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4 years ago

Simplify the polynomial

1 answer:

5 0

The answer is A –x^2 + 3x + 15

3x² + 6 – 2x + 5x – 4x² + 9

Rearrange it:
3x² + 6 – 2x + 5x – 4x² + 9
= 3x² - 4x² - 2x + 5x + 6 + 9
= -x² + 3x + 15

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The sum of the series {1(2/3)}²+{2(1)3)}²+3²+{3(2/3)}²+....to 10 term is

ryzh [129]

Step-by-step explanation:

<h3>Given Question </h3>

The sum of the series is

$\tt{ {\bigg[1\dfrac{2}{3} \bigg]}^{2} + {\bigg[2\dfrac{1}{3} \bigg]}^{2} + {3}^{2} + {\bigg[3\dfrac{2}{3} \bigg]}^{2} + - - 10 \: terms}$

$\green{\begin{gathered}\large{\sf{{\underline{Formula \: Used - }}}} \end{gathered}}$

$\boxed{\tt{ \displaystyle\sum_{k=1}^{n}1 = n \: }}$

$\boxed{\tt{ \displaystyle\sum_{k=1}^{n}k = \frac{n(n + 1)}{2} \: }}$

$\boxed{\tt{ \displaystyle\sum_{k=1}^{n} {k}^{2} = \frac{n(n + 1)(2n + 1)}{6} \: }}$

$\large\underline{\sf{Solution-}}$

Given series is

$\rm :\longmapsto\: {\bigg[1\dfrac{2}{3} \bigg]}^{2} + {\bigg[2\dfrac{1}{3} \bigg]}^{2} + {3}^{2} + {\bigg[3\dfrac{2}{3} \bigg]}^{2} + - - - 10 \: terms$

can be rewritten as

$\rm \: = \: {\bigg[\dfrac{5}{3} \bigg]}^{2} + {\bigg[\dfrac{7}{3} \bigg]}^{2} + {\bigg[\dfrac{9}{3} \bigg]}^{2} + {\bigg[\dfrac{11}{3} \bigg]}^{2} + - - - 10 \: terms$

$\rm \: = \: \dfrac{1}{9}[ {5}^{2} + {7}^{2} + {9}^{2} + - - - 10 \: terms \: ]$

Now, here, 5, 7, 9 forms an AP series with first term 5 and common difference 2.

So, its general term is given by 5 + ( n - 1 )2 = 5 + 2n - 2 = 2n + 3

So, above series can be represented as

$\rm \: = \: \dfrac{1}{9}\displaystyle\sum_{n=1}^{10}(2n + 3) ^{2}$

$\rm \: = \: \dfrac{1}{9}\displaystyle\sum_{n=1}^{10}\bigg[ {4n}^{2} + 9 + 12n\bigg]$

$\rm \: = \: \dfrac{1}{9}\bigg[\displaystyle\sum_{n=1}^{10} {4n}^{2} + \displaystyle\sum_{n=1}^{10}9 + 12\displaystyle\sum_{n=1}^{10}n\bigg]$

$\rm \: = \: \dfrac{1}{9}\bigg[4\displaystyle\sum_{n=1}^{10} {n}^{2} +9 \displaystyle\sum_{n=1}^{10}1 + 12\displaystyle\sum_{n=1}^{10}n\bigg]$

$\rm \: = \: \dfrac{4}{9}\bigg[\dfrac{10(10 + 1)(20 + 1)}{6} \bigg] + 10 + \dfrac{4}{3}\bigg[\dfrac{10(10 + 1)}{2} \bigg]$

$\rm \: = \: \dfrac{4}{9}\bigg[\dfrac{10(11)(21)}{6} \bigg] + 10 + \dfrac{4}{3}\bigg[\dfrac{10(11)}{2} \bigg]$

$\rm \: = \: \dfrac{1540}{9} + 10 + \dfrac{220}{3}$

$\rm \: = \: \dfrac{1540 + 90 + 660}{9}$

$\rm \: = \: \dfrac{2290}{9}$

Hence,

$\boxed{\tt{ {\bigg[1\dfrac{2}{3} \bigg]}^{2} + {\bigg[2\dfrac{1}{3} \bigg]}^{2} + {3}^{2} + {\bigg[3\dfrac{2}{3} \bigg]}^{2} + - - 10 \: terms = \frac{2290}{9}}}$

6 0

3 years ago

I have 3 slots left and 3 answers left. Fill them in pls and u get a brainlist :)

gulaghasi [49]

Answer:

Water (one oxygen atom bonded to two hydrogen atoms)

Step-by-step explanation:

The chemical formula for water is H²O. The H is the chemical symbol for Hydrogen and O is the chemical symbol for Oxygen. The 2 is a subscript which represents how many atoms of a certain element are in a molecule. In this case, the subscript ² comes after H, indicating that there are two Hydrogen atoms inside water. There is no subscript after O, meaning there is only one Oxygen atom. Therefore, there are two Hydrogen atoms and one Oxygen atom that bond to form water. Hope this helps :))

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3 years ago

What is the magnitude of an earthquake that is 5,011 times more intense than a standard earthquake?

puteri [66]

Answer: it’s 3.7

Step-by-step explanation:

I got it wrong I purpose just to see the answer your welcome

7 0

3 years ago

Read 2 more answers

34 POINTS - LOGICAL ANSWERS

Alecsey [184]

These are the answer that I got:

A. That means: "The more it costs, the fewer people you can invite."

B. Amount you can spend = M; You will have to come up with this number - whatever you think is reasonable.

C. (C = Cost per person, P = number of people you can invite )

D. You will have two equations. In the first equation, C will be the per-person cost at the first bowling alley. In the second equation, C will be the per-person cost at the second bowling alley.

E. Be sure to think this through. Yes, you will be able to host more guests at the bowling alley with the lowest per-person cost, but is that the only factor you need to consider? What about location? Quality of lanes and bowling equipment? Music? Food? Customer Service? Consider ALL aspects. You might pick the more expensive bowling alley because you feel would have a better experience, or maybe you don't want to invite lots of people anyway.

Hope this helps!

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3 years ago

For his long distance phone service, Reuben pays a $6 monthly fee plus 8 cents per minutes. Last month,Reuben’s long distance bi

Nuetrik [128]

I believe it 4004 mins i need to check up on it but im 95% positive its that

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3 years ago