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

vbbv

step-by-step explanation:

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3