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3 years ago

Please help, I have attached a picture of the question! Thank you!

Mathematics

1 answer:

tigry1 [53]3 years ago

6 0

Answer:

Factors:

A. $x+3$

B. $4x+3$

C. $x-5$

Step-by-step explanation:

Given polynomial:

$4x^4-21x^3-46x^2+219x+180$

Rewrite it as follows:

$4x^4-21x^3-46x^2+219x+180\\ \\=4x^4+12x^3-33x^3-99x^2+53x^2+159x+60x+180\\ \\=4x^3(x+3)-33x^2(x+3)+53x(x+3)+60(x+3)\\ \\=(x+3)(4x^3-33x^2+53x+60)$

Now factor polynomial $4x^3-33x^2+53x+60:$

$4x^3-33x^2+53x+60\\ \\=4x^3-16x^2-17x^2+68x-15x+60\\ \\=4x^2(x-4)-17x(x-4)-15(x-4)\\ \\=(x-4)(4x^2-17x-15)$

Now factor polynomial $4x^2-17x-15:$

$4x^2-17x-15\\ \\=4x^2-20x+3x-15\\ \\=4x(x-5)+3(x-5)\\ \\=(x-5)(4x+3)$

Hence,

$4x^4-21x^3-46x^2+219x+180=(x+3)(x-4)(x-5)(4x+3)$

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Sophie has to choose seven different positive (non zero) whole numbers whose mean is 7.

Anna71 [15]

Answer:

The largest possible number is 28.

Step-by-step explanation:

Sophie has to choose seven different numbers whose mean is 7, this means that the sum of the numbers is 49. (since the mean is the sum of them all divided by 7 and if we want the mean to be 7, then the sum would need to be 49).

We are asked what is the largest possible number she could choose, so therefore, the other six numbers should be non-zero and the smallest ones so she would have to choose the numbers from 1 to 6 first.

Let's see how much they sum up: $1+2+3+4+5+6=21$

So now, she needs one more number to sum up to 21 and that will give her 49 in total, this number is 28 (since 28 + 21 =49).

Thus, 28 is the largest number she could choose because if she chose any other greater number the mean would be bigger than 49.

4 0

3 years ago

Find RT please and thank you.

valkas [14]

RQ × RP = RS × RT

9 × ( 9 + 13 ) = 11 × RT

9 × 22 = 11 × RT

Divide sides by 11

9 × 22 / 11 = 11 × RT / 11

Simplification

9 × 2 = RT

RT = 18

8 0

3 years ago

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andreev551 [17]

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Key:

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Step-by-step explanation:

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$-\left(1-\tan ^2\left(\theta\right)\right)=-1+\tan ^2\left(\theta\right)$

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2 years ago

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IgorLugansk [536]

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3 years ago

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prohojiy [21]

Answer:

Step-by-step explanation:

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3 years ago