Explain how you could use the construction tool or a compass and straightedge to create a line segment that is twice as long

We can construct the given segment by using the following steps:

Step 1:  Adjust the compass width equal to the length of the segment AB.

Step 2: Draw another line that is greater than the twice of the segment AB in length.

Step 3 : Without changing the compass settings, draw an arc from end of the line on the line (this is equal to length AB)

Step 4 : Now again put the compass tip on the intersection of the arc drawn above, and make another arc on the line (this is also equal to length AB from the arc)

Now, we get a double line segment from the end of the line.

Its like AB + AB = 2AB.

You can see the attached figure to get a clear view of construction.

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