Matthew is driving his car to visit a farm. he covers a distance of 112.25 miles in 60 minutes. he visits a friend on the way, and thereafter drives 45 miles at the same speed. he estimates that he took 30 minutes to cover the last distance. is this a reasonable estimate?

His estimate is not reasonable because the time it took to cover the last distance is 24.1 minutes and it is below his estimate

Step-by-step explanation:

On his way to the farm, he covered a distance of 112.25 miles in 60 minutes.

Speed = distance/time.

So his speed is 112.25/60 = 1.87 miles per hour.

He visits a friend on the way, and thereafter drives 45 miles at the same speed. So he covered 45 miles at a speed of 1.87 miles per minute.

Time taken = distance / speed

Time it took him to cover 45 miles = 45/1.87 = 24.1 minutes

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step-by-step explanation:

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the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.