at the start of your vacation, you drive for four hours and 28 minutes, from your home to a cottage you have rented for a week. the car odometer says that the trip covered a distance of 178.7 miles. when you check your gps, however, it tells you that the straight-line distance from your home to the cottage is 123.3 miles. you might find it to know that there are 1.609344 km in a mile.

(a) what is your average speed for your trip from your house to the cottage? express your answer in units of m/s.
m/s

(b) what is the magnitude of your average velocity for your trip from your house to the cottage? express your answer in units of m/s.

a) 17.88 m/s

b) 12.34 m/s

Step-by-step explanation:

Given:

Total time time taken to reach the cottage = 4 hours and 28 minutes

or

= 4 × 60 + 28 = 268 minutes

= 268 × 60 = 16080 seconds

Total distance covered = 178.7 miles

also,

1 miles = 1.609344 km

thus,

178.7 miles = 178.7 × 1.609344 km = 287.5897728 Km

also,

1 Km = 1000 m

287.5897728 Km = 287.5897728 × 1000 = 287589.7728 m

Total displacement = 123.3 miles = 123.3 × 1.609344 km = 198432.1152 m

Now,

a) Speed =

or

Speed =

or

Speed = 17.88 m/s

b) Velocity =  

or

Velocity =

or

Velocity = 12.34 m/s

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.

the image is given below

since the options are not given so we draw it from the equation

the given equation is

y = (x-1) (x+4)

y = y² + 3x - 4

the above equation is a quadratic equation which will have two roots. if we draw the graph for it, it will look like this