A terrarium is built in the shape of a triangular prism. The prism is 10 inches in height and contains 450 cubic inches of space
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20: Let be the amount of money. If this amount is shared between 8 people, each person will get x/8 dollars. But there actually are 6 people, so everyone is getting x/6 dollars. We know that this difference results in 30 dollars more, so we have
Rearrange the left hand side as
And multiply both sides by 24 to get
21: Let and
be the number of marbles owned by Mike and Judy, respectively. At the beginning, we have
If they both get 9 more marbles, Mike will have marbles, and Judy will have
marbles. So, we have
Plug this value in the first equation and we have
And we deduce
So, the difference is
22: Let be the number of $10, $20 and $50 coupon, respectively. We're given:
Rearrange as follows:
And now we can deduce the number of the other coupons:
So, the total value is
23: a) In order to find the first three terms of the sequence, you just need to plug n=1,2,3:
b) We have
c) 105 is a term of the sequence if and only if there exists an integer k such that
So, 105 is not a term of the sequence.
Rewrite the parabola in standard form and use this formula to find the vertex (h,k).
= (2,-1)
= (2,-1)