50 points
part a: explain why the x-coordinates of the points where the graphs of the equations y = 4–x and y = 2x + 3 intersect are the solutions of the equation 4–x = 2x + 3. (4 points)

part b: make tables to find the solution to 4–x = 2x + 3. take the integer values of x between −3 and 3. (4 points)

part c: how can you solve the equation 4–x = 2x + 3 graphically? (2 points)

Can you draw an isosceles triangle with only one 80 degree angle?

If x = 12 and y = 3, what is the value of x - y 2? 81 6 3 18

Asmall (but heavy) particle placed in a glass of water will follow a zigzag motion because the particle will bounce off of the water molecules it meets. this is called brownian motion. a physicist simulates this on a computer, by varying the distance a particle can travel (called the mean free length), on average, before it collides with a water molecule and assigning the change in motion to be one of 8 directions, each with a similar probability. by running the simulated particle (with the same mean free length) many times she determines that it should take 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. next she lets a real particle fall through a glass of water and finds that it took 18 seconds. what does she conclude, and why?