There are 9 children playing in a playground. in a game, they all have to stand in a line such that the youngest child is at the beginning of the line. how many ways can the children be arranged in the line?

a. 40,320
b. 362,880
c. 16,777,216
d. 387,420,489

a

Step-by-step explanation:

There are 9 children, but the youngest is always the first one in line. So, there are really only 8 to arrange.

8*7*6*5*4*3*2*1

what is the original number? you forgot to add it.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)