Mathematics College

Solve the equation x^16 – 2x^15 – x^14 + 4x^13 – x^12 – 2x^11 + x^10 = 0 in the real number system.


a) x = 0 with multiplicity 10, x = –1 with multiplicity 4, x = 1 with multiplicity 2

b) x = 0 with multiplicity 10, x = –1 with multiplicity 3, x = 1 with multiplicity 3

c) x = 0 with multiplicity 10, x = –1 with multiplicity 2, x = 1 with multiplicity 4

d) x = –1 with multiplicity 2, x = 1 with multiplicity 4

Answers

Answer 1
Start by taking out a common factor.
x^10
x^10(x^6 - 2x^5 - x^4 + 4x^3 - x^2 - 2x + 1) = 0
So far we know that D won't work.
x - 1 is a factor because putting 1 in for the xs in the expression inside the brackets gives 0 Now you need to do a division. I'm going to assume you can do that.
Using division, I get
x^5 - x^4 - 2x^3 + 2x^2 + x - 1 Now divide x - 1 into this mess again. You get
x^4 - 2x^2 + 1 which factors into
(x^2 - 1)(x^2 - 1) which factors into
(x - 1)(x + 1)(x - 1)(x + 1) = 0

The first two divisions add (x -1)(x - 1)
========================
So we have (x - 1) with a multiplicity of 4 and (x + 1) with a multiplicity of 2
or x = 1 with a multiplicity of 4 and x = -1 with a multiplicity of 2 and x = 0
with a multiplicity of 10
That's the answer.
===========================
C <<<< ===== Answer.


 
Answer 2

Answer:

C:x = 0 with multiplicity 10, x = –1 with multiplicity 2, x = 1 with multiplicity 4

Related Questions

Find the (real-valued) general solution to the differential equation. z″+8z′=0 z(t)=

Answers

Try this option (see the attached picture).
Final answer:

The general solution to the differential equation z″+8z′=0 is z(t) = Ae^(-8t) + B, where A and B are arbitrary constants.

Explanation:

The differential equation z″+8z′=0 can be solved by separating variables and integrating.

Let v = z′ be the derivative of z.

Then the equation becomes v′+8v=0.

This is a first-order linear homogeneous differential equation, which can be solved by multiplying both sides of the equation by the integrating factor e^(∫8 dt) = e^(8t).

After solving for v, we can integrate it again to find z(t) by substituting back the expression for v in terms of z.

The general solution to the differential equation is z(t) = Ae^(-8t) + Be^(0t) = Ae^(-8t) + B, where A and B are arbitrary constants.

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What is the order of 5x10^4 , 7x10^-5 , 3x10^-9 , 8x10^4 from least to greatest?

Answers

The numbers given in the problem are written in Scientific Notation. By definitios, this is a product of two factors: the first one is a number between 1 and 10, and the second number is 10. This method is used when you have to write numbers that are too large or too small. So, let's write them in their decimal form to understand it better:

 5x10^4=50000
 7x10^-5=0.00007
 3x10^-9=0.000000003
 8x10^4=80000

 Therefore, the order of 5x10^4, 7x10^-5, 3x10^-9, 8x10^4 from least to greatest is:

 3x10^-9, 7x10^-5, 5x10^4, 8x10^4 

The order from least to greatest of the given numbers 5x10^4, 7x10^-5, 3x10^-9, 8x10^4 is 3x10^-9, 7x10^-5, 5x10^4, and finally 8x10^4. This is determined by comparing the exponents and coefficients of the scientific notation.

To find the order of 5x10^4, 7x10^-5, 3x10^-9, and 8x10^4 from least to greatest, we have to compare their exponents as they determine the size of the numbers. The exponent indicates how many times the number 10 is used in a multiplication.

Here are these numbers in order from the smallest to the largest:

3x10^-97x10^-55x10^48x10^4

The smaller the exponent (more negative), the smaller the number. The first is the smallest because it has the most negative exponent (-9), and the last is the largest with the exponent of 4. When exponents are the same, we then compare the coefficients (the numbers before the 'x10'), in this case, 5 is less than 8, so 5x10^4 is smaller than 8x10^4.

a baker used 4 cups of flour to make 5 batches of brownie. How many cups of flour does the baker need to make 1 batch of brownies

heeelp
please I will mark the brainliest, please help and show your work

Answers

hello

the asnwer is 6.4 ounces of flour per batch U have to add the batches and brownies then divide

Have  a nice day
6.4 ounces. you have to divide the batches of brownies by the cups of flour

Clark and his brother Kent played floor hockey in their living room. Each goal was worth 2 points. Clark scored 6 points. Kent scored 8 points. How many points did they score all together?

Answers

28 is the answer because multiply 6 times 2 and multiply 8 times 2 you would get 12 and 16 which when u add them it equals 28

B= [2 8 .6 3 ] A= 3 0 2 -1]
what is BA ?

Answers

The product of matrices[tex]\(B\) and \(A\) is \([12 \, 24 \, 4 \, -2]\).[/tex]

To find the product (BA), we multiply each row of (B) by each column of (A) and sum the products.

Let's calculate the elements of the resulting matrix (BA):

  a. First row, first column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

  b. First row, second column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

  c. First row, third column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

  d. First row, fourth column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

Therefore, the first row of [tex]\(BA\) is \([4.2 \, 4.2 \, 4.2 \, 4.2]\).[/tex]

Similarly, for the second row of (BA):

  a. Second row, first column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

  b. Second row, second column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

  c. Second row, third column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

  d. Second row, fourth column:

[tex]\[ (2)(3) + (8)(0) + (0.6)(2) + (3)(-1) = 6 + 0 + 1.2 - 3 = 4.2 \][/tex]

Therefore, the second row of [tex]\(BA\) is \([4.2 \, 4.2 \, 4.2 \, 4.2]\).[/tex]

Hence, the product [tex]\(BA\) is \([12 \, 24 \, 4 \, -2]\).[/tex]

Alexa's friends got her a skydiving lesson for her birthday. Her helicopter took off from the skydiving center, ascending in an angle of 20^\circ20
∘
20, degree, and traveled a distance of 3.43.43, point, 4 kilometers before she fell in a straight line perpendicular to the ground.
How far from the skydiving center did Alexa land?

Answers

Answer:

3.19495491 rounded to the nearest hundredth is 3.19

Step-by-step explanation:

The distance from the skydiving center did Alexa land will be 3.19 km. The formula of trigonometry is used in the given problem.

What is trigonometry?

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

From ΔABC it is obtained that;

[tex]\rm Cos A = \frac{AC}{AB} \\\\ COS 20^0 = \frac{AC}{3.4} \\\\ AC= 0.9694 \times 3.4 \\\\ AC = 3.19 \ km[/tex]

Hence the distance from the skydiving center did Alexa land will be 3.19 km.

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Samatha has 24 cards. Chelsea saw 15 more cards than Samatha. How many cards does Chelsea have?

Answers

15 more than 24 is the same as 24 + 15.
24 + 15 = 39
24+15=39   
Chelsea has 39 cards    

Find (19 x 10*5) -(5 x 10 *4)

Answers

(19 x10*5) is 950
(5 x 10*4) is 200
soo 950 - 200 = 750

Answer:d


Step-by-step explanation:


You have two summer jobs. At the Burger Palace you earn $8 per hour. At the community center you teach soccer clinics for $10 per hour. You want to earn at least $200 a week. If x is the number of hours you work at Burger Palace and y is the number of hours you work at the community center, which graph shows all the ways you can earn at least $200 a week? A. 2003-09-04-00-00_files/i0160000.jpg B. 2003-09-04-00-00_files/i0160001.jpg C. 2003-09-04-00-00_files/i0160002.jpg D. 2003-09-04-00-00_files/i0160003.jpg Please select the best answer from the choices provided A B C D Mark this and return

Answers

the complete question in the attached figure
 we have that
x-------------> number of hours works at Burger Palace -----> $8
y-------------> number of hours works at community center -----> $10

8x+10y>=200

using a graph tool
see the attached figure

the answer is the option B

With two dice, each numbered 1-6, there are two possible ways to roll a 3: thus, for the outcome of 3 (a particular macrostate) there are 2 microstates. how many possible ways are there to roll a 4?

Answers

Microstates for a sum of 3 :  (1,2) and (2,1)
Microstates for a sum of 4:  (1,3),(2,2),(3,1)  so three possible microstates.

The total weight of 15 boxes is 45 pounds .how much would 40 boxes weigh

Answers

40 boxes would weigh would weigh 120 pounds
To answer this, we must first assume that each box weighs the same.  If this is true, you would make a rate of how many pounds in 15 boxes: 45 lbs/15 boxes.  From here determine the weight per box by dividing 45 by 15.  This means each box is 3 pounds.  Multiply this by the total number of boxes (3 x 40).  This gives you a total weight of 120 pounds for 40 boxes.

-6x+5-4(x-1)=-4x-(5x-3)+4

Answers

Hello there!

-6x + 5 - 4(x - 1) = -4x - (5x - 3) + 4

We need to use the distributive form

-6x + 5 + (-4)(x) + (-4)(-1) = -4x - 5x + 3 + 4

-6x + 5 - 4x + 4 = -4x - 5x + 3 + 4

-10x + 9 = -9x + 7

Now we can subtract 9 from both sides

-10x + 9 - 9 = -9x + 7 - 9

-10x = -9x - 2

Add 9x to both sides

-10x + 9x = -9x + 9x - 2

-x = -2

We cannot leave it with a negative sign, divide both sides by -1

-x/-1 = -2/-1

x = 2

I hope the steps are clear to understand. If you have any misunderstanding feel free to let me know.

As always, I am here to help!

What is the area of this figure?
Select from the drop-down menu to correctly complete the statement.

The area of the figure is ? cm2.

A. 102
B. 132
C. 168
D. 340

SOMEONE PLEASE HELP ASAP!!

Answers

First of all we can draw a parallel line to divide the figure into a triangle and a rectangle as shown in the figure. To find the area of our rectangle, remember that the area of a rectangle is length times width, so [tex]A_{r} =lw[/tex]. Since we know for our figure that the length and width of our rectangle are 13cm and 6cm respectively, lets replace those values in our formula to get its area:
[tex]A _{r} =(13cm)(6cm)[/tex]
[tex]A=78cm^{2} [/tex]
Similarly, the area of a triangle is one half times base times height, so [tex]At=( \frac{1}{2})bh [/tex]. Since we know that our base is 8cm and our height 6cm, lets replace those values in our equation to find the area of our triangle:
[tex]A_{t} =( \frac{1}{2})(8cm)(6cm) [/tex]
[tex]A_{t} =24cm^{2} [/tex]

Now the only thing left is add our areas:
 [tex]A_{total} =78cm^{2}+24cm^{2} =102cm^{2} [/tex]

We can conclude that the correct answer is A. 102

A pair of angles can be complementary and supplementary. The answers are sometimes? always? or never true? Justify the answer

Answers

 The complementary angles are those angles whose measures add up to 90 degrees, that is, if two complementary angles are in turn consecutive, the non-common sides of them form a right angle.
 Two angles are supplementary if their sum equals 180 °:
 The supplementary angles are those that added are worth two right angles, that is, 180º.
 answer:
 A pair of angles can be never complementary and supplementary

ILL CHOOSE BRAINLIEST!!!Which region represents the solution to the given system of inequalities?

A
B
C
D

Answers

The answer is D, because that is the place where the lines intersect.

The solution of a set of inequalities is the place where the lines intersect.

Hope I helped!

Let me know if you need anything else!

~ Zoe

Answer :- D region represents the solution to the given system of inequalities.


Explanation:

In the graph we can see the two lines drawn from the given system are intersecting in the fourth quadrant.

⇒The solution of the system lie in the fourth quadrant.

∴region D represents the solution to the given system of inequalities.

The graph of the linear inequality is the graph of all solutions of the system where the solution of the system of inequalities is the intersection region of the solutions of the two inequalities.

Which property can be used to expand the expression -2(3/4x + 7)?

Answers

distributive property
-2(3/4 x + 7)
-3/2 x - 14 <<<<<------- answer.

Warning. don't go any further.

Answer:

C

Step-by-step explanation:

Right in edge2020

The dining room table in Logan’s dollhouse is a replica of the dining room table in the actual house . The replica is 4 7/8 in. Long how long is the table in the actual house

Answers

To find the length of the actual table, multiply the replica's length by the scale factor:
4 7/8 x 1/16 = ___ ↓
39/8 x 1/16 = 39/128.

Hope this helps,
♥A.W.E.S.W.A.N.♥

Answer:

6ft 6 in

Step-by-step explanation:

Write a proportion that uses the scale factor 1/16. The numerator corresponds to the dollhouse, and the denominator corresponds to the actual house. So 4 7/8 goes in the numerator, and the variable goes in the denominator.

1/16=478xx=16⋅478x=78

There are 12 in. in a foot, so 78 in. equals 6 ft 6 in.

what's the area of a square picture with 16 inch sides

Answers

To find the area of a square picture with 16 inch sides, we must use the formula for the area of a square: A=s^2, where s represents the value of the side length of the square.  

To solve, we must plug in the given side length of 16 inches into the formula.

A = (16 inches)^2
A= 256 inches^2

Therefore, your answer is 256 inches^2.  

Hope this helps!

Answer:

256

Step-by-step explanation:

factor completely y^2-xy-56x^2

Answers

You can factor this out by thinking of the factors of 56 that have a sum of -1. 7 and 8 are factors of 56 and to get a sum of -1, 8 should be negative. 7 + -8 = -1

So [tex] y^{2} - xy - 56x^{2} [/tex] factored out is (y+7x)(y-8x)

We can check this using FOIL
F = (y)(y) = [tex] y^{2} [/tex]
O = (y)(-8x) = -8xy
I = (7x)(y) = 7xy 
L = (7x)(-8x) = [tex] -56x^{2} [/tex]
[tex] y^{2} - 8xy + 7xy - 56x^{2} [/tex] Combine like terms
[tex] y^{2} - xy - 56x^{2} [/tex]

Answer: I got (y-8x)(y-7x) by factoring out the factors of 56, that have a sum of -1.

8 and 7 are factors of 56 when you multiply them and to get a sum of -1, 8 should change to negative. 7 + -8 = -1

Can someone verify this for me please!

Answers

It's true, friend. I take similar tests through ARVA (Arkansas Virtual Academy/k12).

Factor the expression 8x3y − 8x2y − 30xy.

Answers

Answer:  Our factorized term will be

2xy(2x+5)(2x-3)

Explanation:

Since we have given that

[tex]8x^3y-8x^2y-30xy[/tex]

All we need to do is to factorise this expression.

Here are the steps given below:

[tex]2xy(4x^2-4x-15)[/tex]

By manipulating the terms, we get:

[tex]2xy[(2x)^2-4x+1-16]\\\\2xy[(2x-1)^2-16]\\\\2xy[(2x-1)^2-(4)^2]\\\\2xy[(2x-1-4)(2x-1+4)]\\\\2xy[(2x-5)(2x+3)][/tex]

Alternatively,

By using splitting the middle terms,

[tex]2xy(4x^2-4x-15)\\\\2xy(4x^2-10x+6x-15)\\\\2xy[2x(2x-5)+3(2x-5)]\\\\2xy(2x-3)(2x+5)[/tex]

Hence, our factorized term will be

2xy(2x+5)(2x-3)

an appliance store sells lamps at $ 95.00 for two.a department store sells similar lamps at five for 250.00 which store sells at a better rate? how much is better?

Answers

the appliance store sells sells it at a better rate because if 250$ is for 5 lamps then it's $50 per lamp but if it's $95 than one lamp is $47.50.

Dana wants to make two types of dog treats. She has 10 cups of peanut butter and 12 cups of flour. Her dog bone treat recipe uses 3 cups of peanut butter and 2 cups of flour to make one tray. A tray of her oatmeal dog treat recipe uses 1 cup of peanut butter and 4 cups of flour. She plans to sell trays of dog treats at the town festival and charge $6 for a tray of dog bone treats and $7 for a tray of oatmeal treats. Dana wants to maximize her income from selling the dog treats.
When writing constraints for the problem, what is the most reasonable definition for the variables x and y?

A) Let x represent the number of cups of peanut butter used and y represent the number of cups of flour used.

B) Let x represent the number of cups of peanut butter used and y represent the number of trays of dog bone treats made.

C) Let x represent the number of dog bone treats made and y represents the number of cups of flour used.

D) Let x represent the number of trays of dog bone treats made and y represent the number of trays of oatmeal dog treats made.

Answers

D. Let x represent the number of trays of dog bone treats made and y represent number of trays of oatmeal dog treats made.

Answer with explanation:

Number of cups of peanut that Dana has =10 cups

Number of cups of flour that Dana has =12 cups

Let x represent the number of trays of dog bone treats made and y represent the number of trays of oatmeal dog treats made.

Constraints

⇒x>0, y>0

⇒3 x+y ≤10

⇒2 x+4 y ≤ 12

Maximize(Objective Function):

Z=6 x +7 y

⇒⇒ The most reasonable definition for the variables x and y as Dana wants to maximize her income from selling the dog treats

Option D: Let x represent the number of trays of dog bone treats made and y represent the number of trays of oatmeal dog treats made.

3c-d=t solve for d

I'm confused on this

Answers

d= 3c-t

Hope this helps ;)
To solve for d simplify both sides of the equation then isolate the variable
d=3c-t

Ally bought a mattress and 4 pillows. The mattress cost $769
more than the 4 pillows. She gave the cashier $1300 and
received $51 change.
How much did each pillow cost?

Answers

each pillow costs $120

Answer:

Cost of each pillow is $120.

Step-by-step explanation:

Let P denotes cost of each pillow and M denotes cost of mattress.

Then, given cost of mattress is $769

also, Ally gave the cashier $1300 and received $51 change.

Total amount Ally paid = total amount she gave - total amount she receives back.

                                     = $( 1300 - 51 )

                                     = $1249

Since, Ally brought one mattress and 4 pillow . Thus, Total cost is given as,

⇒ M + 4 P = 1249

⇒ 769 + 4 P = 1249

⇒ 4 P = 1249 - 769

⇒ 4 P = 480

⇒ P = 120

Thus, cost of each pillow is $120.




What is the answer. Do not need to explain.

Answers

Add 5% of what the balance is every year for four years.

5% of $1200 is $60.
5% of $1260 is $63.
5% of $1323 is $66.15.
5% of $1389.15 is $69.45. So the final balance is $1458.45.
1200(.20)=240
1200+240=1440

dividing fractions (pt. 2)

Answers

A) 2/3 / 1/4 = 2/3 x 4/1 = 8/3 = 2 and 2/3

b) 7 / 2/3 = 7/1 x 3/2 = 21/2 = 10 and 1/2
1. 0.167
2. 1.16666666667

identity the pair of numbers that does not belong with the other three. explain.

Answers

3/5 and 5

In the first pair, the only numbers are 9 and 6. Converting 4 into a fraction leaves us with 4/1 - the only numbers in that pair are 1 and 4. In the final one, the only numbers are 2 and 7.
However, converting 5 gives 5/1. What this means is that the top and bottom numbers are not flipped in this pair, making it the odd one out. 

Hope I helped!
3/5 and 5 is the pair that doesn't belong
The other pairs are made of reciprocal numbers .
9/6*6/9=1
4*1/4=4/1*1/4=1
2/7*7/2=1

but 3/5*5/1=3, not 1.

A zoo has two male lions 1/6 of the line on male lions how many lions are there at the zoo

Answers

2 is 1/6 of ?
6x2=12
12 lions in total

!!!!!30 POINTS!!! HELP ME ON THESE GEOMETRY QUESTIONS PLEASE! PLEASE SHOW WORK AND EXPLAIN

Answers

1. Corresponding angles are equal.
.. a) ∠H = ∠B
Corresponding sides have the same relationship.
.. b) GH/DJ = AB/DC

2. Segments of the same line are proportional, so
.. FG/(47 m) = (73.8 m)/(82 m)
.. FG = (47 m)*(73.8/82) = 42.3 m
The distance between the two campsites is 42.3 m.

3. Corresponding sides are proportional.
.. (x -3)/8 = 2.5/2
.. x -3 = 8*(2.5/2) = 10
.. x = 13

4. Expand the fractions and subtract 1.
.. (x +3)/3 = (y +2)/2
.. x/3 +3/3 = y/2 +2/2
.. x/3 = y/2

5. Solved elsewhere.
https://brainly.com/question/8861591
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