Consecutive integers are integers that differ by one. You can represent
consecutive integers as x, X + 1,
x + 2 and so on. Write an equation
and solve to find three consecutive
integers whose sum is 33.

  The three numbers are 10, 11, and 12.

10+11+12 = 33

Work Shown:

Each is a positive whole number

Add them up and set the result equal to 33. Solve for x.

(x) + (x+1) + (x+2) = 33

3x+3 = 33

3x+3-3 = 33-3 subtract 3 from both sides

3x = 30

3x/3 = 30/3 divide both sides by 3

x = 10

x+1 = 10+1 = 11

x+2 = 10+2 = 12

Note how 10+11+12 = 33 to help confirm our answer.

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

trapezoid

step-by-step explanation:

first i plotted all my points on a grid graph

i made sure all of them were in the correct quadrant

then i saw it was a trapezoid or a quadrilateral