LagTho

When you're adding or subtracting fractions, you always want to start by giving them all a common denominator. So, we have \(\frac {3/4 + 1/3}{2/12} - 1/2 = \frac {9/12 + 4/12}{2/12} - 6/12\). This helps us calculate the value without messing anything up. So adding the top part, we get \(\frac {13/12}{2/12} - 6/12\). The fraction on the bottom is pesky, so we flip 2/12 to 12/2, and now it's multiplying. \(13/12 \cdot 12/2 -6/12 = (13/2) \cdot 6 - 1/2\). 6 times 13 is 78, but we can't forget the denominator of two, so it turns out to be 39 - 1/2. The answer is 38 1/2. 

Hope this helps!

Yes. Good job!

Degrees = 60

Radians = 1.0472

Put these approximate coordinates on a graph paper, and it's easy to say that this point lies on the unit circle. It doesn't give us any degrees, so that makes me think special right triangles. Let's call the point we have P. Draw a perpendicular line to the x axis from P, connect it to the origin, (0, 0) and connect that line to P. Given the coordinates, we can see that one leg is 1/2, and the other is \(\sqrt3/2\) . Time to use Pythagoras, and square both of these numbers. 1²/2² + \(\sqrt3^2/2^2\) = c². This turns out to 1/4 + 3/4 = c² . So c = 1. Since this side is twice one of the legs,this means that this triangle is a 30-60-90 triangle, so the angle is 60 degrees. To get the radians, I just looked up degrees to radians and that's what it gave me.

In case you wanted to check for yourself, formula for unit circle is x ² + y² = 1. I couldn't find out how to upload the pic. 

Hope this helps!

That's a good answer. Also if you meant how do you square the square root of seven, then you can use this. Any square root times itself is the number inside the radical

How far have you gotten so far?

Yeah, that's definitely possible, I've found that my methods are often unorthodox, and sometimes require some assuming. Sorry I couldn't be more help! Good job Guest for solving it!

1 + \(\sqrt2\) . My method isn't really orthodox and required a little bit of eyeballing it, but I'm sure it's right. Add the right side to the left, and plug it into a graphing calculator, because it's a formula for a circle. This is where the eyeballing comes in, but the largest value for x is when y equals 1. Substitute this into your equation, and you get x² + 1 -2x - 2 = x² - 2x -1. Using the quadratic formula, you get 1 - \(\sqrt 2\). and 1 + \(\sqrt 2 \). We want the larger value for x, so the largest value of x = 1 + \(\sqrt 2\) . Sorry this isn't an official method, but this is the best I could do.

Hope this helps!

For example, if you have xy + xz -yz, no matter what you have for y and z, it will always be positive right? So reverse the signs, and you have xy - xz + yz, it will always be negative. So if x is negative, then xy + xz + yz will always be negative. So going through it, we've ruled out there being one negative variable, two, and three. So all of them must be positive.

Is there an equation to go with this?

Power of a point on M, you get TU = 12. AM * BM = MU² = 36. So we get MU = 6. Do this on the other side, and you find that TM = 6 as well. So TU = 12