I've been stuck on this for a couple of days now.

  see the attachment

Step-by-step explanation:

The attached array shows the column number to which each tile needs to be dragged. The table has the same layout as the tile array, so matching tiles to column numbers should be straightforward.

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There are a couple of tricks that make this fairly simple to do. The square roots will only be associated with lengths, so anything that says "length" will go into one of the square root columns.

The square roots are multiples of √10 and of √5. It helps to recognize that ...

so, if the components of the difference of endpoints are in the ratio 1:3, they will go in the √10 column. If they are in the ratio 1:2, they will go in the √5 column.

Consider the upper left tile. Endpoints of the segment are (0, -1) and (4, 7). Their differences are (4, 8), numbers that have the ratio 1:2. This tile goes in column 4, under 4√5.

Consider the tile below that one, the first tile in the second row. Endpoints of that segment are (2, -1) and (4, 5). The differences are (2, 6), numbers that have the ratio 1:3. This tile goes in column 3, under 2√10.

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The "midpoint" tiles are more easily classified. The midpoint is the average of the endpoint coordinates, so is half their sum. If the sum of the x-coordinates is 4, then the midpoint will have an x-coordinate of 2, and the tile will go in the first column.

If the sum of x-coordinates is 6, the midpoint will have an x-coordinate of 3, and the tile will go in the second column. All you have to do is add the x-coordinates to find the column the tile goes to.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.