Consider the parabola whose equation is y=x^2-4x and the line whose equation is y=2x+b, where b is some unknown constant determine the value of b such that the line and the parabola will intersect at exactly one location. Then, sketch the system of equations on the axes below. Label their intersection point.

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?

Adepartment store purchases screen-printed t-shirts at a cost of $5 per shirt. they mark up the price 150% (making the selling price 250% of the store's purchase price) and put them on the sales floor. every month that a t-shirt doesn't sell, the store reduces the selling price by 25%.

Ageologist had two rocks on a scale that weighed 4.6 kilograms together.rock a was 0.5 of the total weight.how much did rock a weigh?