Express each ratio as a fraction in its simplest form: 0.034 yards to 60 feet

17/10000

Step-by-step explanation:

Let's compare apples to apples and oranges to oranges:  convert 0.034 yard to feet and leave the other measurement as it is.

(0.034 yd)(3 ft)/(1 yd) = 0.102 ft

Now write 0.102 ft / 60 ft.  Simplifying, we get 102/60000.

Reduce this by dividing numerator and denominator by 2:  51/30000.

Now it happens that 51 = 3*17, so this last result is equivalent to 17/10000.

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