A car entered a roundabout from Mason Avenue, traveled 280 feet, then turned onto Perry Street. If the roundabout has a diameter of 150 feet, find the angle of rotation to the nearest degree the car traveled

The angle of rotation is 214°.

Step-by-step explanation:

Formula for arc length:

The length of arc is the product of radius and the central angle ( in radian).

L= rθ

L= Length of arc

r= Radius

θ= Central angle (in radian).

Here L= 280 feet and diameter =150 feet.

Radius feet =75 feet

L= rθ

radian.

We know that,

π  radian= 180°

                      = 214°

The angle of rotation is 214°.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .