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From the formula for the sum of the angles in a polygon, the number of sides is 6, and the unknown interior angle is 30 degrees.

Wow. Good job!

Really close it was (25/8, 15/8) but thanks for the help :)

Its 60

= i^2   * i^2 * i^2........* i

    -1      -1     -1   ........twenty nine times      * i     =             (even # of i^2  = 1    odd number of i^2 = -1  )

                       -1   * i      = -i

Graph Y is a function.....there is only one value of y for every value of x

    graph x is not a funtion...several values of x have multiple values of y

(3x-2)(2x+3)

\(\frac{2}{9}*\frac{4}{5}*5 = \frac{8}{9}\)

By geometric probability, the probability that BD < sqrt(2) is 1/3.

We can quickly figure out that the line through A must have slope 1/2.  So y = x/2, and the line CD is y = -3x + 12.  Solving these equations, you can find (x,y) = (24/7,12/7).

Nevermind. I was running out of time to get the answer down so I chose a random one and got it correct. :)

There is only one pair: (x,y) = (26,25).

thanks!

For the first problem, where u and v are the roots, u + v = -5 and uv = 7 by Vieta.  Then

u/v + v/u = (u^2 + v^2)/(uv) = 11/7.

For the second problem, a + b = -1 and ab = -5.  Then

(a - 4)(b - 4) = ab - 4(a + b) + 16 = -5 - 4(-1) + 16 = 15.

The vertex of the graph is (5,-4), so the equation of the parabola is

x = -(y + 4)^2 + 5

= -y^2 - 8y - 16 + 5

= -y^2 - 8y - 9.

a + b + c = (-1) + (-8) + (-9) = -18.

volume of a sphere is \(\frac{4}{3}\pi r^2\)

plugging in 4, we have\(\frac{4}{3}\pi*(4^2)=\frac{4}{3}\pi*16=\frac{4*16}{3}\pi=\frac{64}{3}\pi\)

\(\frac{64}{3}\pi\approx\boxed{67.02}\)

3.8/2=1.9

1.9*680+1.9*720\(\approx 2736\)

I would help you with this topic, but I honestly have not heard of modular arithmetic inverses before, so I unfortunately am not knowledgeable enough to give you a helping hand.

using the distance formula, or pythagorean theorem, we have \(\sqrt{0^2+9^2}=9\)

I learned this in class recently. I will try to help you.

Let's say I want to convert \((1011)_2\) into base 10. By the way, the subscript denotes the base of that number. In this case, I will convert from binary to decimal.

Since this number is in base 2, the nth digit represents (n-1) power of 2 of the number.

In the example I created, \((1011)_2 = 1* 2^3 + 0 * 2^2 + 1 * 2^1 + 1 * 2^0\\ (1011)_2 = 8 + 2 + 1\\ (1011)_2 = 11 \). In base 10, the subscript is usually omitted.

What if I wanted to convert from base 10 to binary? Let's use 11 as our example. Well, here is one method to use. Binary, once again, is base 2. I can use the following iterative formula.

\(11 = bq_0 + r_0\\ 11 = 2q_0 + r_0\\ 11 = 2*5 + 1\) where b is the base, q is the largest multiple without exceeding 11, and r is the whole number remainder.

Now, replace the 11 with q_0 and do this process iteratively until q_i = 0.

\(11 = 2 * 5 + 1\\ 5 = 2 * 2 + 1\\ 2 = 2 * 1 + 0\\ 1 = 2 * 0 + 1\\\)

Now that q_i equals 0, we read the remainders we got backwards, which gives us our answer: 1011.

I hope this made sense to you.

Thanks for the praise! Good luck on your future solving adventures!

Yikes! This looks ugly, but I think I cracked this one after some deep thinking. Let me show you my working. This one is quite intimidating, but some key observations and some determination should be enough to figure out the answer to this question successfully.

I started by adding x + y + z and seeing if I could get anywhere with adding the three equations together. I cleverly grouped terms together to make some patterns clearer to me as I solved.

\(x + y + z =(py + qz + r) + (pz + q + rx) + (p + qx + ry)\\ x + y + z = (p + q + r) + (py + pz) + (qx + qz) + (rx + ry)\)

I stopped here to reflect on my strategy thus far. While it certainly looks like I have made this much worse, I noticed that p+q+r = -3, so I could at least do that substitution. I then also noticed that px + qy + rz = 1 would maybe be useful because it would allow me to factor out another factor of p+q+r again. Let's show this in action. The answer just falls out on its own without much effort after that.

\(x + y + z = -3 + (py + pz) + (qx + qz) + (rx + ry)\\ x + y + z + 1 = -3 + (py + pz) + (qx + qz) + (rx + ry) + px + qy + rz\\ x + y + z = -4 + (px + py + pz) + (qx + qy + qz) + (rx + ry + rz)\\ x + y + z = -4 + p(x + y + z) + q(x + y + z) + r(x + y + z)\\ x + y + z = -4 + (p + q + r)(x + y + z)\\ x + y + z = -4 - 3(x + y + z)\\ 4(x + y + z)= -4\\ x + y + z = -1\)

\(\frac{67 - 18}{7} \cdot 3 = \frac{49}{7} \cdot 3 = 7 \cdot 3 = 21\)

The domain of a function is the set of inputs in which the output is defined. 

Here, there is only one input that will cause the output to be undefined. The undefined behavior occurs at x = -8. I know this because the denominator of this function will yield 0, which will lead to an undefined answer.

The domain may be represented in many different ways, but I chose interval notation for this particular occasion.

D: \((-\infty,-8) \cup (-8, \infty)\)

You did it! It was right! Good job!