Simplify the expression . explain

1/2 + 5/2 i

Step-by-step explanation:

(-5+i)         i

*

2i             i

cannot have i in the denominator so we multiply by i

(-5+i)         i             -5i + i^2

*  =

2i             i              +2i^2

remember i^2 = -1

     -5i + -1        -1 -5i

= =

    +2(-1)                        -2

get rid of the negative in the denominator by multiplying the top and bottom by -1

    (-1 -5i) * -1

=

          -2*(-1)

    (1 +5i)

=   =   1/2 + 5/2 i

          2

- "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."

$79500

step-by-step explanation: