Abird leaves its nest and travels 20 miles per hour downwind for x hours. on the return trip, the bird travels 4 miles per hour slower and has 6 miles left after x hours.
a. what is the distance of the entire trip?

b. how long does the entire trip take?

30 mi/ 24 mi (6 mi slower)

Step-by-step explanation:

distance = rate x time

distance = 20 mph * X hr = 20 X miles

return trip:

    distance = 16 mph * X hr + 6 miles = 16X + 6

They are the same:

 20X = 16X + 6

 4X = 6

 X = 6/4 = 3/2

20 mph * 3/2 hr = 30 miles.

On the return trip: 16 mph * 3/2 hr = 24 miles, which is 6 miles short of 30 mi.

The distance is 30 miles.

The bird flies all 30 miles in 3/2 hr = 1 and 1/2 hour = 1 hour 30 minutes.

On the return trip, the bird flies 24 miles in 1.5 hours, which is 6 miles short.

127

whether it's diameter, or radius, i believe if i remember correctly from school, every amount has to always add up to 180. so if you take 53, and starting adding, long story short, taking 127 and adding it to 53, gives you 180.

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: