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3 years ago

What is the coefficient of x4y4 in the expansion of (x + y)8?

Mathematics

2 answers:

dimulka [17.4K]3 years ago

5 0

Answer:

Step-by-step explanation:

If you use Pascal's Triangle, you will need 9 lines, since there are 9 terms in a binomial raised to the 8th power. Those 9 terms are:

1, 8, 28, 56, 70, 56, 28, 8, 1

The first expansion through the one we need are below (I hope you know how to use Pascal's Triangle!):

$1(x^8)(y^0)+8(x^7)(y^1)+28(x^6)(y^2)+56(x^5)(y^3)+70(x^4)(y^4)+...$

Korolek [52]3 years ago

5 0

Answer:

Step-by-step explanation:

apex

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This figure is made up of a quadrilateral and a semicircle.

Arturiano [62]

Answer:

The correct option is B. The area of the figure is 40.4 units².

Step-by-step explanation:

The line AB divides the figure in two parts one is a rectangle and another is semicircle.

The distance formula is

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The length of AB is

$AB=\sqrt{(2+3)^2+(4-2)^2}=\sqrt{25+4}=\sqrt{29}$

The length of AD is

$AD=\sqrt{(-1+3)^2+(-3-2)^2}=\sqrt{4+25}=\sqrt{29}$

Since AB=AD, therefore ABCD is a square. The area of the of square is

$A_1=a\times a=\sqrt{29}\times \sqrt{29} =29$

The area of square is 29 units².

The area of a semicircle is

$A_2=\frac{\pi}{2}r^2$

Since AB is the diameter of the semicircle, therefore the radius of the semicircle is

$r=\frac{d}{2}=\frac{\sqrt{29}}{2}$

The area of the semicircle is

$A_2=\frac{3.14}{2}(\frac{\sqrt{29}}{2})^2=40.3825$

The area of the figure is

$A=A_1+A_2=29+11.2825=40.3825\approx 40.4$

Therefore the area of the figure is 40.4 units². Option B is correct.

5 0

3 years ago

there are 10 crates of eggs stacked in the corner. each crate of eggs holds 20 eggs. If there is only 1 broken egg in the entire

alisha [4.7K]

Answer: 5%

Step-by-step explanation: If there is one broken egg in each crate (1/20), you would change that to5%

And if there are ten crates, then you see how many eggs there a re total.

(10 × 20 = 200)

If there are 200 eggs and for every 20 eggs there is on broken one, then there will be 10 broken eggs total. or 10/200

convert the fraction to a decimal ( 10 ÷ 200 = .05)

then convert the decimal to a percent. .05 is equal to 5%

PLEAZE RATE BRAINLIEST!!!

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2 years ago

Kim has a $10 bill, a $20 bill, and 2 $5 gift certificates. she uses the gift certificates toward the purchase of a cd for $14.0

uysha [10]

When Has $26 Left !!

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3 years ago

It takes Andre 4 minutes to swim 5 laps.

soldier1979 [14.2K]

It takes Andre 1.25 minutes to swim a lap.

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2 years ago

Read 2 more answers

PLZ HELP!!! WILL GIVE HIGHEST POINTS IF THE ANSWER IS RIGHT!!

PilotLPTM [1.2K]

Step-by-step explanation:

Standard polynomial is:

$- 20 {x}^{3} - 3 {x}^{2} + 4x$

Leading co effecient is:

-20

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2 years ago