The denominator of a fraction is four more than three times the numerator. If both numerator and denominator are increased by four, the simplified result is 925. Find the original fraction. (Do NOT simplify.)

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.

answer: hence, function will be

explanation:

since we have given that

cost of a new textbook = $85

according to question, the resale value of a textbook decreases by 25% with each previous owner,

so, our function becomes,

here, y is the total value of the text book after x owners.

hence, function will be

1. a^4+8a^3+24a^2+32a+16

2.y^8+8y^7+28y^6+56y^5+70y^4+56y^3+28y^2+8y+1

3.x^6-3x^4y^2+3x^2y^4-y^6