What is the difference of the polynomials? (–2x3y2 + 4x2y3  – 3xy4)  – (6x4y  – 5x2y3  – y5) a–6x4y  – 2x3y2 + 9x2y3  – 3xy4 + y5 b–6x4y  – 2x3y2  – x2y3  – 3xy4  – y5 c–6x4y + 3x3y2 + 4x2y3  – 3xy4 + y5 d–6x4y  – 7x3y2 + 4x2y3  – 3xy4  – y5

The correct answer is:

A) –6x⁴y – 2x³y² + 9x²y³ – 3xy⁴ + y⁵

Explanation:

To simplify this, we combine like terms.  Like terms are those with the same variables and exponents.

Our original expression is

(-2x³y²+4x²y³-3xy⁴)-(6x⁴y-5x²y³-y⁵)

The first term, -2x³y², does not have any like terms; there no other terms with x and an exponent of 3 and y and an exponent of 2.

The second term, 4x²y³, has a like term, -5x²y³.  They have the same variables and exponents.  These are to be subtracted:

4x²y³--5x²y³ = 4x²y³+5x²y³ = 9x²y³

The third term, -3xy⁴, has no like terms.

The fourth term, 6x⁴y, has no like terms; but since it is in the expression being subtracted, it is negative.

We have already combined like terms with the fifth term.

The sixth term, -y⁵, has no like terms; but since it is in the expression being subtracted, it is a double negative, which makes it a positve.

This gives us

-2x³y²+9x²y³-3xy⁴-6x⁴y+y⁵

Rewriting this in order by exponent of x, we have

-6x⁴y-2x³y²+9x²y-3xy⁴+y⁵

b or 2, just plug these equations into your graphing calculator then check the graph to see the image. if it matches up then that's your answer!

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50