Tom went on a bike to the store 3 miles away. If it took Tom 1/2 of an hour to get there and 2/3 of an hour to get back , what was his average rate of speed for the entire trip

5.14 mi/h

Step-by-step explanation:

To find the average speed, we simply find the total distance traveled by Tom and divide that by the total time the entire journey took him.

Average speed = (total distance traveled) / (total time taken)

TOTAL DISTANCE TRAVELED

He traveled 3 miles to and 3 miles fro. Hence:

3 + 3 = 6 miles

TOTAL TIME TAKEN

He spent ½ hr to go and ⅔ hr to return back. Hence:

½ + ⅔ = 7/6 hr

Therefore, the average speed is:

v = 6 / (7/6)

v = 36 / 7 = 5.14 mi/h

Tom's average speed was 5.14 mi/h.

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )