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

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

hope this !

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.