A cup of coffee contains 100 mg of caffeine, which leaves the body at a continuous rate of 17% per hour. (a) Write a formula for the amount, A mg, of caffeine in the body t hours after drinking a cup of coffee. Explain. (b) Graph this function. Use the graph to estimate the half-life of caffeine. (c) Use logarithms to find the half-life of caffeine.

In the image, point a marks the center of the circle. which two lengths must form a ratio of 1 : 2? (options are in the images since thought they were harmful phrases)

The sum of the squares of two numbers is 8 . the product of the two numbers is 4. find the numbers.

Astudent draws two parabolas on graph paper. both parabolas cross the x-axis at (–4, 0) and (6, 0). the y-intercept of the first parabola is (0, –12). the y-intercept of the second parabola is (0, –24). what is the positive difference between the a values for the two functions that describe the parabolas? write your answer as a decimal rounded to the nearest tenth