A 47-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is two inches more than six times the
length of the first piece. Find the lengths of the pieces
2x
6x+2
First, find an equation that represents the total length of the piece of steel in terms of x by adding the three pieces together,

Step-by-step explanation:

x   - the length of the first piece

2x    - twice the length of the first piece (the length of the second piece)

6x   - six times the  length of the first piece

two inches more:

6x+2    - the length of the third piece

first + second + third = 47 in  {total length of the pieces of steel}

x + 2x + 6x + 2 = 47

9x + 2 = 47

9x = 45

x = 45:9

x = 5 in

first piece:   5 in

second piece: 2×5 = 10 in

third piece:   6×5 + 2 = 30 + 2 = 32 in

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

1/3

step-by-step explanation:

to find this, you can divide 12 by 4 which is 3 or you can multiply 4 until you reach 12 (4x3=12). both should give you 3, meaning theres three times less bananas than there are oranges.