Ascale model of a city has a scale of 1 cm : 2.5 km. two buildings in the model are 1.7 cm apart. to the nearest tenth of a kilometer, what is the actual distance between the buildings in the city

This is the concept of linear proportionality, we are required to calculate the actual length between two buildings which have a distance of 1.7 cm when drawn to scale of 1 cm: 2.5 km. This can be calculated as follows;
actual distance= (distance on the map)*(scale factor)
actual distance=1.7*2.5=4.25 km

The answer is 4.25 km

You threw the baseball 40 feet.

This can be represented as two right triangles.  The legs of your friend's triangle, the forward distance and distance right, are 15 and 20.  Using the Pythagorean theorem, we find the diagonal distance from your friend's starting point:

20²+15²=c²
400+225=c²
625=c²

Take the square root of both sides:
√625=√(c²)
25=c

The legs of your right triangle are 12, your distance forward, and 9, your distance right:
12²+9²=c²
144+81=c²
225=c²

Take the square root of both sides:
√225=√(c²)
15=c

The total diagonal distance is 25+15=40 feet.