Which of the following sets of numbers could represent the three sides of a right
triangle?
{44, 60, 75}
{30, 73, 78}
{37, 77,85}
{39, 52, 65}

"{39, 52, 65}"

Step-by-step explanation:

Whenever there is a right-triangle, we can use the Pythagorean Theorem to find this answer

Pythagorean Theorem tell us that:

Leg^2 + Another Leg^2 = Hypotenuse^2

Note: Hypotenuse is the longest side

So, for each set, we can check if the Pythagorean Theorem holds.

{44, 60, 75}

75^2 = 5625

and

44^2 + 60^2 = 5536

This is not correct.

{30, 73, 78}

78^2 = 6084

30^2 + 73^2 = 6229

This is not correct as well.

{37, 77,85}

85^2 = 7225

37^2 + 77^2 = 7298

This isn't correct.

{39, 52, 65}

65^2 = 4225

and

39^2 + 52^2 = 4225

Here, pythagorean theorem holds, so this is the correct set.

we don't have enough info to solve this

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