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

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!

1 + (6 / x - 1)

step-by-step explanation:

divide using polynomial division.