Sam can paint the house in 7 days by himself, while Betty can paint the same house in 42 days. How long would it take Sam and Betty to paint the same house together?

It would take 6 days for Sam and Betty to paint the same house together.

Step-by-step explanation:

Let x represent the time it takes ( in days ) to complete painting the house working together. Our approach here is to add the rates of the two people, equal to the total rate, or 1 / 7.

Sam's rate = 1 / 7 ( 7 days to paint 1 house ),

Betty's rate = 1 / 42 ( 42 days to paint 1 house )

1 / 7 + 1 / 42 = 1 / x - now let us solve for x, our solution

1 / 7 + 1 / 42 = 1 / x ( multiply either side by 42x )

7x = 42,

x = 42 / 7 = 6 days

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752

3

step-by-step explanation: