Here is another interesting proof. the smaller white square is inside a larger square. each blue area is a right triangle. to find the area of the white square, you can find the area of the big square and subtract the areas of the right triangles. use these areas to write an equation for the area of the white square. simplify the equation if possible.

Area of square = (a+b)^2
Area of 4 triangles= 4(1/2 ab)

Area of white square = (a+b)^2 - 4(1/2 ab

Or area of white square= (a+b)^2 - 2ab

Or area of white square= a^2 + b^2 +2 ab - 2ab
Or area of white square= a^2 + b^2

Thus the simplified expression is
a^2 + b^2

Ithink the answer will be d yes

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 .