College Algebra (MATH 8)

In calendar year 2015, retired rock stars Kim and Francis together made a total of $285,571.60. Also, Kim made 15% more than Francis did in 2015. How much money did Francis make in 2015?

Let f(x) = 5x^2 + x. Simplify f(7 + h) − f(7)/h completely. Show all your work.

Find all possible solutions to the following system: 11x − 3y = 2, 2x − y = 7.
If there are no solutions, or infinitely many solutions, briefly EXPLAIN how you know this is true. Show all your work, and leave all numerical answers in exact form (fractions, radicals, etc.). Note that solutions need not be whole numbers.

Write the quadratic function f(x) = x^2 + 10x − 7 in standard form and sketch its graph. Label the vertex and the y-intercept of your graph. (You do not need to label the x-intercept(s), if any.)

Find the domain of the function g(x) = 1/√x^2 − 3x − 4. Show all your work. You may express your answer either in interval notation (e.g., “[−16, 3] ∪ (22, 55)”) or by inequalities (e.g., “x > 325”).

Let f(x) = x^3 − 19x + 30. Find the rational zeros of f(x) by factoring f(x) completely. Show all your work. Make sure you include both the complete list of zeros of f(x) and the factorization of f(x) in your final answer.