Suppose a polynomial of degree 4 with rational coefficients has the given numbers as zeros. Find the other zero
-2, square root 5, 10/3

Suppose A Polynomial Of Degree 4 With Rational Coefficients Has The Given Numbers As Zeros. Find The

Answers

Answer 1

Step-by-step explanation:

The root is

-sqr root of 5.

First, we put these roots in the forn of

[tex](x - a)[/tex]

where a is the root

So we have

[tex](x - ( - 2))(x - \sqrt{5} )(x - \frac{10}{3} )[/tex]

[tex](x + 2)(x - \sqrt{5} )(3x - 10)[/tex]

[tex](3 {x}^{2} - 4x - 20)(x - \sqrt{5} )[/tex]

To get rid of that square root, let have another root that js the conjugate posive root of 5.

[tex](3 {x}^{2} - 4x - 20)(x - \sqrt{5} )(x + \sqrt{5} )[/tex]

[tex](3 {x}^{2} - 4x - 20)(x {}^{2} + 5)[/tex]

Which will gives us a rational coeffeicent of degree 4.

Why we didn't do

[tex](x - \sqrt{5} )[/tex]

?

Because

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

If we foiled out we will still have a irrational coeffceint.


Related Questions

4. If you spin the spinner twice, what is the probability that the spinner will land on 5 on the first spin and 2 on the second spin?

1/16
3/16
1/8
1/4

Answers

Answer:

1/16

Step-by-step explanation:

Given in comment:

5,4,3,2 = Spinner

Thus, there are 4 possible answer

Given:

If you spin the spinner twice, what is the probability that the spinner will land on 5 on the first spin and 2 on the second spin?

1/16

3/16

1/8

1/4

Solve:

Knowing that there only One 5 and One 2 on the spinner.

Thus, in fraction form - 1/4 and 1/4

Probability land on 5 = 1/4

Probability land on 2 = 1/4

Because there are 4 possible solution and one of each is 5,4,3,2

Now, multiply then together:

1/4 × 1/4 = {1 ×1 = 1 and 4 × 4 = 16}

Put Together:

1/16

Hence, the answer is " The Probability that the spinner will land on 5 on the first spin and 2 on the second spin is 1/16  

~Lenvy~

Answer:

1/16

Step-by-step explanation:

so, per your additional information the "spinner" has 4 possible results : 5, 4, 3 ,2

I guess, they are like the six numbers on a die equally probable.

that means the probabilty to get one of the 4 possible answers is 1/4 (desired outcomes over all possible outcomes).

now, to make the experiment twice and link the results as one desired outcome (like a 5 and a 2, or two 4s, or ...), we can multiply the probabilities as combined events without overlapping.

why ?

similar to a die with 6 possible results, we have here for every one of the 4 possible results of the first spin, we have 4 possible results of the second spin.

so, the probability of one particular set of 2 results is

1/4 × 1/4 = 1/16

in other words, it is 1/4 to get 5 on the second spin, and 1/4 to get 2 on the second spin. because we want both to happen as one desired result, both events have to happen as combination (and not as "or"). hence the multiplication.

(b) The volume of water in a container is
directly proportional to the cube of its depth.
When the depth is 12 cm, the volume is 576 cm3.
Calculate
(i) the volume when the m is 1300 cm?. [2]

Answers

Answer:

See below.....Something is wrong with your question

Step-by-step explanation:

v = k d^3    or     k = v/d^3   = 576/12^3 = 1/3

when depth (???   m??)  is 1300 :

  1/3 =  v / (1300^3)  = 732 333 333 .3 cm^3

   

x/4+<2/7 I need help i'm stuck

Answers

Answer:

X< 7/8

Step-by-step explanation:

X< 2/7×4

X< 2×4/7

X< 7/8

Answer:

[tex]\boxed{\sf{x < -\dfrac{20}{7} }}[/tex]

Step-by-step explanation:

To solve this problem, all you have to do is isolate it on one side of the equation.

x/4+<2/7

First, multiply by 4 from both sides.

x/4*4+4<2/7*4

Solve.

2*4=8

Rewrite the problem down.

x+4<8/7

Then, you subtract by 4 from both sides.

x+4-4<8/7-4

Solve.

x<-20/7

Therefore, the correct answer is x<-20/7.

I hope this helps you! Let me know if my answer is wrong or not.

What is the area of this quadrilateral(Please show a step by step process)

Answers

Answer:

40ft

Step-by-step explanation:

What you need to know is the formula for the air of a rectangle:

the long side * the short side.

First calculate the area of the rectangle in the middle: 3*8=24ft

Then we are left with two right-angled triangles, one on the left and one on the right. If we juxtapose them, we realize that it forms a rectangle whose large side measures 8 and the small 2 so 2*8=16ft.

Finally, just add the area of the middle rectangle with the area of our rectangle formed by the two triangles on the right and on the left. So 16+24=40ft

[tex]\sqrt[2]{80x^{2}y^{25} }[/tex]

Answers

Answer:

4xy^5√5

Step-by-step explanation:

√80 x √x² x √y^25

=4√5 x x x y^5

= 4√5xy^5

Answer:

  4xy^12√(5y)

Step-by-step explanation:

Squares under the radical can be factored out.

  [tex]\displaystyle \sqrt{80x^2y^{25}}=\sqrt{(4xy^{12})^2\cdot5y}=\boxed{4xy^{12}\sqrt{5y}}[/tex]

_____

Additional comment

Some versions of this question may have different exponents.

What is the area of the quadrilateral

Answers

To calculate the rectangular area in the middle we do:
Area = base*height
Area = 4*6 = 24
To calculate the triangular area on both sides it’s:
Area = 1/2* base* height
Area = 1/2*2*6 = 6

Since there is two triangular area and one rectangle it’s:

24+6+6 = 36 square feet
C. 36 square feet. So, first you take you square in the middle and multiply the bottom by the side which is 6x4= 24 then you take the outside triangles and put them together so it would be 6x2= 12 then add them together which is 36

Please help!!!
Mr. Johnson's class will study one sea animal for the next week. Which group should Mr. Johnson survey to find the type of sea animal his students should study?
A: His students
B: Teachers at his school
C: Parents of his students
D: Workers at a sea animal park

Answers

Answer:

A He should ask his students to know what they prefer

Step-by-step explanation:

What's the answer pls help

Answers

Answer:

x = 8

Step-by-step explanation:

Both these angles are equal because they are equal. So we make this equation:

8x + 36 = 5x + 60

-5x          -5x

3x + 36 = 60

      -36   -36

3x = 24

Divide both sides by 3:

x = 8

What is the space between two intersecting lines called?.

Answers

Answer:

The space between two intersecting lines is called an:
Angle



An angle is formed when two lines meet at a shared point. They are measured in degrees. There are four important types of angle; acute, right, obtuse, and reflex. A full circle has 360 degrees. If you see an angle of 720 degrees, it means it has rotated twice around a full circle.

360 degrees (one time round) x 2 = 720 degrees (two times round)




Step-by-step explanation:

Have a great rest of your day
#TheWizzer

May currently has a balance of $1,817.43 on her credit card. if she must make a minimum monthly payment of 3.44% of her total balance, what is her minimum payment, to the nearest cent? a. $5.21 b. $62.52 c. $40.84 d. $51.49 please select the best answer from the choices provided a b c d

Answers

She makes a minimum monthly payment of 62.52 dollars. Then the correct option is B.

What is the percentage?

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

May currently has a balance of $1,817.43 on her credit card.

If she must make a minimum monthly payment of 3.44% of her total balance.

Then the minimum payment will be given as

Minimum payment = 0.0344 × 1817.43

Minimum payment = 62.519 ≅ 62.52

More about the percentage link is given below.

https://brainly.com/question/8011401

Consider functions f and g

Answers

Answer:

A

Step-by-step explanation:

[tex] f(x) = \dfrac{x - 16}{x^2 + 6x - 40} [/tex]

[tex] g(x) = \dfrac{1}{x + 10} [/tex]

[tex] f(x) + g(x) =  \dfrac{x - 16}{x^2 + 6x - 40} + \dfrac{1}{x + 10} [/tex]

[tex] f(x) + g(x) =  \dfrac{x - 16}{x^2 + 6x - 40} + \dfrac{(x - 4)}{(x + 10)(x - 4)} [/tex]

[tex] f(x) + g(x) =  \dfrac{x - 16 + x - 4}{x^2 + 6x - 40} [/tex]

[tex] f(x) + g(x) =  \dfrac{2x - 20}{x^2 + 6x - 40} [/tex]

Answer: A

A sample of size 38 has s = 15.5 and yields this confidence interval for the mean:
(304.67, 322.48). What's the t* for this confidence interval?

6.29
3.14
2.514
2.026
3.542

Answers

Answer:

6338.7

Step-by-step explanation:

Explain why 10 to the zero power equals 1

Answers

Answer:

Because any number to the power of zero will be one.

need help with this pls

Answers

The volume of the square base pyramid is 588 ft³

The Volume of the rectangular prism is 120 ft³

The Volume of a rectangular pyramid is 360 ft³

What is volume of a shape?

Volume can be defined as the 3-dimensional space enclosed by a boundary or occupied by an object.

Volume of a square base pyramid = 1 / 3 × B × h

where

B = base area

Therefore,

Volume of a square base pyramid = 1 / 3 × 7² × 12

Volume of a square base pyramid = 1764 / 3 = 588 ft³

Volume of a rectangular prism = lwh

Volume of a rectangular prism =  6 × 5 × 4 = 120 ft³

Volume of a rectangular pyramid = 1 / 3 lwh

Volume of a rectangular pyramid = 1 / 3 × 10 × 12 × 9 = 1080 / 3 = 360 ft³

learn more on volume here: https://brainly.com/question/1578538

Evaluate −x^2+4x+1 when x=−2.

Answers

-(-2)²+4(-2)+1-(4)-8+1-4-7-11

Hey there!

In order to evaluate this expression, we need to plug in the value of x (-2)

So we have

-x²+4x+1

plug in -2

-(-2)²+4(-2)+1

-4-8+1

-12+1

-11

Hence, the answer's

[tex]\boxed{\boxed{\bold{-11}}}[/tex]

Hope everything is clear.

Let me know if you have any questions!

#ILoveLearning

:-)

2x-10=12 what is the value of x+4

Answers

Answer:

15

Step-by-step explanation:

if 2x-10=12 then

2x=22 so

X=11

X+4= 15

Answer:

15

Step-by-step explanation:

1. we find what x is by finding out the first equation:

2x - 10 = 12

Add 10 to both sides (it cancels out on the first side)

-10 + 10 = 0 (cancels out)

12 + 10 = 22

2x = 22

Now we divide both sides by 2 to get x alone

22 divided by 2 = 11

X = 11

2. Now we can solve the equation x + 4:

Just fill in x, which as we solved, is 11

x + 4 = 11 + 4 = 15

Therefore, the value of x + 4 is 15.

Find the measure of the missing angle in this triangle.

Answers

180-110-45= 25 degrees

Answer:

b = 25°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , that is

b + 110° + 45° = 180°

b + 155° = 180° ( subtract 155° from both sides )

b = 25°

HELP.

can someone give me an explanation of how to do this? i just want to know how to apply the explanation to other problems!

Answers

Mid point of any two points (x1,y1) and (x2,y2)

is ((x1+x2)/2,(y1+y2)/2)

using this

we get coordinates of d are (a,-2b)

THIS IS MY LAST QUESTION PLEASE HELP ME
Zion Sun Chairs manufactures 3,575 beach chairs each month. Determine the minimum sales price
Zion Sun Chairs must sell each chair for to break even if the total annual fixed costs are $17,363.50
and the variable cost per chair is $52.17.
O $57.03
O $64.50
O $81.25
O $79.65

Answers

Answer:

81.25

Step-by-step explanation:

Which statements are true regarding the regular dodecagon? Check all that apply

Answers

Answer:

A dodecagon is a shape with 12 sides

Step-by-step explanation:

Decagon is 10 and do is 2 so 12

how do i do

6w cubed - w

i am so confused

Answers

216w^3
You can separate it to 6w*6w*6w so then 6*6*6=216 and w*w*w=w^3

Which statement accurately describes the contents of the two boxes in the image?


A. The box on the top consists of a mixture while the box on the bottom consists of a pure substance.


B. Both boxes consist of pure substances.

C. The box on the top consists of a pure substance while the box on the bottom consists of a mixture.

D. Both boxes consist of mixtures. ​

Answers

The statement that describes the content of the two boxes is that the box on the top contains a pure substance, while the one on the bottom contains a mixture.

What is the difference between a pure substance and a mixture?

A pure substance often refers to a specific element such as nitrogen, helium, etc. that has not been modified or mixed with others.

On the other hand, a mixture includes two or more elements mixed.

What is the content of the first box?

The first box contains only nitrogen, which is a pure substance.

What is the content of the second box?

Different from the first box, this box contains two types of substances carbon and oxygen, which is why particles have two different colors. This means the content is a mixture.

Learn more about substances in: https://brainly.com/question/24372098

Kaylee was out at a restaurant for dinner when the bill came. her dinner came to $24. after adding in a tip, before tax, she paid $28.08. find the percent tip.

Answers

Answer:

17%

Step-by-step explanation:

subtract/originial*100=lercent change

4.08/24=0.17*100=17

The answer is 17%

200 divided by 5 what is the answer

Answers

Answer:

40

Step by Step:

200/5 = 40

please help me will give branlist

Answers

Answer:

A. 8(3 + 8x)

Step-by-step explanation:

Hope it helps you in your learning process

To determine the number of rams in a conservation area, a researcher catches and marks 103 rams. Then the researcher releases them. Later, 89 rams are caught and it is found that 21 of them are tagged. About how many rams are in the conservation area?

There are about rams in the conservation area.

(Round your answer to the nearest whole number as needed.)

Answers

Answer:

19 the explanation is 19 46

Please Help!!!!!!!!!!!!!!! I need this ASAP!

Answers

It’s the second choice
The answer is x=4; (4,11)
Hope this helps:)

30 POINS Find the measures of the numbered angles in the parallelogram. Please help

Answers

Answer:

Is there supposed to be an attachment? if so please send it so I can answer your question.

what is equivalent to 24x + 32y

Answers

Answer:

8*(3x-4y)

Step-by-step explanation:

Just did the test

solve pls brainliest

Answers

Multiply 1/4 by 2/2 to get the same denominator of 8. Then the first blank would be 2/8 then your answer is 3/8
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