Consider the polynomial: x/4– 2x^5 + x^3/2 + 1 which polynomial represents the standard form of the original polynomial? a. x^3/2 – 2x^5 + x/4 + 1 b.–2x^5 + x^3/2 + x/4 + 1 c. –2x^5 + x/4 + x^3/2 + 1 d. 1 – 2x^5 + x^3/2 + x/4

  b.  –2x^5 + x^3/2 + x/4 + 1

Step-by-step explanation:

In the given expression, the degrees of the terms, in the order given, are ...

  1, 5, 3, 0

When the terms are properly arranged in standard form, they will be ...

  5, 3, 1, 0 . . . . descending order

The standard form of this expression is ...

  -2x^5 +x^3/2 +x/4 +1 . . . . . . matches choice B

- "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."