Which measurements of two similar triangles are the same?

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?

Factor the polynomial 4x4 – 20x2 – 3x2 + 15 by grouping. what is the resulting expression? (4x2 + 3)(x2 – 5) (4x2 – 3)(x2 – 5) (4x2 – 5)(x2 + 3) (4x2 + 5)(x2 – 3)

A3-dimensional figure has a square base and 4 lateral faces that meet at a point. explain the difference between the cross sections when a slice is made perpendicular to the base through the vertex, and when a slice is made perpendicular to the base and not through the vertex