)) Rachel is using ribbon to create girls' hair barrettes. For a craft fair in Springfield, she
made 12 small barrettes and 12 large barrettes, using a total of 156 yards of ribbon. Then,
for another craft fair in Norwood, she made 10 small barrettes and 11 large barrettes, which
used a total of 138 yards. How many yards of ribbon does Rachel use for each?

Step-by-step explanation:

Using s and L to represent the amount of ribbon used for small barrettes and large barrettes, respectively, we have ...

  12s +12L = 156

  10s +11L = 138

Dividing the first equation by 12 gives ...

  s +L = 13

Substituting s = 13-L into the second equation gives ...

  10(13 -L) +11L = 138

  130 +L = 138 . . . . . . . simplify

  L = 8 . . . . . . . . . .  subtract 130

  s = 13 -8 = 5 . . . . find s

Rachel uses 5 yards for a small barrette, and 8 yards for a large barrette.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

p = 6s

step-by-step explanation: