x(x+1)=2550

x^2+x-2550=0

x=-51

x+1=-50

sum=-101

8/x=x/5 (similar triangles)

x^2=40

x=sqrt40=2sqrt10

Problem 1:

a) 20, 22, 24

b) 32

c) 16

d) Never. All the numbers will be even

Formula for b and c: If first day is a and common difference if r then formula for day n is a+r*(n-1) (Make sure you see why)

Problem 2:

a) 6, 10, 15

b) These are all triangle numbers. (1+2+3+4+5...+n)

c) 1+2+3+4...10=55

d) 1+2+3+4...30=465

e) n(n-1)/2

Maybe pay attention next time :)

Smallest: 17*-2

Largest: 17*14

14-2+1=13

Let's see here...

The odd digits must be going 1,3,5,7,9

The even: 8,6,4,2,0

Normally, there would be 10! ways to arrange it, but we must divide by 5!^2 because there is only one way to arrange even and odds. Therefore there are 252 numbers.

1800/2^3/3^2=25=5^2

20%*97.49=19.5$ rounded to the nearest cent

Case 1: Red ball second

There are 19 balls so it is 1/19

Case 2: Red ball picked third

The second ball must not be a red ball: prob 18/19. The probability of the third being red has a probability of 1/18. 18/19*1/18=1/19

Total: 1/19+1/19=2/19

:D

If the points are equidistant from A and B, then it must be on their perpendicular bisector. The midpoint of AB is (.5,-2) and the slope is 4/3. That means the slope of the bisector is -3/4 and must contain (.5,-2). That gives us the equation is y=-3/4x-13/8. Therefore the y intercept is -13/8.

If empty and full sets count as a subset, then there are 2^n subsets for a set with n elements. 256-64 is 192 so there are 8 elements in A and 6 elements in B.

The ones digit must be one of 1, 3, or 5 so there are 3 choices

After selecting the first digit, there are 5 choices left but the first digit cannot be a 0 so there are 4 choices.

4*3=12 numbers

You can divide this into 3 equilateral triangles with side length 2 and each of those triangles has an area of sqrt3 so the total area is 3*sqrt3

At the end, the price is 81%. That means each time the price becomes 90% of what it was previously. There was a 10% decrease each time.

Let's say the missing angle is x. Then the corresponding angle is 360-x. So when we replace x with 360-x, the sum changes by 360-2x. The current sum is 610 but we want it to be 720. That means 360-2x is 120 so x is 120.

18sqrt8 can be written as 36sqrt2 and 8sqrt18 is 24sqrt2. 36sqrt2-24sqrt2 is 12sqrt2 which can be written as sqrt288.

The yellow area is 1/2 of the area of 2 equilateral triangles so it has an area of 1/6 of the hexagon. Quadrilateral CDEF has an area of 1/2 and 1/2-1/6 is 1/3 so the blue area is 1/3. of the hexagon. 1/3:1/6=2