The scale on the map indicates 1 inch= 150 miles. The distance from Philadelphia to Miami is 1200 miles. on the map, how far apart are Philadelphia and Miami?

9514 1404 393

  8 in

Step-by-step explanation:

  (1200 mi)×(1 in)/(150 mi) = (1200/150) in = 8 in

The cities are 8 inches apart on the map.

Additional comments

You can think of it as a units conversion problem (as above), or as a proportion:

  (map distance)/(1200 mi) = (1 in)/(150 mi)

  map distance = (1200 mi)(1 in)/(150 mi) = 1200/150 in = 8 in

__

When doing units conversion, you multiply by a scale factor that has units you want in the numerator, and units you want to cancel in the denominator. The numerator and the denominator have the same value, so multiplying by that fraction changes the units but not the value. Here, 1 in = 150 mi, so (1 in)/(150 mi) ≡ 1.

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3

345

step-by-step explanation: