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3 years ago

Select the correct answer from each drop-down menu. Consider the following polynomials equations.

Mathematics

2 answers:

DedPeter [7]3 years ago

7 0

Answer:Yes to all 3 questions.

Step-by-step explanation:

3x^2(x-1) + -3x^3+ 4x^2-2x+1

= 3x^3 - 3x^2 - 3x^3 + 4x^2 - 2x + 1

= x^2 - 2x + 1,

So A + B is a polynomial.

3x^2(x-1) - (-3x^3+ 4x^2-2x+1)

= 3x^3 - 3x^2 + 3x^3 - 4x^2 + 2x - 1

= 6x^3 - 7x^2 + 2x - 1.

So A - B is also a polynomial.

3x^2(x-1)( -3x^3+ 4x^2-2x+1)

= (3x^3 - 3x^2) ( -3x^3 + 4x^2 - 2x + 1)

= -9x^6 + 12x^5 - 6x^4 + 3x^3 + 9x^5 - 12x^4 + 6x^3 - 3x^2

= -9x^6 + 21x^5 - 18x^4 + 9x^3 - 3x^2.

So A * B is a polynomial.

Step-by-step explanation:

Zolol [24]3 years ago

5 0

Answer:

Yes to all 3 questions.

Step-by-step explanation:

3x^2(x-1) + -3x^3+ 4x^2-2x+1

= 3x^3 - 3x^2 - 3x^3 + 4x^2 - 2x + 1

= x^2 - 2x + 1,

So A + B is a polynomial.

3x^2(x-1) - (-3x^3+ 4x^2-2x+1)

= 3x^3 - 3x^2 + 3x^3 - 4x^2 + 2x - 1

= 6x^3 - 7x^2 + 2x - 1.

So A - B is also a polynomial.

3x^2(x-1)( -3x^3+ 4x^2-2x+1)

= (3x^3 - 3x^2) ( -3x^3 + 4x^2 - 2x + 1)

= -9x^6 + 12x^5 - 6x^4 + 3x^3 + 9x^5 - 12x^4 + 6x^3 - 3x^2

= -9x^6 + 21x^5 - 18x^4 + 9x^3 - 3x^2.

So A * B is a polynomial.

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3 years ago

How many liters of pure water should be mixed with a 18-L solution of 80% acid to produce a mixture that is 90% water?

Sphinxa [80]

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Solution:

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Then, 18 + x is the liters of final solution

18 Liter solution of 80% acid, which means 100 - 80 = 20 % of water is used

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Then according to question, we can say,

"x" liters of pure water 100 % is mixed with a 18 liter solution of 20 % water to produce a mixture (18 + x) liter that is 90 % water

Thus we frame a equation as:

Equation:

water + water = water

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$x \times \frac{100}{100} + 18 \times \frac{20}{100} = (18+x) \times \frac{90}{100}\\\\Simplify\ the\ above\ equation\\\\x + 0.2 \times 18 = (18+x) \times 0.9\\\\x + 3.6 = 16.2 + 0.9x\\\\0.1x = 12.6\\\\Divide\ both\ sides\ of\ equation\ by\ 0.1\\\\x = 126$

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