Let ABC be any triangle. Equilateral triangles BCX, ACY, and BAZ are constructed such that none of these triangles overlaps triangle ABC. a) Draw a triangle ABC and then sketch the remainder of the figure. It will help if triangle ABC is not isosceles (or equilateral).

b) Show that, regardless of choice of triangle ABC, we always have AX = BY = CZ.

You must include a diagram for any complicated geometry problem that does not come with its own diagram. Diagrams are extremely important in geometry because they help your reader understand what is going on. Diagrams also help you to keep track of your work and possibly give you useful insight.

Thanks so much!

Quadrilateral ghjk has vertices g(2, 3), h(8, 2), j(6, 8), and k(3, 6). it is transformed according to the rule t(–4, –5). what are the coordinates of g”? (–7, 3) (–2, 2) (–1, –7) (2, –2)

The rate of decay of a radioactive substance depends upon the amount present initially. the mass y (mg) of the radioactive substance cobalt-60 present in a sample at time t (years) is represented by the exponential equation y=50e −0.1315 t . answer the following questions in complete sentences. 1. how does the exponential equation above compare to the equation for simple interest that is compounded continuously? explain the similarities. 2. what is the initial amount of cobalt-60 in the sample? 2. how much cobalt-60 is left after 8.4 years? show your work. 3. what would be the y-intercept of the graph? what does it represent? 4. after how many years will the amount of cobalt-60 left be 6.25 mg? explain what happens to the cobalt-60 after 50 years? 5. discuss some “real-world” examples and uses of cobalt-60

An initial investment of $100 is now valued at $150. the annual interest rate is 5%, compounded continuously. the equation 100e0.05t = 150 represents the situation, where t is the number of years the money has been invested. about how long has the money been invested? use your calculator and round to the nearest whole number. years