PLEASE HELP what is the simplified expression to represent the area of the shaded region???

29x+23

Step-by-step explanation:

In order to find the area of the shaded region, we need to subtract the unshaded region in middle from the large rectangle

Step 1. Find the area of the large rectangle

A=lw (length × width)

A=(2x+4)(3x+6)

A=6x²+12x+12x+24 ⇔ Use FOIL (First Outer Inner Later)

A=6x²+24x+24

Step 2. Find the area of the unshaded region

A=lw

A=(2x-1)(3x-1)

A=6x²-2x-3x+1 ⇔ Use FOIL

A=6x²-5x+1

Step 3. Subtract unshaded from the large rectangle to get the area of shaded region

A (shade region)=large rectangle-unshaded region

A (shade region)=(6x²+24x+24)-(6x²-5x+1)

A (shade region)=6x²+24x+24-6x²+5x-1 ⇔ get off parenthesis

A (shade region)=6x²-6x²+24x+5x+24-1 ⇔ move the like term together

A (shade region)=29x+23 ⇔ combine like term

d

gimmee one of those gold crowns!

~coco

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be