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anzhelika [568]

3 years ago

6

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

2 answers:

dimulka [17.4K]3 years ago

5 0

Answer:

70

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:

70

Step-by-step explanation:

apex

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In the sport competition, France won more gold medals than Italy, who won more gold medals than Korea. If the total number of

worty [1.4K]

Answer:

France = 15, Italy = 14, Korea = 13

Step-by-step explanation:

We are trying to find 3 consecutive integers whose sum is 42, then the highest integer will be France's gold medal count since they won the most, the second highest will be Italy, and the lowest integer will be Korea.

let n be the first/smallest integer, since they are consecutive, the next two integers are n+1 and n+2. Summing these, we get n + (n+1) + (n+2) = 42. Solve to get n = 13, n + 1 = 14, and n + 2 = 15

5 0

3 years ago

Read 2 more answers

Heather counted the number of crickets in her greenhouse every month and recorded the data in the table below.

skelet666 [1.2K]

Answer: Its B

Step-by-step explanation:

I did this test and got it right

7 0

3 years ago

Read 2 more answers

Elan Coil [88]

Answer:

{x,y,z} = {-22/13,29/13,6/13}

7 0

2 years ago

Read 2 more answers

Simplify this equation <br> Thanks a lot!!!

den301095 [7]

Answer:

-1

Step-by-step explanation:

We need to simplify the given expression . The given expression is ,

$\rm\implies ( 2 \sqrt6 +5)^{2n-1} ( 2\sqrt6 - 5)^{2n-1}$

Here we can see that the power of the both exponent is same that is (2n+1) . Recall the property of exponents ,

$\bf\implies a^m \times b^m = (ab)^m$

Using this property , we have ,

$\rm\implies ( 2 \sqrt6 +5)^{2n-1} ( 2\sqrt6 - 5)^{2n-1}$

This can be written as ,

$\rm\implies\{( 2 \sqrt6 +5) ( 2\sqrt6 - 5)\}^{2n-1}$

Simplifying using ( a+b)(a-b) = a² - b² ,

$\rm\implies\{( 2 \sqrt6)^2 -5^2 \}^{2n-1}\\\\\rm\implies ( 24 - 25)^{2n-1}$

Subtracting the numbers inside the brackets ,

$\rm\implies (-1)^{2n - 1 }$

Now we know that every odd number is in the form of 2n -1 , where n is any integer. Therefore , the <u>power is odd</u> .

Since the base is (-1) , for even power it is 1 and for odd power it is -1 . Therefore the final answer is ,

$\rm\implies\boxed{\quad \red{ -1 }\quad }$

<u>Hence </u><u>the</u><u> </u><u>required</u><u> answer</u><u> is</u><u> </u><u>(</u><u>-</u><u>1</u><u>)</u><u> </u><u>.</u>

4 0

3 years ago

You drive 75 miles and use 3 gallons of gas, at the same ratio, how may miles can you drive with 12 gallons of gas?

umka2103 [35]

When you say "at the same ratio", you mean that you consume the same amount of gas for the same amount of miles.

We know that everytime you drive 75 miles, you use 3 gallons of gas.

Since 12 gallons of gas is four times 3 gallons of gas, if the ratio remains the same, you can drive four times the distance:

You drive 75 miles, and use 3 gallons.

You drive 75 more miles (so you are at $75+75 = 150$ miles) and use 3 more gallons, so you use $3+3 = 6$ gallons.

You drive 75 more miles (so you are at $150+75 = 225$ miles) and use 3 more gallons, so you use $6+3 = 9$ gallons.

You drive 75 more miles (so you are at $225+75 = 300$ miles) and use 3 more gallons, so you use $9+3 = 12$ gallons, and you're done.

4 0

3 years ago