Four puzzles that were manufactured contained a total of 420 pieces. the next 6 puzzles contained a total of 630 pieces. if the relationship between the number of puzzles and the total number of puzzle pieces continues to be proportional, which could be the missing entries in the table? number of puzzles number of pieces (y) (x) 4 420 6 630 8 puzzles and 800 pieces 8 puzzles and 840 pieces 10 puzzles and 1,000 pieces 10 puzzles and 1,200 pieces

Option B is correct

8 puzzles and 840 pieces

Step-by-step explanation:

The direct variation says that:

then equation is in the form of:

.  where, k is the constant of variation.

As per the statement:

Here, y represents the number of puzzles and x represents the number of pieces.

If the relationship between the number of puzzles and the total number of puzzle pieces continues to be proportional

then by definition:

y = kx           ....[1]

From the given table,

Let y = 4 and x = 420

Substitute these in [1] to solve for k;

Divide both sides by 420 we have;

then;

         .....[2]

To find which could be the missing entries in the table.

For y= 8 (number of puzzles)

Substitute in [2] we have;

Multiply both sides by 105 we have;

or

x = 840 pieces.

therefore, the missing entries in the table is,

8 puzzles and 840 pieces

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)