The area of a parallelogram is 96 cm2. the height of the parallelogram is 4 cm less than the length of the base. what is the length of the base?

a) 5 cm

b) 8 cm

c) 12 cm

d) 14 cm

The answer is 12 cm

Step-by-step explanation:

Let b = base of parallelogram; then, (b − 4) = height of the parallelogram

A = bh

96 = b(b − 4)

96 = b2 − 4b

0 = b2 − 4b − 96

0 = (b − 12)(b + 8)

b −12 = 0

b = 12

b + 8 = 0

b = − 8

Since length is always positive, the length of the base is 12 cm.

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.

- "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."