Grace and Hannah are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Grace is 250 miles away from the stadium and Hannah is 306 miles away from the stadium. Grace is driving along the highway at a speed of 40 miles per hour and Hannah is driving at speed of 54 miles per hour. Let GG represent Grace's distance, in miles, away from the stadium tt hours after noon. Let HH represent Hannah's distance, in miles, away from the stadium tt hours after noon. Write an equation for each situation, in terms of t, t, and determine the number hours after noon, t, t, when Grace and Hannah are the same distance from the stadium.

F(x)= 1/x-4, g(x)=4x+1/x a. use composition to prove whether or not the functions are inverses of each other. b. express the domain of the compositions using interval notation.

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

(mc 02.03) what set of reflections and rotations would carry rectangle abcd onto itself? reflect over the y-axis, reflect over the x-axis, rotate 180° rotate 180°, reflect over the x-axis, reflect over the line y=x reflect over the x-axis, rotate 180°, reflect over the x-axis rotate 180, reflect over the y-axis, reflect over the line y=x