Asap which statement is true? a. the value of f(6) is 125 times the value of f(3).b. the value of f(6) is 2 times the value of f(3).c. the value of f(6) is 1/125 times the value of f(3).d. the value of f(6) is 15 times the value of f(3).

Given the recursive formula, each terms is five time the previous one.

This means that:

In general, since you have , each time you compute a new term you multiply by a factor of 5, so if , you have

a)

x  |  y

16  |  3

12  |  6

8   |  9

4   |  12

b) A large basket contains 23 eggs

Step-by-step explanation:

a) Isolating 3x, we get

3x = 60-4y

This means that 60-4y is a multiple of 3.

Besides, as x is a positive integer, then x = 60-4y has to be greater than zero

60-4y>0

Solving the inequality for y

60>4y

60/4 > y

15>y (or y<15, which is the same)

The multiples of 3 which are smaller than 15 are 3,6,9 and 12

Now we draw a table for these values of y and found the value of x by replacing in the equation 3x = 60-4y---> x = (60-4y)/3

x  |  y

16  |  3

12  |  6

8   |  9

4   |  12

And these are all the solutions in positive integers.

b) This problem is pretty much like problem a)

Let's call x the number of eggs contained in the large baskets and y the number of eggs contained in the small baskets.

Then

Number of eggs bought - number of eggs sold = number of eggs left over.

In this case

11x-39y = 19

But we also know that 0<y<12 because the small baskets hols fewer than a dozen.

Isolating x in the equation 11x-39y + 19, we get

x=(19+39y)/11

Now we make a table with these values of x and y remembering that y is a positive integer smaller than 12

x   | y

5.2  | 1

8.8  | 2

12.4 | 3

15.9 | 4

19.5 | 5

23   | 6

26.6 | 7

30.1 | 8

33.6 | 9

37.2 |10

40.7 |11

From this table we see that the only integer solution for x is 23, so a large basket contains 23 eggs.