For the polynomial 6xy2 – 5x2y? + 9x2 to be a trinomial with a degree of 3 after it has been fully simplified, the missing exponent of the y-term must be

e

Exponent of y is 1.

Step-by-step explanation:

We have been given the polynomial

Also it has been given that the degree of the polynomial is 3.

We know that  the degree of a polynomial is highest exponent.

In case of more than one variables in a polynomial, we add the exponent of the variables of each term. The highest number must be the degree of the polynomial.

Now, since the degree of the polynomial is 3. Hence, the sum of the exponent of the variables x and y must be 3.

Mathematically, we can write

exponent of x + exponent of y = 3

2 + ? = 3

Subtract 2 to both sides

? = 1

Hence, the exponent of y is 1.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form

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