At a museum you can see the four cable lines that are used to pull cable cars up and down a hill. each cable travels at a speed of 12.65 miles per hour, caused by a rotating wheel whose diameter is 6.5 feet. how fast is the wheel rotating? express your answer in revolutions per minute.

54.514 rev/min

Step-by-step explanation:

Data provided in the question:

Speed of the cable car = 12.65 miles per hour

Diameter of the rotating wheel, d = 6.5 feet

Now,

The speed of rotation of the wheel will be equal to the speed of the cable car

thus,

The speed of rotation of the wheel = 12.65 miles per hour

also,

1 miles = 5280 feets

1 hour = 60 minutes

Thus,

The speed of rotation of the wheel =

= 1113.2 ft/ min

Circumference of the wheel = πd

= 6.5π feet

= 20.42 feet

Therefore,

The speed of rotation of the wheel in  revolutions per minute

=  1113.2 ÷ 20.42 rev/min

= 54.514 rev/min

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.