three angles are adjacent to each other and form 140.the largest angle is twice the smaller angle and the angle which is middle size is 24 more than the smallest. find the angles

Smallest: 29, Middle: 53, Largest: 58

Step-by-step explanation:

We can represent the angles in this problem using an equation.

We'll use x to represent the smallest angle, and work out other ways to represent the others.

As the largest angle is twice that of the smaller angle, we can represent the largest angle as 2x as 2x is two times x.

The middle angle is 24 more than the smallest, so we can represent that one as x + 24, since it is 24 more than the smallest.

Now we have our angles all represented with x:

Smallest angle = x

Middle = x+24

Largest = 2x

We know that they all add together to 140 so our equation is:

x+2x+(x+24) = 140

Now we can solve for x!

We can remove the brackets (addition does not change the terms) and combine the terms:

x+2x+x+24=140

4x+24=140

Next we move the 24 to the other side so we can solve for x:

4x + 24 - 24 = 140 - 24

4x = 116

Finally we divide both sides by 4:

x=29

The smallest angle is 29!

Now we can use our representations to find the other angles:

Middle angle = x+24, therefore it is 29+24 = 53

Largest angle = 2x therefore it is 2*29 = 58

58+53+29=140 so we have successfully worked out our angles!

Hope this helped!

1

step-by-step explanation:

you are throwing one dart

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