⟼ A = 22/7 × 5 × 5

⟼ A = 3•14 × 5 × 5

⟼ A = 3•14 × 25

⟼ A = 78•5

the area of circle is 78•5 centimeters

the area is 78.5 cm because the formula is A=3.14r^2 or area=3.14•5^2

the winner of a raffle will receive a 21-foot outboard boat. if 2000 raffle tickets were sold and you purchased 50 tickets, what are the odds against your winning boat?

Answers

i honestly have no idea

Which equation shows how to find the
angle measure of the part of the circle
without the arrow?

Answers

B because it can be A since a circle is 360 degrees and an arrow is only 90 degrees so that is why i think B

What is the area of triangle BCD to the nearest tenth of a square centimeter? Use special right triangles to
help find the height. Show your work.

Answers

Answer:

Area = 13.8 cm²

Step-by-step explanation:

Area of a triangle = ½*base*height

base = 4 cm

height = ?

Find height using trigonometry function:

Reference angle = 60°

Opp = height = BC

Adj = 4 cm

Apply TOA:

Tan 60 = Opp/Adj

Tan 60 = BC/4

BC = 4*Tan 60

BC = 6.92820324 ≈ 6.9 cm

✔️Area of triangle = ½*4*6.9

= 13.8 cm²

what is the measurement?

Answers

this question involves trig

sinx=p/h -----> some people have  

cosx=b/h ----> curly brown hair  

tanx=p/b -----> through proper brushing

we have p and h in this question so we can use the first formula

[tex]sinx=\frac{23}{28} \\x=sinx^{-1} \frac{23}{28} \\x=55.2[/tex]

Answer:

55.2

Step-by-step explanation:

sinx= 23/28

multiple both sides by inverse sin

x= sin^-1(23/28)

x= 55.2

Jack has a bag of coins. The bag
contains 8 dimes, 4 nickels, 3
pennies, and 1 quarter. He will
randomly select 2 coins from the bag
at one time without replacement
What is the probability that Jack will
select 2 dimes?

a. 15/23
b. 7/30
c. 5/9
d. 1/2

Answers

Answer:

i think 1 half sorry if i am wrong

Step-by-step explanation:


An appliance repair company charges $22 per hour to do repairs. In addition, the company charges a $35 flat-rate
fee per repair visit. Which equation represents the total cost, C, of a single repair visit that takes h hours?
A c (22 35)
B. C3522
C. C2335

Answers

The answer is C to your question

plz help no links or you will get reported and no brainlest meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answers

Answer:

49

Step-by-step explanation: no idea i just evaluated like that

Answer:

49

Step-by-step explanation:

Alrighty, PEMDAS, lets get started:

9 + 3(10 ÷ 2) + 5²

So we start with the parenthesis:

10 ÷ 2 = 5

Now we do the exponent:

5² = 25

So we now have:

9 + 3 x 5 + 25

we do multiplication first:

3 x 5 = 15

so we have:

9 + 15 + 25 = 49

So 9 + 3(10 ÷ 2) + 5² = 49

hope this helps:)

Help ASAP????? Please

Answers

Answer:

C. (-5,-1)

E. (10,2)

F. (15,3)

------------------

hope it helps...

have a great day!!

All real numbers greater than or equal to -7 and less than 2

Answers

Answer:

-7=<x<2

Step-by-step explanation:

Please help I’ll mark you brainliest

Answers

Answer:

The perimeter is 25.

Step-by-step explanation:

Darling, I'm not always accurate but I hope this helps you with math!

Use the fundamental counting principle to determine all the possible outcomes from rolling a die once then spinning the spinner.

Answers

The answer is there are 6 possible outcomes: {1, 2, 3, 4, 5, 6} Hope this helps!

im almost done with this hw. plz help!!! give explanation if you actually know the answer so ik u dont just want points....

Answers

Answer:

D

Step-by-step explanation:

1/12 X 110 = .0833333333 x 110 = 9.16

D. 9

Step-by-step explanation:

110÷12 = 9.1 however just round down to 9

since there are 12 equal pieces of the pie graph you would also count yellow and not exclude it

Which of the following is a true statement about ecology?
Ecology is the study of relationships of living organisms and their environment.

Ecology is the study how animals adapt to their environment.

Ecology studies how living organisms have changed over time.

Ecology studies the difference between living organisms.

Answers

Ecology is the study of relationships of living organisms and their environment

Step-by-step explanation:

Ecology in a simple sense is the the study of ecosystems

A chili recipe calls for ground beef, beans, green pepper, onion, chili powder, crushed tomatoes, salt and pepper. You have lost the directions about the order in which to add the ingredients, so you decide to add them in a random order. What is the probability that the ingredients are added in the exact order listed above?

Answers

Answer:

1 out of 8 chance it will be listed exactly

What is the volume of this prism?

Answers

Answer:

The answer is 42ft ^3 (42 ft units cubed)

Step-by-step explanation:

To find the volume for a rectangular prism, first of all you need to know the formula. The formula is V=lwh (volume= length x width x height)

The formmula for this problem is V= 7ft x 2ft x 3ft= 42ft

5
Which of the following is the result of expanding 22"-2,
n=1
O 8.5
O 15.5
O 32
60

Answers

Answer:

[tex]\sum\limits^5_{n=1} {2^{n-2}} = 15.5[/tex]

Step-by-step explanation:

Given

[tex]\sum\limits^5_{n=1} {2^{n-2}[/tex]

Required

The result

To do this, we simply substitute 1 to 5 for n.

So, we have:

[tex]\sum\limits^5_{n=1} {2^{n-2}} = 2^{1-2} + 2^{2-2} + 2^{3-2} + 2^{4-2} + 2^{5-2}[/tex]

[tex]\sum\limits^5_{n=1} {2^{n-2}} = 2^{-1} + 2^{0} + 2^{1} + 2^{2} + 2^{3}[/tex]

Evaluate each exponent

[tex]\sum\limits^5_{n=1} {2^{n-2}} = 0.5 + 1 + 2 + 4 +8[/tex]

[tex]\sum\limits^5_{n=1} {2^{n-2}} = 15.5[/tex]

Answer:

Answer is B edg2021

soknasoiegspeoigapoiegaoig

Can someone please help me find the area.

Answers

Answer:

51 ft²

Step-by-step explanation:

The figure is composed of two different triangles (triangle 1 and 2) and a rectangle

Area of the composite figure = area of triangle 1 + area of triangle 2 + area of rectangle

✔️Area of triangle 1 = ½*bh

b = 3 ft

h = 2 ft

Area of triangle 1 = ½*3*2 = 3 ft²

✔️Area of triangle 2 = ½bh

b = 3 ft

h = 3 ft

Area of triangle 2 = ½*3*3 = 4.5 ft²

✔️Area of rectangle = L*W

L = 3 + 8 = 11 ft

W = 4 ft

Area of rectangle = 11*4 = 44 ft²

✅Area of the composite figure = 3 + 4 + 44

= 51 ft²

What is the area of the shaded region below?
7 m
30 m
7 m
21 m

Answers

Answer:

322.28

A

Step-by-step explanation:

Area of the rectangle

L = 30

W = 21

Area = 30 * 21

Area = 630

Area of the circles

Radius = 7 m

Area = pi r^2

Area = 3.14 * 7^2

Area = 153.86 m^2

Area of both circles = 307.72

Area of the Shaded Region

Area of shaded region = area of the rectangle - area of 2 circles.

Area of Shaded Region = 630 - 307.72

Area of Shaded Region = 322.28

Find the product. Simplify.
(x + 7)(x + 4) =

Answers

Answer:

Hi! The answer to your question is [tex]x^{2}[/tex]+11x+28

Step-by-step explanation:Answer:

☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆

☆Brainliest is greatly appreciated!☆

Hope this helps!!

Stay Safe!!

- Brooklynn Deka

Please help me fast if possible :(

Answers

It’s b I hope this helps!

Answer:

B

Step-by-step explanation:

Hi there!

The first one is addition because if she got more, we are adding to it.

The last one seems to be a multiplication problem, "each friend"

I am so sorry if this is wrong, Hope you have a good day/night.

If sinθ = a, then cscθ =

1/a
a
1

Answers

Answer:

[tex]\csc\theta=\dfrac{1}{a}[/tex]

Step-by-step explanation:

Given that,

[tex]\sin\theta=a[/tex]

We need to find the value of [tex]\csc\theta[/tex].

We know that, the relation is given as follows :

[tex]\sin\theta=\dfrac{1}{\csc\theta}\\\\\csc\theta=\dfrac{1}{\sin \theta}[/tex]

Put [tex]\sin\theta=a[/tex]

So,

[tex]\csc\theta=\dfrac{1}{a}[/tex]

So, the answer is equal to [tex]\dfrac{1}{a}[/tex].

Please help me immediately... i need help
Tory sold 50 balloons for School Spirit Day. He raised $37.50. He wrote this equation to show how much he charged for each balloon.

= 37.50

What mistake did Tory make in writing his equation? What is a correct equation and its solution?
A. He divided b by 50 instead of by 37.50. A correct equation is = 50. Its solution is $1,875.
B. He divided b by 50 instead of dividing 50 by b. A correct equation is = 37.50. Its solution is $1.33.
C. He divided b by 50 instead of multiplying b by 50.A correct equation is 50b = 37.50. Its solution is $0.75.
D. He divided b by 50 instead of setting up a proportion. A correct equation is = . Its solution is $1,875.

Answers

Answer:

Answer is C $0.75

Step-by-step explanation:

50b = 37.50

divide both sides by 50

50 cancels out b is by itself.

37.50 divide by 50= 0.75

The mistake Tory made is he divided b by 50 instead of multiplying b by 50. A correct equation is 50b = 37.50. Its solution is $0.75.

What does division mean?

Division is a mathematical operation that involves the grouping of  a number into equal parts using another number. The sign used to denote division is ÷.

The equation that represents the total amount raised: total balloons sold x cost of one balloon

b x 50 = 37.50

b = 37.50/ 5-

b = $0.75

To learn more about division, please check: https://brainly.com/question/13281206

Which ratio is equivalent to 7:3?


A. 21: 7

B. 28 : 12

C. 12 : 8

D. 49:9

Answers

Answer:

The answer is B.

Step-by-step explanation:

7x4 is 28 which means you have to multiply 3x4. That gives you 12. 28:12 is the proper ratio. (Hope this helped!)

Answer:

b.28/12

Step-by-step explanation:

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