The graphs of f(x) and g(x) are shown below:

graph of function f of x open upward and has its vertex at negative 7, 0. graph of function g of x opens upward and has its vertex at negative 5, 0

if f(x) = (x + 7)^2, which of the following is g(x) based on the translation?

g(x) = (x + 5^)2

g(x) = (x − 5)^2

g(x) = (x − 9)^2

g(x) = (x + 9)^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

Line gh passes through points (2, 5) and (6, 9). which equation represents line gh? y = x + 3 y = x – 3 y = 3x + 3 y = 3x – 3

You are designing a rectangular pet pen for your new baby puppy. you have 30 feet of fencing you would like the fencing to be 6 1/3 feet longer than the width