The u. s. senate is composed of 2 senators from each of the 50 states. in order for a treaty to be ratified, at least two thirds of the senators present must approve the treaty. suppose all senators are present and 48 of them have voted in favor of a treaty. what are the possible numbers of additional senators who must vote in favor of the treaty in order to radify it?

So there are 100 senators. 
All are present. 
You need at least 2/3 of the senators present. 
So you need at least 66.66667 
66 is not at least 66.66667, 67 is at least 66.66667. 
So you need 67 total votes. 
You already have 48. 
Thus you need an additional 19. 

I can't find any trick which would make the number 18. 

The question asks for possible numbers which would ratify the treaty 
so the answer should be 19, 20, 21, 22 and 52

Where are the graphs?

and y≤ -x +4 .

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

y≤ -x +4 .