A camper leaves her cabin and hikes 8 miles due south. Then, she turns and hikes 12 miles due west. If there was a direct path from her cabin to her current position, how far is she from her cabin? Round your final answer to the nearest tenth of a mile.

8.9

14.4

104.0

20.0

14.4

Explenation

We just use the pythagorus theorum

a^2+b^2=c^2

8^2+12^2=c^2

208=c^2

sqrt208=c

14.4=c

so the answer is c

thank you, hope it helps :)

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.