Afamily drove 180 miles to disneyland. if they left at 10: 30 a. m. and got there at 3: 00 p. m., what was their average speed in mph

Average speed = Distance/ time

Distance = 180 mi

Time = time(final) - time(initial)

To find time will be easier if we translate am and pm into 24 h scale.

am will  stay the same, so   10:30 am   is 10:30. (initial)

pm will be turned (am time + 12), 3: 00 pm = 3:00 +12 =15:00 (final)

Time = time(final) - time(initial)= 15:00 - 10:30 = 14:60 - 10:30 =4h 30 min

4h + 30 min = 4h + 1/2 h= 4.5 h (time)

Average speed = Distance/ time = 180 mi / 4.5 h = 40 mi/h

Answer is 40 mi/h.

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 .

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3