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george has opened a new store and he is monitoring its success closely. He has found that this store’s revenue each month can be modeled by r(x)=x2+5x+14 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars. He has also found that his expenses each month can be modeled by c(x)=x^2−4x+5 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars.

the new store will sell 900 items in its fifth month in business

the store will have a profit of $900 after its fifth month in business

the store will have a profit of $5400 after its fifth month in business

the new store will sell 5400 items in its fifth month in business

Step-by-step explanation:

The correct answer is that the new store will have a profit of $5400 after its fifth month.

Profit is given by subtracting revenue minus cost:

(R-C)(x) = (x²+5x+14)-(x²-4x+5) = x²-x²+5x--4x+14-5 = 5x+4x+14-5=9x+9

Using 5 for x,

(R-C)(5) = 9(5) + 9 = 45+9 = 54

This is in hundreds of dollars, so it represents $5400.

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have

, 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