Eric ran from school to the town monument and back again. On his way to the monument, he ran at 10kph and went back to school at 8kph. The entire trip took 2 hours and 15 minutes. How far is the monument from school?

Distance = 10 km

Step-by-step explanation:

Let x be the number of hours taken from school to town and y be the number of hours taken back to the school

Then distance covered during first trip would be 10x (distance = speed*time) and during the second trip would be 8y. Both distances are equal.

=> 10x = 8y  

Dividing both sides by 2

=> 5x = 4y

=> 5x-4y = 0   (1)

The total time for both the trips is:

=> x + y = 2.25 (2)

Multiplying eq (2) by 5

=> 5x+5y = 11.25  (3)

Subtacting (3) from (1)

=> 5x-4y-5x-5y = 0-11.25

=> -4y-5y = -11.25

=> -9y = -11.25

Dividing both sides by -9

=> y = 1.25 hrs

Putting in (2)

=> x + 1.25 = 2.25

=> x = 2.25 - 1.25

=> x = 1 hr

Now, Calculating the Distance

=> Distance = 10x

=> 10 ( 1 )

=> Distance = 10 km

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it