jilin73

Use the formula for area of a regular hexagon.

You get $27\sqrt3 \over 2$.

Rounded to the nearest thousandth, the answer is 28.383

The formula for the area of a rhombus is $A=\frac{pq}{2}$  A representing the area, and p and q as the two diagonal lengths

You can plug in the area and one of the diagonals to get $20=\frac{10q}{2}$

Now you just solve for q. 40 = 10q, q=4

The length of the other diagonal is 4

Using Stewart's theorem, you can find that BM and CM are both √37 and not 4√2, which means our third side (BC) is of length 2√37 (= √148)

Then, using Heron's formula given by:

$16| \triangle ABC|^2 = 2a^2b^2+2b^2c^2+2c^2a^2-a^4-b^4-c^4$

you can calculate the area to be equal to exactly 42

Solve by multiplying the first two polynomials first.

This gets you $3a^3-2a^2-12a+6a^2-4a-24$ which simplifies down to $3a^3+4a^2-16a-24$

Now you do $(a^2-2a+1)(3a^3+4a^2-16a+24)$

After multiplying, you get $3a^5+4a^4-16a^3-24a^2-6a^4-8a^3+32a^2+48a+3a^3+4a^2-16a-24$

$3a^5+4a^4-16a^3-24a^2-6a^4-8a^3+32a^2+48a+3a^3+4a^2-16a-24$ simplifies down to $3a^5-2a^4-21a^3+12a^2+32a-24$

So the answer is $3a^5-2a^4-21a^3+12a^2+32a-24$

$\sqrt{200} = 10\sqrt2$, so $a^2 + b^2 = 200$ 

Assuming that a and b are both integer side lengths, $10^2+10^2=200$, so the sides are 10 and 10.

10 times 10 is 100, so the area of the rectangle is $\bf100$

I would assume that DX = 3.

If CX, AX, and BX all equal three, the point X will have to be the center of the rectangle, so DX = 3.

C                                                                                                                               D

                                                            .x                                                                   

A                                                                                                                               B

I would assume that DX = 3.

If CX, AX, and BX all equal three, the point X will have to be the center of the rectangle, so DX = 3.

C                                                                                                                               D

A                                                                                                                               B

Any two-digit number with a 2 is cozy (and all cozy numbers have at least one 2) There are nine two-digit numbers with ones digit 2 and there are nine additional two-digit numbers with tens digit 2 (excluding 22 which we've already counted, since its ones digits is 2) Therefore, there are 9 + 9 = 18 cozy two-digit numbers.

To solve this problem, we can break it down into steps:

Step 1: Seat the first pair of siblings in the first row. There are 3 ways to do this.

Step 2: Seat the second pair of siblings in the first row. There are 2 ways to do this (since they can't sit directly in front of their siblings).

Step 3: Seat the third pair of siblings in the first row. There is only 1 way to do this, as they must sit in the remaining seats.

Step 4: Seat the first pair of siblings in the second row. There are 2 ways to do this (since they can't sit directly in front of their siblings).

Step 5: Seat the second pair of siblings in the second row. There is only 1 way to do this, as they must sit in the remaining seats.

Step 6: Seat the third pair of siblings in the second row. There is only 1 way to do this, as they must sit in the remaining seats.

Multiplying the number of ways for each step, we get: 3 x 2 x 1 x 2 x 1 x 1 = 12

Therefore, there are 12 ways to seat three pairs of siblings from different families in two rows of three chairs following the given conditions.

Start out by drawing out your answer on graph paper.

Point A is at (0,0), Point B is at (10,0), Point C is at (10,10) Point D is at (0,10).

Then you can draw each of the lines. The equations for each of the lines are: DL: y = -2x + 10, NB: y = -2x + 20, OC: y = 1/2x + 5, and AM: y = 1/2x. 

After drawing out all of the lines, you can find that Point R is at (6,8) and point P is at (4,2).

Use the distance formula or pythag to find the length between the two points.

$\sqrt{2^2+6^2}=\sqrt{40}=2\sqrt10$

Answer: $2\sqrt10$