Mathematics High School

Using Pascal triangle, write down the binomial expansion of
[tex] {(1+y)}^{8} [/tex]
simplifying all the terms.​

Answers

Answer 1

Answer:

1 + 8y + 28y² + 56y³ + 70[tex]y^{4}[/tex] + 56[tex]y^{5}[/tex] + 28[tex]y^{6}[/tex] + 8[tex]y^{7}[/tex] + [tex]y^{8}[/tex]

Step-by-step explanation:

For the expansion of [tex](1+y)^{8}[/tex]

Using the row of Pascal's triangle for n = 8 , that is the coefficients are

1  8  28  56  70  56  28  8  1

Decreasing powers of 1 from [tex]1^{8}[/tex] to [tex]1^{0}[/tex]

Increasing powers of y from [tex]y^{0}[/tex] to [tex]y^{8}[/tex]

Then

[tex](1+y)^{8}[/tex]

= 1 . [tex]1^{8}[/tex].[tex]y^{0}[/tex] + 8. [tex]1^{7}[/tex].[tex]y^{1}[/tex] + 28. [tex]1^{6}[/tex].y² + 56. [tex]1^{5}[/tex].y³ + 70. [tex]1^{4}[/tex].[tex]y^{4}[/tex] + 56. 1³.[tex]y^{5}[/tex] + 28. 1².[tex]y^{6}[/tex] + 8. [tex]1^{1}[/tex].[tex]y^{7}[/tex] + 1. [tex]1^{0}[/tex].[tex]y^{8}[/tex]

= 1 + 8y + 28y² + 56y³ + 70[tex]y^{4}[/tex] + 56[tex]y^{5}[/tex] + 28[tex]y^{6}[/tex] + 8[tex]y^{7}[/tex] + [tex]y^{8}[/tex]

Answer 2

Answer:

y⁸ + 8y⁷ + 28y⁶ + 56y⁵ + 70y⁴ + 56y³ + 28y² + 8y + 1

Step-by-step explanation:

Given binomial

(1 + y)⁸

Expanding using Pascal triangle (attached)

Replace a and b with y and 1 in the bottom row of the triangle

(1 + y)⁸ = (y + 1)⁸ = y⁸ + 8y⁷ + 28y⁶ + 56y⁵ + 70y⁴ + 56y³ + 28y² + 8y + 1
Using Pascal Triangle, Write Down The Binomial Expansion Of [tex] {(1+y)}^{8} [/tex]simplifying All The

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What is the image of (-9,0) after a dilation by a scale factor of 2 centered at
the origin?

Answers

Answer:

The image is (-18,0)

Step-by-step explanation:

Here, we want to find the image of the given point after dilation by the given scale factor

Mathematically, given a point with the pre-image (x,y) going under the dilation of scale factor k, centered at the origin, the coordinates of the image will be;

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Applying this in the given scenario, we have

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= (-18,0)

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a

Step-by-step explanation:

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what is 2.006 + 6.001?

Answers

   2.006

+ 6.001

__________

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So, therefor, the answer is 8.007.

What's 64/4 in the simplest form

Answers

Answer:

16

Step-by-step explanation:

64 divided by 4 is equal to 16.

64 can be divided by 4 perfectly, so 16

4x + (-3) = -11
What is my answer can You please help me

Answers

Answer:

-2

Step-by-step explanation:

Let's solve your equation step-by-step

4x−3=−11

Step 1: Add 3 to both sides

4x−3+3=−11+3

4x=−8

Step 2: Divide both sides by 4

4x

4

=

−8

4

x=−2

Answer:

[tex]4x + ( - 3) = - 11 \\ 4x (- 3) = - 11 \\ 4x = - 11 + 3 \\ 4x = - 8 \\ x = \frac{ - 8}{4} \\ x = - 2[/tex]

Which of the following is the correct expanded form for the series below?
4
Σ-22
»=0
O-1-2-4-8-16
1-2 + 4-8 + 16
O-2-4-8-16
0-2 + 4 - 8 + 16

Answers

Answer:

-1-2-4-8-16

Step-by-step explanation

The solution is, 1-2 + 4-8 + 16, is the correct expanded form for the series Σ-2^n, n = 0 to 4.

What is an exponent in math?

An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.

here, we have,

given that,

the  series Σ-2^n, n = 0 to 4.

now, we have to find,

the correct expanded form for the series ,

as , we get,

the value of n = 0 to 4

so, putting the value of n = 0,1,2,3,4

we get the series as,

Σ-2^n

= -2^0 + (-2)^1 + (-2)^2 + (-2)^3 + (-2)^4

= 1 -2 + 4 - 8 +16

Hence, The solution is, 1-2 + 4-8 + 16, is the correct expanded form for the series Σ-2^n, n = 0 to 4.

To learn more on exponent number click:

brainly.com/question/19467739

#SPJ7

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Answers

Answer:

64 square ft^3

Step-by-step explanation:

If the side lengh is 3 then you would have 4^3 which is 64.

Answer:

64

Step-by-step explanation:

Simplify the expression so there is only one power for each base.

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Answer:

Step-by-step explanation:

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Quick help please!!!

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Answer:

D

Step-by-step explanation:

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Don Pedro tenía una parcela de 10 hectareas, vendió la quinta parte y el resto lo dividió entre sus 4 hijos, cuantas hectareas recibió cada uno?

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If we give the cashier a $20 bill for a shirt that costs $22.95, how much more do we owe the cashier?

Answers

Answer:

$2.95

Step-by-step explanation:

$22.95-$20

we owe the cashier $2.95

explanation:
20 - 22.95 = -2.95

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Answers

It is(A) 116
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It will be 61 trust me men 100%not 116

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Answers

Answer:

you mean the decimal point?

Step-by-step explanation:

You will know when you cross the decimal point when multiplying.

Answer: it would just be like putting a comma normally, just all you have to do is get your new number but then just add both the comma and decimal it shouldn’t effect on where its put! If that’s what your asking!

Step-by-step explanation:

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Answers

Answer: Greetings my dude. The volume of the triangular prism is around 1,138 Centimeters Cubed.

Hope this helps!

Answer:

volume = length * breadth * height

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Answer:

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Answers

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Step-by-step explanation:

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Answers

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Answers

Answer:

x = 60

Step-by-step explanation:

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After that you have to add what you already have (49 degrees) with what you just found (71 degrees)

49 + 71 = 120

Now that you have 120, you have to again subtract 180 by 120 to get your answer, 60 degrees. And that's it.

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Answers

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Answer:

50$

Step-by-step explanation:

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(do u mean 7.50 cuz if u did its 0.50 cents)

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Answers

Answer:

answer is 175 miles, have a good day <3

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Answers

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Answers

Answer:

x = 69 degrees

Step-by-step explanation:

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180 - 77 - 34 = 69

x = 69 degrees

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B
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C
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Answers

Answer:

1884.95

Step-by-step explanation:

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1884

Step-by-step explanation:

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Answers

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Step-by-step explanation:

that's what gogle said

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Step-by-step explanation:

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Answers

Answer:

your answer will be option B

you are right

Step-by-step explanation:

have a nice day!!

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Answers

Answer:

i recommend math-way's they give you step by step or if you are work on Big ideas work use Slader they have all the answers  

Step-by-step explanation:

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Please help me need it done ASAP

Answers

Answer:

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Step-by-step explanation:

You just need to combine like terms ;)

Hope it helps, let me know

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