Two lighthouses are located 20 miles from one another on a north-south line. If a boat is spotted S 25o E from the northern lighthouse and N 35o E from the southern lighthouse, how much closer is the closest lighthouse to the boat than the lighthouse furthest away?

The northern lighthouse is 7.2 miles closer than the southern lighthouse.

The southern lighthouse is 9.8 miles closer than the northern lighthouse.

The southern lighthouse is 3.4 miles closer than the northern lighthouse.

The southern lighthouse is 23 miles closer than the northern lighthouse.

6, 10

9, -13

12, -21

18, -23

step-by-step explanation:

you just add 6 to the x-coordinate and subtract 10 from the y-coordinate.

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.