HELP ME GUYS THANK YOU! :)

The binomial theorem says

[tex]\displaystyle (a + b)^n = \sum_{k=0}^n \binom nk a^{n-k} b^k \\\\(a+b)^n= \binom n0 a^n + \binom n1 a^{n-1}b + \cdots + \binom n{n-1} ab^{n-1} + \binom nn b^n[/tex]

where

[tex]\dbinom nk = \dfrac{n!}{k!(n-k)!}[/tex]

is the so-called binomial coefficient. The binomial coefficients follow a neat pattern called Pascal's triangle:

1

1   1

1   2   1

1   3   3   1

1   4   6   4   1

where the n-th row, starting with n = 0, lists the coefficient of the k-th term in the sum (with 0 ≤ k ≤ n). For example,

[tex]\displaystyle n=0 \implies (a + b)^0 = \sum_{k=0}^0 \binom nk a^{0-k} b^k = \binom00 a^{0-0} b^0 = \underline{1}[/tex]

[tex]\displaystyle n=1 \implies (a + b)^1 = \sum_{k=0}^1 \binom 1k a^{1-k} b^k = \binom10 a^{1-0} b^0 + \binom11 a^{1-1}b^1 = \underline{1}a + \underline{1}b[/tex]

[tex]\displaystyle n=2 \implies (a + b)^2 = \sum_{k=0}^2 \binom 2k a^{2-k} b^k = \binom20a^{2-0}b^0+\binom21a^{2-1}b^1+\binom22a^{2-2}b^2 = \underline{1}a^2 + \underline{2}ab+\underline{1}b^2[/tex]

Each row starts and ends with 1, and every coefficient in between is obtained by adding the coefficients directly above and to the left. The next row, for instance, would be

1   1 + 4   4 + 6   6 + 4   4 + 1   1

or

1   5   10   10   5   1

which is to say,

[tex]\displaystyle (a + b)^5 = \underline{1}a^5+\underline{5}a^4b+\underline{10}a^3b^2+\underline{10}a^2b^3+\underline{5}ab^4+\underline{1}b^5[/tex]

In your case, we have (d - 4b)², so we take a, b, and n above with d, -4b, and 2, respectively:

[tex]\displaystyle (d - 4b)^2 = \sum_{k=0}^2 \binom 2k d^{2-k} (-4b)^k[/tex]

[tex]\displaystyle (d - 4b)^2 = \sum_{k=0}^2 \binom 2k (-4)^k d^{2-k} b^k[/tex]

[tex]\displaystyle (d - 4b)^2 = \binom20 (-4)^0 d^{2-0} b^0 + \binom21 (-4)^1 d^{2-1} b^1 + \binom22 (-4)^2 d^{2-2} b^2[/tex]

[tex]\displaystyle (d - 4b)^2 = 1\cdot1\cdot d^2\cdot1 + 2 \cdot (-4) d \cdot b + 1 \cdot 16 \cdot 1 \cdot b^2[/tex]

[tex]\boxed{(d - 4b)^2 = d^2 - 8bd + 16b^2}[/tex]

a) Write an expression to describe the journey of the yellow submarine.

-> ((0 - 40) + 30) - 25

[] Sea level = 0

[] The descend 40 meters = -40

[] After examining the sea, they rose 30 meters = + 30

[] They dove 25 meters to look at an octopus = -25

b) At what depth did they stop to look at the octopus?

-> -35 meters

[] The started at 0 (0), descended 40 (-40), rose 30 (-10), and then sove 25 (-35) to see the octopus

[] Another way to think of this is to simplify our previous expression completely

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

no

.........................................................

Answer:

a meme

Step-by-step explanation:

Answer:

meem

Step-by-step explanation:

meet bc it is crazy and I luv it

Hey there!

4y + 2x - y + 8

= 4y + 2x - 1y + 8

COMBINE the LIKE TERMS

= (4y - 1y + (2x) + (8)

= (4y - y) + (2x) + (8)

= (2x) + (4y - y) + 8

= 2x + 3y + 8

Therefore, your answer is: 2x + 3y + 8

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

3y+2x+8

Step-by-step explanation:

All you really do is combine the like terms, which in this case is the 3y and the -y. think of the y more as -1y and that is why it's subtrcated.

Answer:

0.681818 miles per min

Step-by-step explanation:

Answer:

  B = (-17, -29)

Step-by-step explanation:

The midpoint (M) of AB is ...

  M = (A +B)/2

Solving for B gives ...

  B = 2M -A = 2(-9, -10) -(-1, 9) = (-18+1, -20 -9)

  B = (-17, -29)

Answer:

Step-by-step explanation:

Let w represent the width. Then 3w represents the length. The perimeter formula is ...

  P = 2(L +W)

  P = 2(3w +w)

  86 cm = 8w

  w = 10.75 cm

  3w = 32.25 cm

The rectangle is 32.25 cm long and 10.75 cm wide.

Answer:

Step-by-step explanation:

[tex]\sf 4+4\div 5[/tex]

[tex]\sf 4\div 5 =0.8[/tex]

[tex]\sf 4+0.8[/tex]

[tex]\sf 4.8[/tex]

* Hope it helps, ty 4 pts!

* Have a good day!

Answer:

1.

Step-by-step explanation:

1. 1.811/2=3.622 271/3=813

3.622*813=2,944.686

this is number one

2. 32x=729

divide both sides by 32

32x=729/32=

22.78125 approximate=22.8 or 23

Answer:

46 yards.

Step-by-step explanation:

Subtract the new balance from the original balance:

30.00 - 19.88 = 10.12

Therefore, Rachel spent $10.12

Divide the result by the cost of ribbons per yard:

10.12 ÷ 0.22 = 46

Therefore, Racheal bought 46 yeards of ribbon.

Answer:

V = 500 cm³

Step-by-step explanation:

V = 4/3 πr³

V = (4/3) × 3 × (5 cm)³

V = 4 × 125 cm³

V = 500 cm³

The percent error of the measurement, to the nearest tenth of a percent is 3.9%

Given:

Length measured = 12.2 inches

Actual length = 12.7 inches

Error = Actual length - Length measured

= 12.7 - 12.2

= 0.5

Percentage error = error / actual value × 100

= 0.5/12.7 × 100

= 0.039370078740157 × 100

= 3.937%

Approximately,

Percentage error = 3.9%

Therefore, the percent error of the measurement, to the nearest tenth of a percent is 3.9%

Learn more about percentage error:

https://brainly.com/question/5493941

Answer:

y = x² - 9x + 26

hope to help!!

Answer:

x=15

Step-by-step explanation:

Well we start with the fundamentals of a triangle we know that all the angles of a triangle add up to 180*, so you can start by adding 55* and 65* and end up with 120* then you can add 30* and get 150* then you can take the total of 150* and subtract it from 180* to get 30 now you take that 30 and divide it by 2 and get 15* for the final angle of the triangle.

Answer:

y=-1

Step-by-step explanation:

yeah-ya...... right?

Answer:

112º and 73º

Step-by-step explanation:

34º could be base angle

Base angles are equivalent

Vertical angle would be = 180 - 34 - 34

Vertical angle = 112º

34º could be vertical angle

Base angles are equivalent

2x = 180 - 34

Base angle = 73º

Answer:

20

Step-by-step explanation:

Since C is the midpoint of BD, BC must be equal to CD. Therefore, we can set the equation:

x+4=3x-10

Solve:

14=2x

x=7

Then we find AC, which is:

2x-5+x+4 = 3x-1

We can plug x in to get:

3*(7)-1=20

[tex]\\ \sf\longmapsto f(x)=x^2+5x[/tex]

[tex]\\ \sf\longmapsto f(-2)=(-2)^2+5(-2)[/tex]

[tex]\\ \sf\longmapsto f(-2)=4-10[/tex]

[tex]\\ \sf\longmapsto f(-2)=-6[/tex]

.#2

[tex]\\ \sf\longmapsto g(x)=2x+1[/tex]

[tex]\\ \sf\longmapsto g(a)=2a+1[/tex]

[tex]\\ \sf\longmapsto g(a+h)=2(a+h)+1[/tex]

.Now

[tex]\\ \sf\longmapsto g(a+h)-g(a)[/tex]

[tex]\\ \sf\longmapsto 2(a+h)+1-2a-1[/tex]

[tex]\\ \sf\longmapsto 2a+2h+1-2a-1[/tex]

[tex]\\ \sf\longmapsto 2h[/tex]

[tex]\text{Given that,}\\\\\text{First term,}~ a_1= -\dfrac 16\\\\\text{Common ratio,}~ r = 2 \\\\\text{nth term}~ a_n = a_1 r^{n -1} = -\dfrac 16 \left(2^{n-1}\right)[/tex]

[tex]\\ \sf\Rrightarrow LSA=2(h)(l+b)[/tex]

[tex]\\ \sf\Rrightarrow LSA=2(18)(6+4)[/tex]

[tex]\\ \sf\Rrightarrow LSA=36(10)[/tex]

[tex]\\ \sf\Rrightarrow LSA=360in^2[/tex]

Hi!

I can help you, no worries!

Your answer is y = -4/5x - 3

To solve this is much easier than you think. To "solve for y" we just have to get y on one side of the equal sign all by itself. We can see that it's "1 + y" on the left instead of just the y.

To get y by itself, we just subtract "1" from both sides.

1 + y = -4/5x - 2

-1                     -1

     y = -4/5x - 3

If you don't know why we have to subtract from both sides, think of it like this (it's how I like to think of it).

Each side of the equal sign is a twin. They are equal to eachother. If you change something about one twin, such as changing their hair color (or adding a number to one side of the equal sign), you have to do it to both in order for them to be the same. Right?

Hope this helps! Have a great day! :D

Answer:

If friction did not exist, it would be hard for us to slow down in running, or putting breaks on a car, and more!

If friction did not exist, your car will slide down the road even if you try your best to put the brakes on a car. Friction is a very important force to slow down things that are moving very fast

Step-by-step explanation:

Hoped this helped.

[tex]GeniusUser[/tex]

perimeter of the rectangle = 2 ( l + b )

4x + 10 = 40

4x = 40 10 ( transpose 10 to RHS )

x = 30/4 = 7.5 ( divide both sides by 4 )

ATQ

[tex]\\ \sf\longmapsto 2(x+x+5)=40[/tex]

[tex]\\ \sf\longmapsto 2(2x+5)=40[/tex]

[tex]\\ \sf\longmapsto 2x+5=20[/tex]

[tex]\\ \sf\longmapsto 2x=15[/tex]

[tex]\\ \sf\longmapsto x=7.5[/tex]

Answer:

< 1 is 85

X= 50

Step-by-step explanation:

ok the first question has 2 angles given 60 and 65

consider this one shows a 90 degree angle and the other does not. so  60 plus 90 equals 150 degrees

the u must say 65 plus x (x being angle 1) must also equal 150

subtract 65 from 150 and you get 85

now the second problem lets use the

Exterior Angle Theorem

The measure of an exterior angle (our w) of a triangle equals to the sum of the measures of the two remote interior angles (our x and y) of the triangle.

using this we know the 40 degree angle and 2x + 20 equals 3x plus 10

so we subtract 10 degrees from both sides and get

2x plus 10 plus 40 equals 3x now this means x equals 10 plus 40 which is 50

Answer:

5 words per minute

Step-by-step explanation:

To find her rate in words per minute simply divide the number of words she can type in 8 minutes (40) by 8.

40 / 8 = 5

Her rate is 5 words per minute

Let  be the number of pennies,  be the number of nickels, and  be the number of dimes that Vern has. The given ratios tell us that  and  Therefore,  so we haveTo turn this into a ratio of integers, we multiply every part of the ratio by  Doing this, we see that Therefore, we can think of Vern's collection as consisting of several groups, each of which contains  pennies,  nickels, and  dimes. Let  be the number of such groups of coins that Vern has. Then Vern has  pennies,  nickels, and  dimes. Since a penny is worth  cent, a nickel is worth  cents, and a dime is worth  cents, the total worth of Vern's coins in cents is  However, we know Vern has  or  cents, so we can write an equation:Simplifying the left-hand side, we get  Dividing both sides by  we get  This tells us that Vern has  groups of  coins, for a total of  coins.

328

Answer:

  P = 29 units

Step-by-step explanation:

Let h represent the height of the triangle. Then 2h is the length of the base. The area is given by ...

  A = 1/2bh

  36 = 1/2(2h)(h) = h²

  h = √36 = 6

  base = 2h = 12

The base of the isosceles triangle is 12 units, and its height is 6 units.

__

The altitude line makes a right angle with the base, dividing it into two right triangles with sides of length 6. The hypotenuse (s) of each of those is given by the Pythagorean theorem as ...

  s = √(6² +6²) = 6√2

Then the perimeter of the triangle is ...

  P = base +2s = 12 +2(6√2) = 12(1 +√2) ≈ 28.97 ≈ 29

The perimeter of the triangle is about 29 units.

_____

Additional comment

The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the other two sides.

For an isosceles right triangle, this means the hypotenuse is √2 times the side length. (This is a useful relationship to remember, as it is used a lot in algebra and geometry problems.) The acute angles in such a triangle are 45°.

AtQ

[tex]\\ \rm\hookrightarrow \dfrac{1}{2}(2x)(x)=36[/tex]

[tex]\\ \rm\hookrightarrow x^2=36[/tex]

[tex]\\ \rm\hookrightarrow x=6[/tex]

Apply Pythagorean theorem

[tex]\\ \rm\hookrightarrow H^2=6^2+6^2=36+36=72\implies H=8.5[/tex]

Perimeter

Answer:

40-13=27

3*9=27

She bought 9 cups.

Brainliest plz