CubeyThePenguin

There are a total of 5040 arrangements. 

Keep these relationships in mind:

even + odd = odd

odd + even = odd

odd + odd = even

even + even = odd

To have an odd sum of two adjacent numbers, they must have opposite parity (one even, one odd).

If I'm entirely honest, this looks like an interesting problem to solve. Even I haven't figured it out yet! I hope this gets you started.

Lines KL and GJ are paralle, so

2x + 49 = 4x + 29

20 = 2x

x = 10

69 degrees

Let the miles she walked on the first day be a, miles walked on the second day be b, and so on.

first 2 days, she hiked a total of 22 miles  ==>  a + b = 22

2nd and 3rd days, averaged 18 mi/day  ==>  (b + c)/2 = 36

last two days, hiked total of 30 miles ==> c + d = 30

first and third days ==> a + c = 26

We have four equations and four variables, so we can solve. I hope this gets you started.

PQS is a straight line, so:

(3x - 5) + (x + 1) = 180

4x - 4 = 180

4x = 184

x = 46 degrees

Let's label the children's ages:

Jessica = a

Jeremy = b

Jenna = c

(a + b)/2 = 11 

(a + b + c)/3 = 10

From there, we can simplify:

a + b = 22          . (1)

a + b + c = 30     . (2)

Subtract equation (1) from (2) to get c = 8.

If a polynomial has a root of the form \(a + \sqrt{b}\) then it must also have another root of the form \(a - \sqrt{b}.\)

So, our quartic is:

\((x - (1 - \sqrt{2}))(x - (1 + \sqrt{2}))(x - (2 + \sqrt{5}))(x - (2 - \sqrt{5}))\)

I won't do your homework for you, but here's something to get you started.

surface of rectangular pyramid = 

(square) + 4(triangle)

Plug in the values they give you.

Lines WX and TV are parallel, so

77 - 4x = x + 67

10 = 5x

x = 2  ====>  69 degrees

First, find the days when they will tell the truth. January has 31 days:

Prime: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31

Third: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

The dates on which they will both tell the truth are the 3rd, so there is only 1 date that works.