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2 years ago

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1 answer:

____ [38]2 years ago

6 0

Answer:

(0,0) (1,2)

Step-by-step explanation:

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Expand (2x+2)^6<br> How would you find the answer using the binomial theorem?

Yanka [14]

Answer:

Step-by-step explanation:

$\displaystyle\\\sum\limits _{k=0}^n\frac{n!}{k!*(n-k)!}a^{n-k}b^k .\\\\k=0\\\frac{n!}{0!*(n-0)!}a^{n-0}b^0=C_n^0a^n*1=C_n^0a^n.\\\\ k=1\\\frac{n!}{1!*(n-1)!} a^{n-1}b^1=C_n^1a^{n-1}b^1.\\\\k=2\\\frac{n!}{2!*(n-2)!} a^{n-2}b^2=C_n^2a^{n-2}b^2.\\\\k=n\\\frac{n!}{n!*(n-n)!} a^{n-n}b^n=C_n^na^0b^n=C_n^nb^n.\\\\C_n^0a^n+C_n^1a^{n-1}b^1+C_n^2a^{n-2}b^2+...+C_n^nb^n=(a+b)^n.$

$\displaystyle\\(2x+2)^6=\frac{6!}{(6-0)!*0!} (2x)^62^0+\frac{6!}{(6-1)!*1!} (2x)^{6-1}2^1+\frac{6!}{(6-2)!*2!}(2x)^{6-2}2^2+\\\\ +\frac{6!}{(6-3)!*3!} (2a)^{6-3}2^3+\frac{6!}{(6-4)*4!} (2x)^{6-4}b^4+\frac{6!}{(6-5)!*5!}(2x)^{6-5} b^5+\frac{6!}{(6-6)!*6!}(2x)^{6-6}b^6. \\\\$

$(2x+2)^6=\frac{6!}{6!*1} 2^6*x^6*1+\frac{5!*6}{5!*1}2^5*x^5*2+\\\\+\frac{4!*5*6}{4!*1*2}2^4*x^4*2^2+ \frac{3!*4*5*6}{3!*1*2*3} 2^3*x^3*2^3+\frac{4!*5*6}{2!*4!}2^2*x^2*2^4+\\\\+\frac{5!*6}{1!*5!} 2^1*x^1*2^5+\frac{6!}{0!*6!} x^02^6\\\\(2x+2)^6=64x^6+384x^5+960x^4+1280x^3+960x^2+384x+64.$

8 0

1 year ago

The height of a rectangle is 2 less than it’s base x if the perimeter of the rectangle is no less than 36 cm, find the base

Inessa [10]

10 I think because 10+10+8+8=36 and 8 is 2 less than 10

7 0

2 years ago

Jamal pays an initial fee of $50 and $4.00 for each audio book he downloads?

olganol [36]

Answer:

4x + 50 = y

Step-by-step explanation:

Since it is $4 for each audiobook, this means that it is the slope.

Since Jamal started with an initial fee, this makes it the y-intercept.

So the equation is $4 per audiobook = 4x, initial fee of $50 which makes the equation: 4x + 50 = y

<u>Y-intercept</u> is the starting number, in this case, the initial fee.

<u>Slope</u> is the rate at which a value is increasing, in this case, for each audiobook bought, $4 is spent

6 0

1 year ago

Write an expression to describe a rule for the sequence. Then find the 100th term in the sequence. 4, 9, 14, 19, 24, 29, . . . .

Irina18 [472]

The rule is that: You are adding 5 each time

5(100) + 4 = 504

Your answer should be 504

hope this helps

6 0

2 years ago

Whiich is the best estimate of the quotient 14.98 / 2.984

skad [1K]

I would say 15/3= 5 because they are really close

8 0

3 years ago

Read 2 more answers