Pamela drove her car kilometers and used 999 liters of fuel. she wants to know how many kilometers (k)(k)left parenthesis, k, right parenthesis she can drive with 121212 liters of fuel. she assumes the relationship between kilometers and fuel is proportional. answer

When the relationship between two variables are said to be proportional, it means that one variable is a constant multiple of the other variable. They are related by a constant of proportionality, usually denoted as k. 

In this problem, the dependent variable is the distance in kilometers. Your mileage is limited with the amount of fuel you have. Thus, the independent variable is the liters of fuel. When these two are proportional, it could be expressed as

distance = k * liters of fuel, such that 
distance/liters of fuel = k

By variation,

distance,1/liters of fuel,1 = distance,2/liters of fuel,2, where 1 denotes situation 1 and 2 denotes situation 2. Therefore,

 999999 km /999 liters =  x km /121212 liters, where x is the unknown distance. We can now therefore find the value of x.

x = (999999*121212)/999
x = 121333212 kilometers

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.