Replace ∗ with a monomial so that the trinomial may be represented by a square of a binomial: b2 + 20b +*

Given:

The expression is:

To find:

The a monomial so that the trinomial may be represented by a square of a binomial.

Solution:

If an expression is , then be need to add square of half of coefficient of x, i.e., in the given expression to make in perfect square.

We have,

Here, coefficient of b is 20,so wee need to add square of half of coefficient of b, i.e., .

Therefore, we need to add 100 to make a perfect square binomial.

where are the choices?

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