The Rocket Coaster has 15 cars, some that hold 4 people and some that hold 6 people. There is room for 72 people altogether. How many 4-passenger cars are there? How many 6-passenger cars are there?

9, four-seater cars

6, six-seater cars

Step-by-step explanation:

Set up a system of equations

x is the number of 4-seater cars

y is the number of 6-seater cars

there is a total of 15 cars

x + y = 15

and there is a total of 72 people on the ride

4x + 6y = 72

so here is the system

x + y = 15

4x + 6y = 72

now use elimination to solve

x + y = 15           | * -4

4x + 6y = 72

-4x - 4y = -60

4x + 6y = 72

combine

2y = 12

solve using inverse operations

2y = 12

y = 6

now subsitute back in to find x

x + y = 15

y  = 6

x + 6 = 15

inverse operations

x + 6 =1 5

x = 9

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

d

gimmee one of those gold crowns!

~coco