Felicity is placing a rectangle in the coordinate plane. she iknows that the longer side of the rectangle is 3 times it’s shorter side. she places the longer side on the x-axis. what coordinates should she assign to the top-right vertex of the rectangle? enter your answer in the box

(3a, a)

Step-by-step explanation:

We are given that Felicity is placing a rectangle in the coordinate plane.

Assuming,

a to be the shorter side of the rectangle; and

b to be the longer side of the rectangle.

We know that,

Therefore, the dimensions of the rectangle will be .

So the final coordinates that Felicity should assign to the top-right vertex of the rectangle are (3a, a).

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