If m∠abc = 70°, what is m∠abd? justify your reasoning.
  using the addition property of equality, 40 + 70 = 110, so m∠abd = 110°. 
using the subtraction property of equality, 70 − 30 = 40, so m∠abd = 30°. 
using the angle addition postulate, 40 + m∠abd = 70. so, m∠abd = 30° using the subtraction property of equality.
  using the angle addition postulate, 40 + 70 = m∠abd. so, m∠abd = 110° using the addition property of equality.

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

step-by-step explanation:

formula

x = x1 + p/w(x2 - x1)

let the line segment ab with a(x1,y1) and b(x2,y2)

a point(x,y) divide ab in the ratio, 2: 3 the x coordinate can be written as

x = x1 + p/w(x2 - x1)

here p=2 and w = 2+3

therefore,

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

similarly y coordinate y = y1 + 2/5(y2 - y1)

the furthest the dog can be is 508 meters away from the house, and the closest he can be is 492 meters away from the house.