Because of the increase in traffic between springfield and orangeville, a new road was built to connect the two towns. the old road goes south x miles from springfield to freeport and then goes east x + 5 miles from freeport to orangeville. the new road is 9 miles long and goes straight from springfield to orangeville. find the number of miles that a person drove using the old road. ! : (

11.70 miles

The road from Springfield to Orangeville is apparently the hypotenuse of a right triangle whose legs are x and x+5. The value of x can be found from the Pythagorean theorem:

... 9² = x² + (x+5)²

... 2x² +10x -56 = 0 . . . . . . eliminate parentheses, collect terms, subtract 81.

... x² +5x -28 = 0 . . . . . . . . divide by 2 (because we can)

... x² +5x +6.25 = 28 +6.25 . . . . add 28, then add (5/2)² to complete the square

... (x +5/2) = √34.25 . . . . . . . .take the positive square root

... x = -2.5 +√34.25 ≈ 3.352

The total distance via the old road is the sum of the leg lengths:

... x + (x+5) = 2x +5 = 2(3.352) +5 = 11.704 . . . . miles

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,