Retro rides is a club for owners of vintage cars and motorcycles. every year the club gets together for a ride. this year, 38 vehicles participated in the ride. the total number of tires of all the vehicles was 114. assuming each car has 4 tires and each motorcycle has 2 tires, how many each of cars and motorcycles participated in the ride? a. 16 cars; 22 motorcycles b. 23 cars; 15 motorcycles c. 19 cars; 19 motorcycles d. 21 cars; 17 motorcycles

C. 19 cars; 19 motorcycles

Step-by-step explanation:

Let c represent the number of cars and m represent the number of motorcycles that participated this year.

This year a total of 38 vehicles participated. So, we can write the equation as:

c + m = 38                                                (Equation 1)

Each car has 4 tires, so number of tires in c cars will be 4c.

Each motorcycle has 2 tires, so number of tires in m motorcycles will be 2m.

In total there were 114 tires, so we can set up the equation as:

4c + 2m = 114                                          (Equation 2)

From equation 1, m = 38 - c. Using this value in Equation 2, we get:

4c + 2(38 - c) = 114

4c + 76 - 2c = 114

2c = 114 - 76

2c = 38

c = 19

Using this value in equation 1, we get:

19 + m = 38

m = 19

Thus, 19 cars and 19 motorcycles participated in the ride.

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step-by-step explanation:

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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