A portrait without its frame has a height of 2.5 times its width w, in inches. It's frame is 2 in. Wide all along it's perimeter. What is an expression for the area of the frame portrait and in terms of a.

Step-by-step explanation:

Without the Frame

The width of the portrait  =w

Height of the Portrait = 2.5w

Since the frame is on opposite sides of each dimension, it is added twice.

The width of the portrait with frame = w+2+2=4+w

Height of the Portrait with frame = 2.5w+2+2=4+2.5w

We are to write an expression for the area, a of the frame in terms of w (I presume)

Area= Width X Height

a=(4+w)(4+2.5w)

- "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."