What are the factors of
[tex] {x}^{2002} - 1[/tex] ?
I want step-by-step explanation. Spam free answer required

Answers

Answer 1

Step 1: Trying to factor as a Difference of Squares:

Factoring:  x²⁰⁰² - 1

Theory : A difference of two perfect squares,  A² - B²  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

A² - AB + BA - B² =

A²  - AB + AB - B²

 A² - B²

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 1 is the square of 1

Check: x²⁰⁰²  is the square of  x¹⁰⁰¹

Factorization is :       (x¹⁰⁰¹ + 1) × (x¹⁰⁰¹ - 1)


Related Questions

help pleasee
on the image
with the steps.​

Answers

Answer:

  an = 22 -6(n -1)

Step-by-step explanation:

The first term of the sequence is given as a1 = 22. The general term of an arithmetic sequence is ...

  an = a1 +d(n -1) . . . . n-th term for first term a1 and common difference d

The third term will be ...

  a3 = 10 = 22 +d(3 -1)

Then the common difference is ...

  10 -22 = 2d

  -12/2 = d = -6

__

Putting the known values into the formula for the general term, it becomes ...

  an = 22 -6(n -1)

__

This can be simplified to ...

  an = 28 -6n

Plz help with this question

Answers

Answer:

a) 72cm²

b) 9 cm²

c) 9 cm²

d) 54 cm²

Step-by-step explanation:

a) The area A of a rectangle is given by the formula, A=lw

12 * 6 = 72cm²

b) To calculate the area of a triangle, multiply the height by the width (this is also known as the 'base') then divide by 2.

(6 * 3) : 2 = 9 cm²

c) To calculate the area of a triangle, multiply the height by the width (this is also known as the 'base') then divide by 2.

(6 * 3) : 2 = 9 cm²

d) To find the area of the parallelogram, multiply the base of the perpendicular by its height.

(12 - 3) * 6 = 54 cm²

A rectangular garden has a walkway around it. The area of the garden is 4(2.5x + 1.5). The combined
area of the garden and the walkway is 5.5(4x + 4). Find the area of the walkway around the garden as
the sum of two terms.

Answers

Answer:

Area of Walkway = 12x+16

Step-by-step explanation:

Area of Garden = 4(2.5x + 1.5)  [Garden Area]:  (10x + 6)

Area of Garden and Walkway = 5.5(4x+4) [Total Area]:  (22x + 22)

Area of Walkway = [Total Area] - [Garden Area]

Area of Walkway = [5.5(4x+4)] - [4(2.5x + 1.5)]

Area of Walkway = [22x+22)]   - [10x + 6)]

Area of Walkway = 12x+16

Answer:

9x+11 Its hard to explain but if you need a explanation khan academy really helps.

what is the difference in length between a 1 1/4 and 3/8

Answers

Answer:

7/8

Step-by-step explanation:

1 1/4 is the same as 5/4.

5/4 is also the same as 10/8.

The distance from 3/8 to 10/8 is 7/8.

Hope that helps

Answer:

1 1/4 - 3/8

5/4 - 38

10/8 - 3/8

7/8

ASAP HELP PLEASE SHOW ALL WORK
*Find the value of x. Show all the work

Answers

The line of length 48 is passing through the midpoint of traingle so it's half of base

[tex]\\ \sf\longmapsto \dfrac{3x}{2}=48[/tex]

[tex]\\ \sf\longmapsto 3x=96[/tex]

[tex]\\ \sf\longmapsto x=32[/tex]

Pls help me with this

Answers

Step-by-step explanation:

a)

clearly, A and B are mirrored images of each other around the x-axis.

and the equation of the x-axis is simply

y = 0

b)

this is trickier.

first of all, the mirror line is now vertical and not horizontal.

and where is it ? of course, in the middle between A and B.

how many units are there between A and B ?

I am counting 5. so, the middle between them is 2.5 units.

so, let's go e.g. from A 2.5 units to the right (in the direction of B).

where do we end up ? at x = 0.5

and that is also the equation of the vertical line there.

again

x = 0.5

HELPP
what is the integer 23504 into a polynomial ??

Answers

A possible polynomial for this integer is 5y x 94 + 4

A polynomial is a type of mathematical expression that includes:

Numbers, also known as constants.Mathematical symbols such as -, +, x.Variables that represented by letters.

Now, to create a polynomial you will need at least two monomials or terms joined by a symbol. Here are some examples of polynomials:

4x + 5y-2x -x +7

One possible polynomial for the integer 23504 is

5y x 94 + 4

In this polynomial, y is equal to 50. Now, to make sure this is correct you can solve the polynomial.

5y x 94 + 4(5 x 50) x 94 +  4250 x 94 + 423500 + 423504

Learn more about polynomial in: https://brainly.com/question/17822016

The following shapes are congruent. Write the correct congruence statement for shape MJZP.

A. BLXY

B. LXYB

C. XYBL

D. YBLX

Answers

Answer:

B. LXYB.

Step-by-step explanation:

hellllllllllllllllllllppppppppppppppppppppp

Answers

Answer:

Y-intercept: (0, -10)

X-intercepts: (5,0), (1,0)

Axis of symmetry: (3,0)

Step-by-step explanation:

You can tell what the y-intercept is by looking at the function. At the end there is a “-10”, which indicates that it’s the y-intercept.

There are many ways to find x-intercepts. You can factor the function, use the quadratic formula, or complete the square.

By factoring it, you get

-2(x-5)(x-1)=0

If one part of it equals zero, than the whole function equals zero.

So it can be split up like this

(x-5)=0

(x-1)=0

So...

x=5 and x=1 are the the zeros or (5,0) and (1,0)

Finally, you convert the function from standard form to vertex form. By doing -b/2a, you can find the x-coordinate of the vertex, which is the axis of symmetry. The answer is 3 or (3,0) because -12/2(-2)= 3.

Area of square whose side is 11 cm ________

Answers

Answer:

121 cm²

Step-by-step explanation:

Square's area formula is

A=a²

where a stands for a side of the square

A=(11 cm)²

A=121 cm²

whenever you're talking of area you put cm²

Answer:

Given :

✧ Side of square = 11 cm

To Find :

✧ Area of square

Using Formula :

[tex]\star\small{ \underline{\boxed{\sf{\red{Area_{(Square)} = {(Side)}^{2}}}}}}[/tex]

Solution :

Substituting the given value in the required formula to find area of square :

[tex]{\dashrightarrow{\small{{\sf{Area_{(Square)} = {(Side)}^{2}}}}}}[/tex]

[tex]{\dashrightarrow{\small{{\sf{Area_{(Square)} = {(11)}^{2}}}}}}[/tex]

[tex]{\dashrightarrow{\small{{\sf{Area_{(Square)} = {(11 \times 11)}}}}}}[/tex]

[tex]{\dashrightarrow{\small{{\sf{Area_{(Square)} = {(121)}}}}}}[/tex]

[tex]{\dashrightarrow{\small{{\sf{Area_{(Square)} = 121 \: {cm}^{2}}}}}}[/tex]

[tex]{\star{\small{\underline{\boxed{\sf{\pink{Area_{(Square)} = 121 \: {cm}^{2}}}}}}}}[/tex]

Hence, the area of square is 121 cm².

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

enter an algebraic expression for the word expression.
The quotient of -4 and y​

Answers

Hey there!

Guide to follow

“Difference” means subtract

“Is” means equal to

“Product” means multiply

“Quotient” means divide

“Sum” means add

Answering your question….

“The [QUOTIENT] of [-4] and [y]

Remember we said “quotient” means divide

So we’re dividing -4 from y and that will be your answer.

Answer

-4 ÷ y

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Brainliest if correct! Please explain how this is done!
In ΔABC, ∠B is a right angle, AB = 30, and sec A = 5/3. Find the value of csc C in fraction and in decimal form.
I will mark brainliest if you are correct!

Answers

The value of csc C in fraction and in decimal form is as follows:

csc C  = 5 / 3

csc C = 1.66666666667

Using trigonometric ratio,

secant A = 1 / cos A = hypotenuse / adjacent

Therefore,

sec A = 5/3

sec A = 1 / cos A

cos A = adjacent / hypotenuse

cos A = 3 / 5

A = cos⁻¹ 0.6

A = 53.1301023542

Therefore,

∠A = 53°

∠B = 90°

∠C = 180 - 143 =  37°

cosec C = 1 / sin C = hypotenuse / opposite

cosec C = 5 / 3

learn more about trigonometry here: https://brainly.com/question/25942962?referrer=searchResults

Lila planted a tree in her backyard. She made a graph to show the tree growth over 5 years.

1) What does the slope mean in real life in the context of the problem?

2) What does the y-intercept mean in real life in the context of the problem?

Answer in complete sentences.

Answers

Answer:

1. Growth rate of tree 3 ft per year, 2. Beginning height of tree 5 feet, rise/run = 3/1 = 3

Step-by-step explanation:

The solution is

1) The slope of the graph m = 3 represents the growth of the tree per year

2) The y-intercept means the initial height of the tree , when x = 0

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P = P ( 3 , 14 )

Let the second point be Q = Q ( 1 , 8 )

Now , the slope of the two points on the line is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 14 - 8 ) / ( 3 - 1 )

Slope m = 6/2

Slope m = 3

Therefore , the slope is 3 feet per year

b)

The y intercept is calculated from the equation of line , when x = 0

So , the equation of line is given as

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 14 = 3 ( x - 3 )

On simplifying the equation , we get

y - 14 = 3x - 9

Adding 14 on both sides of the equation , we get

y = 3x + 5

Now , when x = 0

y = 3 ( 0 ) + 5

y = 5 feet

From the graph we can see that , at 0 years the initial height of the tree is also 5 feet

Therefore , the y intercept is 5 feet

Hence , The slope of the equation is 3 and y intercept is 5

To learn more about equation of line click :

https://brainly.com/question/14200719

#SPJ2

Sound will travel fastest in air at _____.

Answers

Answer: 15 degrees Celsius

Step-by-step explanation:

Sound travels fastest usually at 25 degrees Celsius when the air is hotter as physics professor Kim strong stated

HI THERE

the answer is 15'C

correct me if I'm wrong

What is the volume of a cube with sides of length 15 mm?

Answers

I think the answer is 3375

How many solutions do 5-2x=2x-5

Answers

Answer:

1 solution is the answer

solve similar triangles (advanced)

Answers

Answer:

x = 1.125 AKA x = 1 1/8 AKA x = 9/8

Step-by-step explanation:

CB to ED = 1 : 9

Scale Factor = 1/9

[tex]\frac{1}{9} = \frac{x}{x+9}[/tex] -> cross multiply

9x = x + 9

-x     -x

8x = 9

[tex]\frac{8x}{8} =\frac{9}{8}[/tex]

x = 9/8

find the sum of that amount to RS 9144 in 3 years at 9%per year simple interest ​

Answers

ANSWER:

4937.76

Step-by-step explanation:

I=PRT

I=9144*0.09*9

I=4937.76

If one plane is flying 40 mph and another plane is flying 100 mph, and they
are 200 miles apart and flying directly toward each other, in how long will the planes
meet2

Answers

Answer:

i think 60 miles

Step-by-step explanation:

I just added the 100+40 then

200-140

Answer:

  1 3/7 hours

Step-by-step explanation:

The planes are closing the 200 mile separation distance at a rate of (40 +100) = 140 miles per hour. The time it takes for that distance to be closed is ...

  time = distance/speed

  time = (200 mi)/(140 mi/h) = 200/140 h = 10/7 h = 1 3/7 h

The planes will meet after 1 3/7 hours, about 1 hour 25 minutes 43 seconds.

At Tasty Dogs, 2 of the last 12 customers wanted mustard on their hot dogs. Considering this data, how many of the next 6 customers would you expect to want mustard?

Answers

Answer:

I would expect 1 person to want mustard.

Explanation:

6 is half of 12, and 1 is half of 2 :)

Hope this helped

I agree with everything that dagaminangel said since two out of 12 wanted mustard one should want mustard out of the six

Tyson is 6 feet 2 inches tall. There are 2. 54 centimeters in 1 inch. What is Tyson's height in centimeters?.

Answers

29.1338583 because if you do the math

Answer:

187.96cm

Step-by-step explanation:

first convert 6 feet to cm=182.88

then convert 2 inches to cm=5.08

add your answers together=187.96

PLEASEEEE WILL GIVE BRAINLIEST TO FIRST RIGHT ANSWER!!!!!!!!!!
Find the solution of the system of equations.

2x-3y=-14
5x+9y=-2

Answers

Answer:

Well to solve this I’m gonna use substitution

So

2x-3y=-14

5x+9y=14

I‘m gonna isolate ”x” on the first equation

So it’ll be

2x-3y=-14

2x=-14+3y

x=-7+1.5y

X is -7+1.5y

Now you can subsitute into other equations to find what Y is worth

So lets use the second equation

5(-1+1.5y) + 9y = 14

Now solve for y which is -2

If you subsitute Y back in an equation you’d get -4 for x

So y = -2

and X= -4


Linda took her son to the batting cages. For the first 5 minutes she paid $10 and for
each additional minute she paid $.50. If Linda, paid $22 for her son to go to the batting
cages, how much time were they there for?

Answers

Answer:

29 minutes

Step-by-step explanation:

what is the factor of this 3x - 12

Answers

Answer:

3 (x - 4)

Step-by-step explanation:

Latasha $289 last week.she earned $213.73 this week how much more did latasha earn last week than this week

Answers

Answer:

75.27

Step-by-step explanation:

Subtract this week from last week

289-213.73

75.27

Prove the following:

1 + cos^2 A = 2 ( cos^4A + sin^4A)​

Answers

The 2 sides of the equation are not equal; hence, I cannot prove them to be true.

what is the answer?

Answers

Answer:

1x+-8(-4)=b

Step-by-step explanation:

f(x) = 8x-3 and g(x) =4x +5; find (f /g) (x)

Answers

Answer:

32x + 37

Step-by-step explanation:

f(g(x)) = 8(4x+5) - 3

= 32x + 40 - 3

= 32x + 37

Can someone help me with this question

Answers

Answer:

what is the lesson? abot?

Step-by-step explanation:

8:07, 8:58, ?, 10:43, 11:37
61
9:51
9:50
9:53
9:49

Answers

Answer:

  9:50

Step-by-step explanation:

It appears the sequence has 0:51 as the first difference, and those differences increase by 0:01 in each interval. That means ? must be chosen so that ...

  ? - 8:58 = 0:52   ⇒   ? = 8:58 +0:52 = 9:50

  10:43 -? = 0:53   ⇒   ? = 10:43 -0:53 = 9:50

The missing time is 9:50.

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