A painter leans a 12-foot ladder against a wall. The angle of elevation of the ladder is 55.

9.83cm

Step-by-step explanation:

Since we are not asked what to look for. We can find the height of the wall.

Let the height of the wall be H

Given

Length of the ladder l = 12fot

Angle of elevation = 55degrees

Required

Height of wall H

Using the SOH CAH TOA identity

SIn theta = opp/hyp

Sin 55 = H/12

H - 12sin55

H = 12(0.8192)

H = 9.83cm

Hence the height of the ladder is 9.83cm

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

i believe the answer is the polygon, heptagon.