Rewrite the given equation so there is a single power of 5,000 on each side. then, set the exponents equal to each other.(1/5000)^2z · 5000^2z+2 = 5000which equation shows the result? a) 2=1b) z=1c) -4z+2=1d) -4z+1=1

The equation shows the result. (Correct choice: A)

In this question we must apply algebra properties for power functions and definition of logarithms to simplify given expression and make conclusions from results:

1)  Given

2)  Definition of division

3)  /

4)  

5) Definition of logarithm

6)  

7)  Compatibility with multiplication/Existence of multiplicative inverse/Modulative property/Result

The equation shows the result. (Correct choice: A)

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A

Step-by-step explanation:

2 = 1

true !

step-by-step explanation:

- "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."