An amusement park offers two options. option 1 involves a $10 admission fee plus $0.50 per ride. option 2 involves a $6 admission fee plus $0.75 per ride. for how many rides do the two options have the same cost ( or, what is the break-even point)?

16 rides

Step-by-step explanation:

Option 1 . Admission fee = $10

                Each ride = $0.50

Option 2 . Admission fee = $6

                Each ride = $0.75

Let no. of rides be x

So, cost of ride according to option 1 = 0.50x

So, total cost after having x rides according to option 1 :

= 10+0.50x  ---1

Cost of ride according to option 2 = 0.75x  

So, total cost after having x rides according to option 2 :

= 6+0.75x  --2

Now to find the beak even point i.e. having the same cost

Equate 1 and 2

Thus for 16 rides , the two options have the same cost .

Hence the break even point is 16 rides

Step-by-step explanation:

Right triangle ABC is reflected over AC to form triangle AFC.

Triangle AFC dilated by a scale factor of two-thirds to form triangle DEC.

Reflection is a rigid transformation which preserves lengths and angles, then

Dilation is a transformation which maps the triangle into similar triangle, so

Thus,

Similar triangle have congruent corresponding angles, so

and proportional corresponding sides

Thus, correct options are: