1. Solve the following system of equations below. What does the solution represent? 5x + 2y = 10 3x + 5y = 2
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1 1. Solve the following system of equations below. What does the solution represent? 5x + 2y = 10 3x + 5y = 2 2. Given the function: f(x) = a. Find f (6) b. State the domain of this function in interval notation 3. For the given equation: 2x 3y = 9, find x, y intercepts, slope, and graph the equation (label intercepts) Page 1
2 4. Given a line that passes through the points (2, 4) and ( 1, 6). a. Determine the slope of the line through these points. b. Write a point slope form of the equation of the line through the points. c. Write the slope intercept form of the equation of the line through the points. 5. Solve the following equations for x. a. 3x + 7 = 5x + 4 b. x x + 4 > 3 6. Assume line, L1 contains the points (3, 1) and (4, 3). a. Find the equation of the line that is perpendicular to L1 and passes through the point ( 1, 2). b. Find the equation of the line that is parallel to L1 and passes through the point ( 1, 2). Page 2
3 7. Given the following system of linear inequalities, answer the questions below. 2x y > 4 x + 2y 4 a. Find the vertex (this is where the 2 lines intersect) b. Rewrite the two inequalities above in slope intercept form by keeping the inequality symbol in each answer. c. Graph the solution region; label the vertex and at least one additional point for each line. Page 3
4 8. Answer the following questions based on the graph below: a. State the domain and range of the function f(x) shown in the graph, express answer in interval notation. b. Indicate where f(x) is increasing, decreasing or constant, express answer in interval notation. c. Identify all x and y intercepts of f(x) as ordered pairs. d. State in interval notation where f(x) < 0. e. Why does this graph represent a function? Explain. 9. The admission fee at a small circus is $1.50 for children and $4.00 for adults. On opening day, 2200 people attended the circus and $5050 of admission fees were collected. How many children and how many adults attended the circus opening day? Page 4
5 10. The graph below represents how tickets are available for a concert hours after the ticket sales began. Answer the questions below. a. What is the y intercept and what does it represent? b. What is the x intercept and what does it represent? c. What is the slope of the line and what does it represent? Page 5
6 11. Determine whether the graphs displayed below represent a function or not. Circle the correct choice and explain your selections. Explain: Yes No Yes No 12. The following data is the number of tons of solid waste generated per year in the state of Florida. Year Tons 26,602,703 27,877,212 31,284,077 32,269,383 32,589,513 37,401,392 a. Use your calculator and find the linear least squares regression line, let x represent the number of years since 2011 and y represent the number of tons of waste generated per year. b. What is the value of correlation coefficient? c. Does this represent a strong correlation, explain? d. Based on the model you found in part (a), predict the number of tons of waste generate in the year Page 6
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