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ahh! i misread the remainder as 6/(x-2) but its actually 6. i see now!

hi there!

im a bit confused because when you multiply x+2 and x-2 together, you get x^2 -4, and then when you add 6/(x-2), you get x^2-4+(6)/(x-2), buta ren't we supposed to get x^2+0x+2?

9x^2 +8x+c       divide thru by 9  ( x^2 coeff needs to be '1' to 'complete the square')

x^2 + 8/9x                      now take  1/2 of 8/9   (which is 8/18)

(x+8/18)² 

x^2 + 16/18  + 64/324   multiply by 9

9x² +  8x     +  16/9

You're welcome, xxJ...........

3 is to 6      as   6 is to x

3/6 = 6/x

x = 6 * 6/3 = 12  units

                 x  +2   R  6/(x-2)

x-2  | x² + 0x +2

         x^2  -2x

                2x +2

                2x- 4

                      6

There is only one way you can buy a gyroscope that costs 97 confusions:

8 x 8 confusions + 3 x 11 confusions = 97 confusions.

There are 12 digaonals that have a length of P_1 P_2, which from the Sine Law, is sin (15 degrees).  There are 12 diagonals that have a legnth of P_1 P_3, which from the Sine Law, is sin (30 degrees).  We can appy the same reasoning to the other diagonals, which gives us a total sum of

(12 sin 15)^2 + (12 sin 30)^2 + (12 sin 45)^2 + (12 sin 60)^2 + (12 sin 75)^2 + (12 sin 90)^2 + (12 sin 105)^2 + (12 sin 120)^2 + (12 sin 135)^2 + (12 sin 150)^2 + (12 sin 175)^2 = 864.

(2, 4, 6, 8, 10, 12, 16, 18, 20, 22, 24, 26, 30, 32, 34, 36, 38, 40, 44, 46, 48, 50, 52, 54, 58, 60, 62, 64, 66, 68, 72, 74, 76, 78, 80, 82, 86, 88, 90, 92, 94, 96, 100) >>Total = 43 such numbers

Probability = 43 / 100

On planet Enigma, the residents use a currency called the confusion. There are only 2 confusion bills on Enigma, one worth 8 confusions and the other worth 11 confusions. There are also some coins of smaller value, but each weighs over 10 kilograms, so they are difficult to carry around. In how many ways can a resident of Enigma use only bills to purchase a toaster that costs 96 confusions? (Everybody knows, of course, that vendors on Enigma do not give change, so residents must make their purchases with exact change.) Solution: Since we have two types of bills, we have the Diophantine equation $8a + 11b = 96$, where $a$ and $b$ are non-negative integers. By inspection, we find the solution $a = 12$ and $b = 0$. Note that once we have found a particular solution $(a,b)$, we can decrease $a$ by 11 and increase $b$ by 8 to obtain another solution, because the overall increase in $8a + 11b$ is $8 \cdot (-11) + 11 \cdot 8 = -88 + 88 = 0$. We can also increase $a$ by 11 and decrease $b$ by 8. Furthermore, every solution to the equation $8a + 11b = 96$ can be obtained from the solution $(a,b) = (12,0)$ in this way. So, decreasing $a$ by 11 and increasing $b$ by 8 repeatedly, we get the solutions $(1,8)$, $(-10, 16)$, $(-21, 24)$, and so on. Increasing $a$ by 11 and decreasing $b$ by 8 repeatedly, we get the solutions $(23,-8)$, $(34,-16)$, $(45,-24)$, and so on. However, since $a$ and $b$ are nonnegative, the only solutions are $(12,0)$ and $(1,8)$. There are 2 solutions.

^^first problem (part a) solution

What denominations are the bills?

thanks you!!

I got it, thanks

180 - 139 =61

c =180 - 61 - 77 = 62

b=180 - 62 = 118

139 - 77 - 36 =26 angle between 77 and 36

a =180 - 118 - 26 = 36

So:a =36,  b= 118,  c =62, or the LAST one on your list.

13.     5x - 5 = 4x + 10     x = 15               6y - 4 + 4x + 10 = 180      y = 19

14.     15x + 30 + 10x = 180      x = 6          3y + 18 = 90         y = 24

The values of G, H are as follows:

G =1  and  H = 5: So that:5411507256 mod 72 = 0

G =5  and  H = 1: So that:5415507216 mod 72 = 0

G =6  and  H =9: So that:5416507296 mod 72 = 0

I will you take care of their sums and products.

x - 10 + 4x - 10 = 90

5x = 110

x = 22 

I miss 5th grade

  One side is     1/2  out of  (1/2 + 1/3 + 1/4)   =   1/2 out of  13/12

1/2 / (13/12)    * 52  = 24 cm

second side is   1/3 / (13/12) * 52 = 16 cm

You can multiply out for the third side or just subtract the first two sides above from 52 to find the third side...

thanks

You're not dumb......you are learning!

So its just a different way of saying it? 

When I graphed it on google it says the Y-intercept is oh. I'm so dumb. I chose the graph that looked most similar to it instead of looking at the x and y-intercepts. Im so dumb 

Substitute in 27 for h in the equation

27 = -16t^2 + 48t        use quadratic formula to find TWO values of t   one is the the shirt going up....the other is the shirt coming down

                                       the time the shirt is at least 27 m above the ground is the difference of these two times.....