Are there any values of x for which the areas of the figures are the same? explain.

Therefore, there aren't any.

Let's assume that there is a value (or values) of x for which the areas of these two figures aer the same:

Triangle Rectangle

A = (1/2)(2)(x + 1) = (x)(1)

Simplifying,

x + 1 = x

This becomes: 1 = 0

This is never true, regardless of what x is chosen.

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.