Roger made a table showing he sleeps 3/8 of a day. how many days will go by before roger has slept the equivalent of one day?

2.66 days

Step-by-step explanation:

We know that a day has 24 hours, so if Roger sleeps 3/8 of a day that means that he sleeps 3/8 • 24 which equals to 9 hours.

Now we want to know how many days it takes Roger to sleep an equivalent of a day if he sleeps 9 hours a day. So:

24 h / 9 h = 2.66 days

Of course we can do it in an easier way, in fractions:

1 : 3/8 = 8/3

8/3 = 2.66 days

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2