Determine the linear factors for x4-2x^2+1

Answers

Answer 1

Use a substitution: let b = x^2
Then b^2 = x^4.

Now you need to factor

b^2 - 2b + 1 =

(b - 1)^2

Since b = x^2, now we replace b with x^2 and factor again.

(x^2 - 1)^2 is the square of a difference of squares.

= (x^2 - 1)(x^2 - 1)

=(x + 1)(x - 1)(x + 1)(x - 1)

= (x + 1)^2(x - 1)^2

Answer 2

Didn't you mean x^4-2x^2+1 ?

Choose "p" to represent x^2. Then p^2 - 2p + 1 = (p-1)(p-1)

These results are equivalent to (x^2-1)(x^2+1).

x^2-1 can be factored: (x-1)(x+1)

x^2-1 (again) can be factored: (x-1)(x+1)

Then the factored expression is (x-1)^2 * (x+1)^2.

Check this by multiplication. Do you obtain x^4 - 2x^2 + 1?

Related Questions

I need help with this problem ASAP. Please.

y=x+√x+5 y=7

Answers

Assuming the square root contained (x+5) not just (x) here is the answer solving for x

Answer:

Solve for

x = 1

y = 7

Step-by-step explanation:

There are 56 trees in an apple orchard. They are arranged in equal rows. There are 8 trees in each row. How many rows of apple trees are there? Which equation can be used to solve this problem?

Answers

Final answer:

In this case, there are 56 trees in the orchard and 8 trees in each row, so there are 7 rows of apple trees in the orchard.

Explanation:

To find the number of rows of apple trees in the orchard, we need to divide the total number of trees by the number of trees in each row.

In this case, there are 56 trees in the orchard and 8 trees in each row.

We can use the equation:

Number of rows = Total number of trees / Number of trees in each row

Plugging in the values:

Number of rows = 56 trees / 8 trees = 7 rows

Therefore, there are 7 rows of apple trees in the orchard.

981,657 rounded to nearest ten thousand

Answers

982,000 is the answer
////////////// sorry i need 20 characters

Answer is 980,000. I think

People drive, on average, 11,900 miles per year. About how many miles each week is that

Answers

Final answer:

To calculate the average weekly driving mileage based on an annual average of 11,900 miles, divide the total miles by 52 weeks, resulting in approximately 228.85 miles driven per week.

Explanation:

The question asks us to calculate how many miles are driven each week if an average person drives 11,900 miles per year. To find the weekly mileage, we can divide the total annual miles by the number of weeks in a year. Since there are 52 weeks in a year, we would perform the following calculation:

Divide 11,900 by 52.11,900 miles \/ 52 weeks = 228.85 miles per week.

Therefore, on average, a person drives approximately 228.85 miles each week.

You drove at 55mph for 4.5 hours. Which of the following equations will tell you how far you drove? A: d=(55)(4.5) B: 55=r(4.5) C: 4.5=55t D: 4.5=r(55)

Answers

A. 55mph x 4.5hrs which makes since because mph is miles per hour, so I drove 55miles every hour.

Answer : The correct equation will be, (A) [tex]d=(55)\times (4.5)[/tex]

Step-by-step explanation :

As we are given that:

Speed = 55 mph

Time = 4.5 hr

As we know that:

[tex]Distance=Speed\times Time[/tex]

So,

[tex]Distance=55mph\times 4.5hr[/tex]

[tex]Distance=55\times 4.5[/tex]

or,

[tex]d=(55)\times (4.5)[/tex]

Thus, the correct equation will be, (A) [tex]d=(55)\times (4.5)[/tex]

20 children plays a game there are 5 children on each team how many teams play the game write a division sentence to represent the problem

Answers

Final answer:

To find the number of teams playing the game, divide the total number of children by the number of children on each team. In this case, there are 20 children and 5 children on each team, so there are 4 teams playing the game.

Explanation:

To find the number of teams playing the game, you can divide the total number of children by the number of children on each team. In this case, there are 20 children and 5 children on each team. So, the division sentence to represent the problem is:

20 ÷ 5 = 4

Therefore, there are 4 teams playing the game.

Let f(x) = k(9x − x2) if 0 ≤ x ≤ 9 and f(x) = 0 if x < 0 or x > 9. (a) for what value of k is f a probability density function?

Answers

We require

[tex]\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx=1[/tex]

Since

[tex]f(x)=\begin{cases}k(9x-x^2)&\text{for }0\le x\le9\\0&\text{otherwise}\end{cases}[/tex]

the integral above reduces to

[tex]\displaystyle\int_0^9 k(9x-x^2)\,\mathrm dx=k\left(\dfrac92x^2-\dfrac13x^3\right)\bigg|_{x=0}^{x=9}=\dfrac{243k}2=1[/tex]
[tex]\implies k=\dfrac2{243}[/tex]

Final answer:

To find the value of k that makes f(x) a probability density function, we need to satisfy two conditions: f(x) must be non-negative for all x and the total area under the curve of f(x) must equal 1. Solving the integral of the function f(x) = k(9x - x^2) from x = 0 to x = 9, we find that the value of k that satisfies these conditions is approximately 0.0696.

Explanation:

In order for the function f(x) to be a probability density function, it must satisfy two conditions:

The function must be non-negative for all values of x.

The total area under the curve of the function must be equal to 1.

Let's analyze the function f(x) = k(9x - x^2) for 0 ≤ x ≤ 9 and f(x) = 0 for x < 0 or x > 9:

If 0 ≤ x ≤ 9, the function f(x) is given by f(x) = k(9x - x^2).The function f(x) is non-negative in the interval [0, 9] if k(9x - x^2) ≥ 0. This is true when k > 0.To find the value of k that makes the total area under the curve equal to 1, we need to integrate the function f(x) = k(9x - x^2) from x = 0 to x = 9 and set it equal to 1:∫09 k(9x - x^2) dx = 1Simplifying the integral gives us k(405 - 364.5) = 1Solving for k, we get k ≈ 0.0696 (rounded to four decimal places).

Therefore, the value of k that makes f(x) a probability density function is approximately 0.0696.

Learn more about Probability Density Functions here:

https://brainly.com/question/35625239

#SPJ2

Find the slope of the line that passes through (90, 93) and (-4, 49).

Answers

93-49/90+4
44/94
22/47

Help please :) ! The dashed triangle is the image of the pre-image solid triangle. What is the scale factor used to create the dilation? Enter your answer in the box.

Answers

Let

x---------> measure of the base of the triangle of the image

y---------> measure of the base of the triangle of the pre-image

sf-------> the scale factor

we know that

the scale factor is equal to

[tex]sf=\frac{x}{y}[/tex]

in this problem we have

[tex]x=6\ units\\y=3\ units[/tex]

Find the scale factor

substitute the values of x and y in the formula above

[tex]sf=\frac{6}{3}=2[/tex]

therefore

the answer is

the scale factor is equal to [tex]2[/tex]

multiply 4xy^3(3×^2y)^2

Answers

[tex]\bf 4xy^3(3x^2y)^2\impliedby \textit{first off, distribute the exponent} \\\\\\ 4xy^3~(3^2x^{2\cdot 2}y^2)\implies 4xy^3~(9x^4y^2)\implies 4\cdot 9xx^4y^2y^3 \\\\\\ 36x^{1+4}y^{2+3}\implies 36x^5y^5[/tex]

What’s the answer to simply
1
-
2
-
4 it’s a fraction.

Answers

[tex]\bf \cfrac{\frac{a}{b}}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c}\\\\ -------------------------------\\\\ \cfrac{\quad \frac{1}{2}\quad }{4}\implies \cfrac{\quad \frac{1}{2}\quad }{\frac{4}{1}}\implies \cfrac{1}{2}\cdot \cfrac{1}{4}\implies \cfrac{1\cdot 1}{2\cdot 4}\implies \cfrac{1}{8}[/tex]

the sum of partial products is equal to the final product?

Answers

the sum of partial product is not always equal to a final product

can someone double check my answers on this integers sheet? (53 points)

Answers

1) -28
2) +36
3) +14114
4)-129
5) - 8
(they are all correct up to this point)

Yes, 1--5 in sentences are all right

hope this helps

Find the area bounded by the curve y = x 1/2 + 2, the x-axis, and the lines x = 1 and x = 4 A. 16 B. 10 2/3 C. 7 1/2 D. 28 1/2

Answers

To find the area of the curve subject to these constraints, we must take the integral of y = x ^ (1/2) + 2 from x=1 to x=4
Take the antiderivative: Remember that this what the original function would be if our derivative was x^(1/2) + 2
antiderivative (x ^(1/2) + 2) = (2/3) x^(3/2) + 2x
* To check that this is correct, take the derivative of our anti-derivative and make sure it equals x^(1/2) + 2

To find integral from 1 to 4:
Find anti-derivative at x=4, and subtract from the anti-derivative at x=1
2/3 * 4 ^ (3/2) + 2(4) - (2/3) *1 - 2*1
2/3 (8) + 8 - 2/3 - 2 Collect like terms
2/3 (7) + 6 Express 6 in terms of 2/3
2/3 (7) + 2/3 (9)
2/3 (16) = 32/3 = 10 2/3 Answer is B

pls help with fractions. (Operations with Rational Numbers) thx, xoxo

ps. This is 7th grade math

Answers

Well I did the math and got 68.75 as his average.

That would be an average of 86.25

12.917 rounded to the nearest ones

Answers

I am pretty sure the answer is 13

To round to the nearest ones, round to the nearest digit for the number 2. Since 9 rounds up, then the answer is 13.

Find the sale price of the item. Round to two decimal places if necessary.

Original price: $217.90

Markdown: 79%

The sale price is $___

Answers

Hello! The markdown of the price is 79%. Even with that, you still have to pay 21% of the price. All we have to do is multiply the original price by the percent. 217.90 * 0.21 is 45.759 or 45.76 when rounded to the nearest hundredth. The sale price is $45.76.

write the following comparison as a ratio reduced to lowest terms.

114 hours to 13 days

Answers

Final answer:

To write the comparison as a ratio reduced to lowest terms, we need to convert both the hours and the days to a common unit of time. There are 24 hours in a day, so we can convert 13 days to hours by multiplying 13 by 24: 13 days x 24 hours/day = 312 hours. Now, the comparison is 114 hours to 312 hours. We can simplify this ratio by dividing both numbers by their greatest common factor, which is 6. 114 ÷ 6 = 19, and 312 ÷ 6 = 52. Therefore, the simplified ratio is 19:52.

Explanation:

WILL GIVE A BRAINLEST AND 20PTS

Which figures can be precisely defined by using only undefined terms? Check all that apply.

angle

arc

circle

line segment

parallel lines

Answers

If my memory seves me well, angle, parallel lines figures which can be precisely defined by using only undefined terms are angle and parallel lines.

Answer:

We can define circle, line segment and parallel lines with the help of undefined terms.

Step-by-step explanation:

The undefined terms in geometry are line, plane and points.

So, we can define line segment, circles and parallel lines with the help of undefined terms.

A line segment is a part of a line that contains two distinct end points.

A circle is defined as a figure with a set of points that are all equidistant from a fixed point called the center.

Parallel lines are lines in a plane that never meet or intersect at any point.

One root of is x = 6. What are all the factors of the function? Use the Remainder Theorem.

Answers

3 and 2 should be the only roots

Answer:

C. (x - 6)(x + 4)(x - 2)

Step-by-step explanation:

i just took the test goodluck

The sum of a 1 digit number and a 3 digit number is 217. The product is 642. One number is between 200 and 225. What are the numbers?

Answers

214 and 3

hope this help :)

3, 214.

3+214= 217
3*214= 642

When a particular machine is functioning properly, 80% of the items produced are non-defective. if three items are examined, what is the probability that one is defective? use the binomial probability function to answer this question?

Answers

15 percent there u go have a good ay

Answer:

The probability is 38.4%

Step-by-step explanation: Here we have two posibilites for each of the 3 items, it is defective or it is not.

Where the probability that the item is defective is equal to 20% (or 0.2 in decimal form)

Now, if only one is defective, this means that the other two are not, so the probabilites (at random) are 20%, 80% and 80%.

Then the joint probability, equal to the product of those 3 probabilities, is:

p = 0.2*0.8*0.8 = 0.128

But we have 3 posible permutations (in which different options are the deffective one) so the probability is 3 times that number:

P = 3p = 3*0.128 = 0.384

So the probbility, in percentage form, is 38.4%

Rohan is checking in poodles for a dog show. A miniature poodle must be between 10 in. and 15 in. at the shoulder. The body length must be no more than 16 in. In addition, the poodle’s shoulder height must be no more than 1 in. longer than its body length.

The graph shows the feasible region, where x represents the poodle’s body length and y represents the shoulder height.

Which ordered pairs meet all the constraints for a successful poodle measurement and make sense in context of the situation?

Select each correct answer.

(11, 14)

(10, 12)

(12, 10.5)

(15, 11)

(11, 9)

Answers

Let

x-------> represents the poodle’s body length

y-------> represents the shoulder height

Constraints

[tex]10\ in \leq y \leq 15\ in[/tex] --------> constraint A

[tex]x \leq 16\ in[/tex] --------> constraint B

[tex]y \leq x+1[/tex] --------> constraint C

Using a graphing tool

see the attached figure

The solution is the shaded area

we know that

If a pair ordered is a solution for a successful poodle measurement

then

the pair ordered meet all the constraints

Let's check each case to determine the solution to the problem

Replace the values of x and y of the point in the different constraints. If all constraints are met, then the point is a system solution

Case A) [tex](11,14)[/tex]

constraint A

[tex]10\ in \leq 14 \leq 15\ in[/tex] ------> is true

constraint B

[tex]11 \leq 16\ in[/tex] --------> is true

constraint C

[tex]14 \leq 11+1[/tex]

[tex]14 \leq 12[/tex] -------> is not true

therefore

the pair [tex](11,14)[/tex] does not meet all constraints

Case B) [tex](10,12)[/tex]

constraint A

[tex]10\ in \leq 12 \leq 15\ in[/tex] ------> is true

constraint B

[tex]10 \leq 16\ in[/tex] --------> is true

constraint C

[tex]12 \leq 10+1[/tex]

[tex]12 \leq 11[/tex] -------> is not true

therefore

the pair [tex](10,12)[/tex] does not meet all constraints

Case C) [tex](12,10.5)[/tex]

constraint A

[tex]10\ in \leq 10.5 \leq 15\ in[/tex] ------> is true

constraint B

[tex]12 \leq 16\ in[/tex] --------> is true

constraint C

[tex]10.5 \leq 12+1[/tex]

[tex]10.5 \leq 13[/tex] -------> is true

therefore

the pair [tex](12,10.5)[/tex] meets all constraints

Case D) [tex](15,11)[/tex]

constraint A

[tex]10\ in \leq 11 \leq 15\ in[/tex] ------> is true

constraint B

[tex]15 \leq 16\ in[/tex] --------> is true

constraint C

[tex]11 \leq 15+1[/tex]

[tex]11 \leq 16[/tex] -------> is true

therefore

the pair [tex](15,11)[/tex] meets all constraints

Case E) [tex](11,9)[/tex]

constraint A

[tex]10\ in \leq 9 \leq 15\ in[/tex] ------> is not true

constraint B

[tex]11 \leq 16\ in[/tex] --------> is true

constraint C

[tex]11 \leq 15+1[/tex]

[tex]11 \leq 16[/tex] -------> is true

therefore

the pair [tex](11,9)[/tex] does not meet all constraints

therefore

the answer is

[tex](12,10.5)[/tex]

[tex](15,11)[/tex]

The data from 200 endothermic reactions involving sodium bicarbonate are summarized as follows: calculate the probability mass function of final temperature

Answers

Given the table below which contains data from 200 endothemic reactions involving sodium bicarbonate:

[tex]\begin{tabular} {|c|c|} Final Temperature Conditions&Number of Reactions\\[1ex] 266 K&48\\ 271 K&60\\ 274 K&92 \end{tabular}[/tex]

We find the probability distribution function as follows:

Let X denote the final temperature, then

[tex]P(X = 266) = \frac{48}{200} =0.24\\ \\ P(X = 271) = \frac{60}{200} =0.3\\ \\ P(X = 274) = \frac{92}{200} =0.46[/tex]

in the greenhouse holds 467 plants how many plants can 6 shelves hold

Answers

To find the answer, divide 467 by 6. 467/6 = 77.83 So each shelf can hold 77.83 plants

If K = {(x, y )|x - y = 5}, find the corresponding range of y for the domain {0, 2, 4}.

Answers

the domain is basically the x value and range is the y value in (x, y). so in this, they are giving you the domain so just plug in the domain numbers into the equation to find the answer.

k = {(x, y)|x - y = 5}

(0, y) (0, -5)
0 - y = 5
y = -5

(2, y) (2, -3)
2 - y = 5
-y = 5 -2
-y = 3
y = -3

(4, y) (4, -1)
4 - y = 5
-y = 5 - 4
-y = 1
y = -1

hope this helped, God bless!

What is the value of the expression? 56−(18÷34) as a fraction in simplest form

Answers

The value of the expression in simplest form is: 55 8/17.

Hope this helps! :D

~PutarPotato

The value of the expression [tex]$ 56 - \left( \frac{18}{34} \right) $[/tex] as a fraction in simplest form is [tex]$ \frac{943}{17} $[/tex].

To solve the expression, we first perform the division within the parentheses:

[tex]\[ \frac{18}{34} \][/tex]

This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

[tex]\[ \frac{18 \div 2}{34 \div 2} = \frac{9}{17} \][/tex]

Now we have:

[tex]\[ 56 - \frac{9}{17} \][/tex]

We need to express the whole number as a fraction with the same denominator as the fraction we are subtracting.

[tex]\[ \frac{56 \times 17}{17} - \frac{9}{17} \][/tex]

[tex]\[ \frac{952}{17} - \frac{9}{17} \][/tex]

[tex]\[ \frac{952 - 9}{17} \][/tex]

[tex]\[ \frac{943}{17} \][/tex]

Twenty-five bakery customers were surveyed to determine if they like cake or pie. The results are shown in the Venn diagram.

Given that a randomly chosen customer likes cake, what is the probability that the customer also likes pie

A. 2/7

B. 2/5

C. 4/7

D.4/5

Answers

In total, 14 people like cake (10+4).
4 of those 14 also like pie.

4/14= 2/7

Final answer: A

From the given Venn diagram. The probability that the customer also likes pie is 2/7.

Given that a randomly chosen customer likes cake

The results are shown in the Venn diagram.

To determine the probability that the customer also likes pie

In total, 14 people liked the cake (10+4).

4 of those 14 also like pie.

What is the formula for probability?

The probability of event A is given by the ratio of the no of a favorable outcome in event A divided by the total outcome in a sample space A.

4/14= 2/7

Option A is correct.

To learn more about the probability visit:

https://brainly.com/question/24756209#SPJ3

What is the slope of the line passing through the points (−1, 7) and (4, −1)?

2nd picture is the choices I have.

Answers

You are given the points (-1, 7) and (4, -1).
You can easily find the slope by using the formula
m = (y₂ - y₁)/(x₂ - x₁)

m = slope
(x₁, y₁) = (-1, 7)
(x₂, y₂) = (4, -1)

m = (-1 - 7)/(4 + 1)
m = (-8)/(5)
m = -8/5

The answer is:
A. -8/5

A student pays for 8.9 pounds of apples with a $10 bill. How much change does the student receive?

Answers

you take 10 - 8.9 = $1.10

Other Questions

The plasma membrane is _____ which means it permits the passage of only certain molecules into and out of the cell, and blocks the passage of some substance altogether though mercantilism limited trade during the age of exploration, european economics grew rapidly during this period, largely because of:a. the natural resources they obtained from their coloniesb. strict regulations that prevented smuggling and other economic crimesc. increased agricultural output the ensured all people were well fedd. the elimination of corrupt corporations and joint stock companies Tyler solved an inequality to determine the number of songs he can buy with a $20 credit at his favorite music website. The solution is graphed below Which phrases accurately describe all the possible quantities of songs he can buy? Check all that apply.no more than 8 songsat least 8 songsa minimum of 8 songsat most 8 songsfewer than 8 songsa maximum of 8 songsno fewer than 8 songs Why does a thermocline form in the ocean? A turtle swims at a speed of 1584 meters per hour. A girl swims at a speed of 1380 millimeters per second how much faster does the girl swim than the turtle in centimeters per minutes? (h) when is the particle speeding up? (enter your answer using interval notation.) (2,4)(6,8) incorrect: your answer is incorrect. f(t) = cos(t/4) Combine the like terms to make a simpler expression: 3k(8)+2 The sum of x and 8 is less than 72 find all possible values of x "The world is made up of two classes the hunters and the huntees. Luckily, you and I are hunters."What is the main purpose of these sentences?A.To explain the theme to the reader B.To show that the character is fearless C.To give the reader a hint about the game D.To tell why the characters are traveling Robert and Tonia are on a date. Tonia is smiling and expressing herself in ways that indicates that she likes Robert. On the other hand, Robert appears less expressive even though he likes Tonia too. How can differences in emotions between Robert and Tonia be BEST explained?" after 5 points are subtracted from every score, the sample mean is found to be m = 24. what was the mean for the original sample? What was a direct result of the Presidential Committee on Civil Rights findings? Starting at sea level, a submarine descended at a constant rate to a depth of 4/5 mile relative to sea level in 3 minutes.What was the submarine's depth relative to sea level after the first minute? Read the passage below carefully and then choose the correct answer. Caesar said to me 'Darest thou, Cassius, now Leap in with me into this angry flood, And swim to yonder point?' Upon the word, Accoutred as I was, I plunged in And bade him follow; so indeed he did. The torrent roar'd, and we did buffet it With lusty sinews, throwing it aside And stemming it with hearts of controversy; But ere we could arrive the point proposed, Caesar cried 'Help me, Cassius, or I sink!' The word in bold means (10 points) A. dressed in uniform B. Greek mythology C. muscle strength D. rushing water Erin and her friends are taking a road trip. She has agreed to drive between hours 3 and 6 of the trip. If h represents the hours of the trip Erin will be driving, then h 3 and h 6 represents her portion of the driving. While she is driving, her distance and time are modeled by the inequality d < 70h. What are the possible hours and distances Erin could be driving? When graphing this scenario, let h be the horizontal variable and d be the vertical variable. Which equation can be used to find the measure of angle LJK?sin(x) = (10/15)sin(x) = (15/10)cos(x) = (10/15)cos(x) = (15/10) The Leukemia and Lymphoma Society sponsors a 5K race to raise money. It receives $55 per race entry and $10,000 in donations, but it must spend $15 per race entry to cover the cost of the race. Write and solve an inequality to determine the number of race entries the charity needs to raise at least $55,000. Mariah borrowed 15 books from the library last month. She's already read 2/5 of them. How many of the 15 books has she read? any math experts? Geometry 1.Justify each step in solving the equation 4x=7(x-3) by writing a reason for each statement.1. 4x=7(x-3)2. 4x=7x-213. -3x=-214. x=7 When creating a writing plan, which of the following should come first? A. The general idea of the essay B. The first section of the body of the essay C. Material that will capture the reader's interest D. A brief summary of the conclusion Steam Workshop Downloader