Someone please help Find a simplified expression to represent the area of the triangle. The area formula for a triangle is 1/2 by, where b is the base and h is the height.
The expression that represents the area of this triangle is ___x2 + ___x + ___cm2.

4x^2 +22x -12

Step-by-step explanation:

The area of a triangle is

A =1/2 bh  where b is the base and h is the height

A =1/2 ( 4x-2) ( 2x+12)

  Distribute

  = (2x-1) ( 2x+12)

FOIL

  first  2x*2x = 4x^2

 outer   2x * 12 = 24x

 inner  -1 *2x = -2x

last   -1 * 12 = -12

Add them together

4x^2 +24x -2x -12

Combine like terms

4x^2 +22x -12

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

a

step-by-step explanation: