Expand (-2x+4)^5 using the binomial theorem (Pascals triangle)

Will award brainiest, (show work)

100 points, silly answers will be reported immediately.

Answers

Answer 1

Answer:

[tex]-32x^5+320x^4-1280x^3+2560x^2-2560x+1024[/tex]

Step-by-step explanation:

We must expand [tex](-2x+4)^5[/tex] using the Binomial Theorem.

To do so, we need Pascal's Triangle. Seeing that the exponent is 5, we look at the 5 + 1 = 6th row of Pascal's Triangle. The numbers here are:

1, 5, 10, 10, 5, 1

These will be the numbers to multiply all the distinct terms in the expansion by.

Remember that when expanding this out, we always start by taking the first term (-2x here) to the nth power (here, it's 5th power) and multiplying that by the second term (4 here) to the 0th power:

(-2x)^5 * 4^0 = -32x^5 * 1 = -32x^5

Since this is our first term, we multiply it by the first Pascal number from above: 1. Then, we simply get -32x^5 as our final first term of the expansion.

We repeat this process, each time lowering the first power by 1 and increasing the second power by 2.

2nd term:

(-2x)^4 * 4^1 = 16x^4 * 4 = 64x^4

Multiply by 5:

64x^4 * 5 = 320x^4

3rd term:

(-2x)^3 * 4^2 = -8x^3 * 16 = -128x^3

Multiply by 10:

-128x^3 * 10 = -1280x^3

4th term:

(-2x)^2 * 4^3 = 4x^2 * 64 = 256x^2

Multiply by 10:

256x^2 * 10 = 2560x^2

5th term:

(-2x)^1 * 4^4 = -2x * 256 = -512x

Multiply by 5:

-512x * 5 = -2560x

6th term:

(-2x)^0 * 4^5 = 1 * 1024 = 1024

Multiply by 1:

1024 * 1 = 1024

Hence, our expansion is:

[tex]-32x^5+320x^4-1280x^3+2560x^2-2560x+1024[/tex]


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Answer:

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Step-by-step explanation:

hope this helped have a nice day!!

Answer: the answer is 20

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Answer:

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Step-by-step explanation:

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Answer:

Step One

Calculate the area of both the skating area and the spectator area.

Area = L * W

L = 4x

W = 4x

Area = 4x * 4x

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Step Two.

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From the diagram

R = The full length - the length given in the red shaded area.

R = 4x - 2x

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Step Three

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Area of a 1/2 circle = [tex]\frac{\pi *4*x^2}{2}[/tex]

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Notice that the 2 in the denominator cancels in part with the 4 in the numerator.

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The answer is the upper right corner choice I think

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Answers

Answer:

x=16

Step-by-step explanation:

(4x+2)+(x+8)=90

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5x=80

x=16

Find the equation of the circle with the given characteristics.

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The solution is:

Answers

Answer:

Step-by-step explanation:

The standard form of an equation of a circle is (x - h)² + (y - k)² = r² , where (h, k) are coordinates of a center and "r" is radius.

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Answers

Answer:

It's repeating.

Step-by-step explanation:

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True or False: Rosa has a beginning balance of $4,750 in her Checking account. After
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Answer:

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Step-by-step explanation:

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Answers

10 is the correct answer

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Answers

Using the equation- y-y0=m(x-x0)
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Answers

Answer:

E stands for the power of ten the number is multiplied by

I thonk

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Answers

Answer:

The leave together every 90 minutes

Step-by-step explanation:

The leave together every 90 minutes:

bus A : 30 + 30 + 30 = 90

bus B : 45 + 45 = 90

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Answers

Well I came up with the answer
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Not sure if this is correct but I hope it is and that it helps!

Have an amazing day✨❤️

Mr. Cornapple is the fruit & vegetable buyer for a large school district. In a given week, he has a budget of $6,550. Bushels of apples cost $40 each, and bushels of corn cost $30 each. The following inequality represents the amount of money that Mr. Cornapple spends on apples and corn.

Answers

Answer:

40x + 30y ≤ 6,550

Step-by-step explanation:

Given:

Cost of each apple bushels = $40

Cost of each corn bushels = $30

Total budget = $6,550

Find:

Inequality

Computation:

Assume;

Total number of apple bushels = x

Total number of corn bushels = y

So,

40x + 30y ≤ 6,550

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Answers

Answer: 1.5 times 20 equals to 300

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Answers

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Answers

Answer:

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Step-by-step explanation:

Because each its 8 dollars per square foot. I multiply 179.25 to get 1,434

Good luck!!!

Answer:

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Step-by-step explanation:

If the cost of the flooring for the court is 8 per square foot. Multiply the area of the court under the goal by the cost per square foot Because each its 8 dollars per square foot. I multiply 179.25 to get 1,434

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

The number of times he will have to fill the smaller measuring cup to equal 1 3/4 cups is 7 times.

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A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

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https://brainly.com/question/24370499

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A.

B.

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D

Answers

MARK ME AS A BRAINLIST..........

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Answer:

Could we get a bit more info?

Step-by-step explanation:

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Answers

Answer:

50

Step-by-step explanation:

let <LPM be x

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<LPM=<KPN (being vertically opposite angle)

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Answer:

Angle NPK° = 50°

Step-by-step explanation:

in triangle MPL

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Angle MPL = 180 -60-70 = 50°

Angle NPK = AngleMPL

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A 64 trucks and 80 cars
B 72 trucks and 73 cars
C 84 trucks and 100 cars
D 96 trucks and 110 cars

Answers

Answer:

The answer is A.

Step-by-step explanation:

I hope this helps!

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Answers

Answer:

3×c+5=9

Step-by-step explanation:

thats the answer ig

Answer:

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Step-by-step explanation:

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Answers

Answer:

B,

Step-by-step explanation:

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Answer:

y = 4x -13

y = 4x -13Step-by-step explanation:

y= mx + b

y= mx + b m is the Slope

y= mx + b m is the Slopem = 4

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + b

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + bSubtract 20 from both sides of the equation

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + bSubtract 20 from both sides of the equation7- 20 = b

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + bSubtract 20 from both sides of the equation7- 20 = b-13 = b

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + bSubtract 20 from both sides of the equation7- 20 = b-13 = bThe line in slope intercept form is

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + bSubtract 20 from both sides of the equation7- 20 = b-13 = bThe line in slope intercept form isy = 4x -13

Mr. Brown bought some books at a book sale, including 4 paperback books. 20% of all the books he bought were paperbacks. How many books did Mr. Brown buy in all?​

Answers

Answer:

20 books

Step-by-step explanation:

20% is 1/5 of 100% so the other 4/5 would be 4 times 5 which equals 20 books it total

Answer:

Mr. Brown bought 20 books.

Step-by-step explanation:

20% times 5 would be 100%. Since Mr. Brown bought 4 books, and that was 20% of all the books he bought, you would have to multiply the number of paper back books by 5 to get the answer of 100% of all books he bought, which would be 20. This problem would look like this 20(5) = 4(5), 100% = 20 books.

29/3 as an a mixed number

Answers

Answer:

9.6 repeating

Step-by-step explanation:

The coordinates of point A on a grld are (-3,-2), Point A is reflected across the y-axls to obtain point B. The coordinates of point B are
-2).

Answers

Answer:

The coordinates of the image of B(-3, -2) is B'(3, -2).

Step-by-step explanation:

We know that when a point (x, y) is reflected across the y-axis, the y-coordinate remains the same, and then the x-coordinate becomes negative.

i.e.

Thus, the image of P(x, y) is P' (-x, y).

Given the point

B(-3, -2)

Hence, the image of B(-3, -2):

(-x, y) → (-(-3), -2) = (3, -2)

Therefore, the coordinates of the image of B(-3, -2) is B'(3, -2).

find the value of x of given figure and solve this question step by step plzz help question number D​

Answers

Answer:

The value of x is 15 cm

Step-by-step explanation:

#(d)

In Δ BDC

∵ ∠D is a right angle

∴ BC is the hypotenuse

∴ BD and DC are the legs of the right angle

→ By using Pythagoras Theorem

(BC)² = (BD)² + (DC)²

∵ BD = 10 cm

∵ DC = 2√11 cm

→ Substitute them in the equation above

∴ (BC)² = (10)² +(2√11)² = 100 + 44 = 144

→ Take √  for both sides

BC = 12 cm

In Δ ABC

∵ ∠B is a right angle

∴ AC is the hypotenuse

∴ AB and BC are the legs of the right angle

→ By using Pythagoras Theorem

(AC)² = (AB)² + (BC)²

∵ AB = 9 cm

∵ BC = 12 cm

AC = x

→ Substitute them in the equation above

∴ x² = (9)² +(12)² = 81 + 144 = 225

→ Take √  for both sides

x = 15 cm

The value of x is 15 cm

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