Prove that the value of the expression: b (36^5−6^9)(38^9−38^8) is divisible by 30 and 37.

Step-by-step explanation:

First factor the second binomial

38^9 - 38^8 = 38^8 (38 - 1 ) = 38^9(37)

So there's your 37. This whole expression is divisible by 37

Now do the first  binomial

36^5 - (36^4)*6

(6^2)^5 - 6^9

6^10 - 6^9  

6^9(6 - 1)

6^9 *5           Take out one of the 6s

6^8 * 6 * 5

6^8 * 30

So the first factor is divisible by 30

and the second factor is divisible by 37

So this factors into 30*6^8*37*38^9

b.-4 units

all you   do is count how many times you move

10.416 meters per second

step-by-step explanation:

distance=1 00 meters

time= 9.6 seconds in decimal form or 9 3/5 as a mixed number

average speed= 100/9.6

=10.416 meters per second or 10 52/125 as a mixed number.