From his home, bob would have to walk 3 miles north to get to his friend lucky’s house and 4 miles east to get to his friend raymond’s house. one day, bob walked from his home to raymond’s house. together, raymond and bob cut directly through the field that separated them from lucky’s house. when they finished playing at lucky’s, bob walked back home. in all how far did bob walk?

  12 miles

Step-by-step explanation:

The diagonal distance from Raymond's house to Lucky's house is given by the Pythagorean theorem as ...

  c = √(a² +b²) . . . . . where c is the hypotenuse length of a right triangle with legs "a" and "b"

Here, we have a=4, b=3, so ...

  c = √(4²+3²) = √(16+9) = √25 = 5 . . . . miles

So, Raymond's trip that day was ...

  distance to Raymond's + distance from Raymond's to Lucky's + distance from Lucky's

  = 4 + 5 + 3 = 12 . . . . miles

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

step-by-step explanation:

bob the banana