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sum of roots = -b/a = m/2 = -6

product of roots = c/a = n/2 = 10

m + n = -12 + 20 = 8

Very very interesting problem.

I can do this with the Lagrange Interpolation Formula. I will write up a solution very soon.

36 possible rolls

What will cover a '9'

5 4

4 5

3 6

6 3       4 rolls

The you can roll greater than 9

10:

6 4

4 6

5 5       3 rolls

11:

5 6   2 rolls

6 5

12 :

6 6    1 roll             10 ways out of 36 rolls           5/18

No 1/6

So the number of ways we can get a number greater then 9, if we roll a 1: 0, 2:0, 3:0, 4:1, 5:2, 6:3 so in total there are 6 ways to cover 9 on the first roll. 36 possible rolls in total divided by 2 for over counting  so 1/3 I would think...

The area of the triangular pyramid is $\frac{1}{3} bh. $ We can make the base the top face, and the base has an area of $\frac{3 \cdot 4}{2} = 6.$ The height that is given is $\frac{1}{2} \cdot 4 = 2.$ Now, we can plug these values in, and we get $$V = \frac{1}{3} bh. $$ $$V = \frac{1}{3} (6)(2)$$ $$\boxed{V = 4 \text{ in}^3}.$$

1-8 to shift it left 8 units so the vertex is at (-7, -2)

2208 because if it is linear then the change in wieght is 165 when you add 30 gallons of fuel making each gallon 5.5 pounds then we add 8*5.5 to 2164 and we get 2208 pounds

Side lengths are half of each side so 3*2*4=24/2=12

We can use 3d vectors.  This pyramid is spanned by the vectors (2,0,0), (0,3,0), and (0,0,4).  Taking the determinant gives us a volume of 8.

I plotted it, and got a range of [3,7] U [8,10].

So the factors of 30 are 30, 1 , 5, 6 , 15, 2 , 3, 10 so their would be 4 polynomials with integer roots because there are four pairs of numbers that multiply to 30...

Expanding \((1+r)(1+s)(1+t)(1+u)\), we get: \(rstu + (rst + rsu + rtu + stu) + (rs + rt + ru + st + su + tu) + (r + s + t + u) + 1\)

We can use Vieta's to get: \(rstu = 2/3, rst + rsu + rtu + stu = -7/3,  rs + rt + ru + st + su + tu = 2/3, r + s + t + u = 1/3\)

Adding, we get \(2/3 - 7/3 + 2/3 + 1/3 + 1 = 1/3\)

1/2 of the painters will obviously take twice as long = 2.5 days       2 1/2 days

So 4% of 800 would be 32 and 32*20 is 640 so she lost that many pounds out of her profits. She earned 1600 in total from selling everything so 1600-640=960 that she gets to donate. 65% of 960 is 624 that would go to charity A so whatever is left after she donates 624 pounds from 960 pounds would be how much money she raised for charity B i think.

x     x + 7      and   x - 8     are the three numbers  (given)

sum to 67

x   +   x+7   +   x-8 = 67

x = 22 2/3      and     29  2/3    and   14  2/3

a = k/b  

6 = k/3     k = proportionality constant = 18

a = 18 / 8      =  9/4 =   2 1/4    when b = 8

z^2 -21z+12 = 0        via quadratic formula z =   21/2 ±  sqrt(393) /2

                                                              sum = 42/2 = 21                              (which is just   - b/a)

Thank you! That clarifys things a lot!

not sure but 1000/4 because the biggest side would be around double the other ones... biggest side around 500 the shorter ones around 250... to make it an actual triangle subtract one from 500 and add one to either of the other sides so the triangle sides would be 499, 251, 249.

The possible values of a is [2,inf).

The domain is the interval of the possible values of $x$. As we can see from the graph, the domain is infinity because the parabola extends infinitely. 

The range is the interval of the possible values of $y$. In this case, we see that the $y$ values cannot go below $-2, $ but they extend towards positive infinity. 

Therefore, the domain is $\boxed{(-\infty, +\infty)},$ and the range is $\boxed{(-2, +\infty)}. $

1. s(3) = 37.

2. f(x) - g(x) + h(x) = -x^2 + 8x + 3.

3. The coefficient of x^3 is 1 - 7 = -6.