Find the area of the shaded polygons:

9

Step-by-step explanation:

You could divide this into several smaller shapes, such as triangles and trapezoids.  But with this one, it might be simpler to count the full squares, half squares, and partial squares.

Full square - 4

Half squares - 3 ( for an area of 1.5)

Two squares divided in half - 2

Three squares divided in half - 1 (for an area of 1.5)

4+1.5+2+1.5=9

9

Step-by-step explanation:

A simpler way of doing this is using pick's theorem.

Pick's theorem is:

i + b/2 - 1 which translates to: interior points + boundary points/2 - 1

Interior points: There is 5 interior points

Boundary points: There is 10 boundary points

 ---> 5 + 10/2 - 1

               = 9

answer:   n ≤ -3 or n < -5

step-by-step explanation:

-5 + 2n ≥ -11

+5             +5

2n ≥ -6

2/2 ≤ -6/2

n ≤ -3

-6 - 10n > 44

+6           +6

-10n > 50

-10/-10 50/-10

n < -5

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