Which polynomial correctly combines the like terms and puts the given polynomial in standard form? –5x3y3 + 8x4y2 – xy5 – 2x2y4 + 8x6 + 3x2y4 – 6xy5 –7xy5 + 5x2y4 – 5x3y3 + 8x4y2 + 8x6 5xy5 + 8x4y2 + x2y4 – 5x3y3 + 8x6 8x6 + 5xy5 + 8x4y2 + x2y4 – 5x3y3 8x6 + 8x4y2 – 5x3y3 + x2y4 – 7xy5

–5x3y3 + 8x4y2 – xy5 – 2x2y4 + 8x6 + 3x2y4 – 6xy5

Which of the following represents the expression written in standard form:

–7xy5 + 5x2y4 – 5x3y3 + 8x4y2 + 8x6

5xy5 + 8x4y2 + x2y4 – 5x3y3 + 8x6

8x6 + 5xy5 + 8x4y2 + x2y4 – 5x3y3

8x6 + 8x4y2 – 5x3y3 + x2y4 – 7xy5

The variables are x and y. All terms have degree 6, so we can choose to write them in order of decreasing powers of x or of decreasing powers of y.

The terms tha can be combined are those involving xy⁵ and x²y⁴. Combining those terms, we have xy⁵(-1-6) = -7xy⁵, and x²y⁴(-2+3) = x²y⁴.

The first offered choice has the powers of y in decreasing order, but it has an incorrect coefficient for x²y⁴. The second and third offered choices have no consistent ordering of powers.

The best choice is the last one:

... 8x⁶ +8x⁴y² -5x³y³ +x²y⁴ -7xy⁵

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation: