Item 5 You buy orange and black streamers for a party. The orange streamers are 9 feet long, and the black streamers are 12 feet long. What are the least numbers of streamers you should buy in order for the total length of the orange streamers to be the same as the total length of the black streamers?

36 streamers

Step-by-step explanation:

The orange streamers are 9 feet long, and the black streamers are 12 feet long.

We have to find the Multiples of 9 and 12

Multiples of 9:

9, 18, 27, 36, 45, 54

Multiples of 12:

12, 24, 36, 48, 60

LCM(9, 12) = 36

The least common multiple which is the first common multiple is 36

Therefore, the least numbers of streamers you should buy in order for the total length of the orange streamers to be the same as the total length of the black streamers is 36 streamers.

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

2x

2

=

10

2

x=5

step-by-step explanation:

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