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For the equation,
y = 1/2(x+3)^2 -5
The vertice is (-3,-5). Therefore the axis of symmetry is X = -3.
To justify the yearly membership, you want to pay at least the same amount as a no-membership purchase, otherwise you would be losing money by purchasing a yearly membership. So set the no-membership cost equal to the yearly membership cost and solve.
no-membership costs $2 per day for swimming and $5 per day for aerobic, in other words, $7 per day. So if we let d = number of days, our cost can be calculated by "7d"
a yearly membership costs $200 plus $3 per day, or in other words, "200 + 3d"
Set them equal to each other and solve:
7d = 200 + 3d
4d = 200
d = 50
So you would need to attend the classes for at least 50 days to justify a yearly membership. I hope that helps!
I could be wrong, but I'm pretty sure here the answer would be 10x^2 + 17x +3 would be the area since you have to multiply length and width. since these are expressions with no answers and no other numbers, we can't find x.
Answer:
see explanation
Step-by-step explanation:
Using the Pythagorean identity
cos²A + sin²A = 1 ( divide terms by cos²A )
+ 
= 
, that is
1 + tan²A = sec²A ← as required
