A freight train departs from one train station to its destination at a constant speed. Suppose the distance the train is from the station in miles is represented as a function of the number of hours after the train departed from the train station. If the graph of the function passes through the points (0.5, 135) and (2,81), what is the distance between the train station and the freight train's destination? (1 point) A. 189 miles B. 171 miles C. 153 miles D. 162 miles

108 miles

Step-by-step explanation:

Given the points (0.5, 135) and (2,81)

Diatnce between two points :

D = √(x2 - x1)² + (y2 - y1)²

X1 = 0.5 ; y1 = 135 ; x2 = 2 ; y2 = 81

D = √(2^2 - 0.5^2) + (81^2 - 135^2)

D = √(4 - 0.25) + (6561 - 18225)

D = √3.75 −11664

D = 107.98263

D = 108 miles

bull

step-by-step explanation:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1