Algebra Homework 1: Linear Equations

Transcription

1 SAN FRANCISCO STATE UNIVERSITY DEPARTMENT OF MATHEMATICS Algebra Homework 1: Linear Equations Andrew Dynneson Due July 12th at 11:59 PM [Last Update: July 9th] [For all questions, do not include units when you submit your answer online] 1. Find the equation of the line passing through the points P 1 ( 1,2) and P 2 (2,3) (A) y 2 = 1 3 (x 1) (B) y 2 = 3(x + 1) (C) y + 2 = 3(x 1) (D) y 2 = 1 3 (x + 1) 1

2 2. The accompanying graph shows the number of Nobel Prizes awarded in science for various countries between 1901 and It contains accurate information but gives the impression that the number of prize winners declined drastically in the 1970s, which was not the case. What flaw in the construction of the graph leads to this impression? (A) The graph only shows percentages, so the figures are misleading. (B) The Nobel prize committee decided to award more prizes the previous two years. (C) There were more categories of prizes in 1970 so it caused an apparent decline. (D) The graph shows total prizes awarded to a few specific countries, not the total number of prizes awarded to all countries. 3. For the next few questions, we will be using the functions L(h), which is the cost for Law advice from various law firms, and h is the number of hours of legal advice. The functions are given: L 1 = h L 2 = h L 3 = h L 4 = 500h Which Option has the highest initial cost? (A) L 1 (B) L 2 (C) L 3 (D) L 4 4. For the same functions as before, which has the largest Hourly cost? (A) L 1 (B) L 2 (C) L 3 (D) L 4 5. If you need five hours of legal advice, which option will be the cheapest? (A) L 1 (B) L 2 (C) L 3 (D) L 4 6. A hiker can walk 2 miles in 45 minutes. What is his average speed in miles per hour? (A) 5/4 (B) 8/3 (C) 7/3 (D) 9/4 2

3 7. A new $25,000 car depreciates in value by $5000 per year. Construct a linear function for the value of the car after t years. (A) t (B) t (C) 5000t (D) 5000t Write the linear equation for the above graph. (A) y = 4 + 3x (B) y = 3x 4 (C) y = 4 x (D) y = 2 + x 9. Which of these two graphs have a steeper slope [Warning: trick question]. (A) Graph A. (B) Graph B. 3

4 10. Match the graph to the appropriate equation. 11. A department store is offering a coupon for 20% off for any purchase over $100. How much would you actually spend if the original purchase price was $101.00? 12. If you travel to China, the exchange rate at the Beijing airport is 1 yuan for American dollars and at the hotel is 1 yuan for American dollars. Which exchange rate should you use? (A) 1 yuan for American dollars. (B) 1 yuan for American dollars. 13. Using the most favorable rate from previous question to construct a function Y to convert dollars d into yuan, Y (d). As your answer, enter Y (50) [Round to nearest cent]. 14. What is the equation of line A? (A) y = 2.5x + 5 (B) y = 5x + 10 (C) y = 2.5x + 5 (D) y = 0.25x + 5 4

5 15. What is the equation of line B? (A) y = 3x (B) y = x + 3 (C) y = (1/3)x (D) y = x True or False: Line A is orthogonal (perpendicular) to line B. (True) (False) 17. Which of these lines are parallel to each other? (A) y = 1 3 x + 2 (B) y = 3x 4 (C) y 3x = 7 (D) y = 3x Which lines are parallel to each other? (A) y = 1 3 x + 2 (B) 2y + 4x = 12 (C) y = 10 2x (D) y = 3x Which lines are perpendicular to each other? (A) y = 1 3 x + 2 (B) y = 3x 4 (C) y = 2x + 10 (D) y = 3x 2 (E) 2y + 4x = 12 (F) y 3x = Determine whether ( 2,3) is a solution for the following system of equations: 3x + y = 3 x + 2y = 4 (True) (False) 21. Determine whether (3, 2) is a solution for the following system of equations: 3x + y = 3 x + 2y = 4 (True) (False) 5

6 [Note: For the previous two problems you will gain more experience by solving the equations directly for the variables rather than simply checking the point, even though it may be a little harder] 22. Which equation represents the equation of a line with slope 3 that goes through the point (0,17)? (A) y = 3x + 17 (B) 1 3 x 17 (C) 3y = x + 17 (D) y = 17x 23. Which of the graphs is the correct set of graphs for the following system of equations: y = 2x + 2 y = 3x + 12 (A) (B) (C) 24. Consider the following job offers. At Acme Corporation, you are offered a starting salary of $20,000 per year, with raises of $2500 annually. At Boca Corporation, you are offered $25,000 to start and raises of $2000 annually. Within what year of employment would the two corporations pay you the same salary [Round Down to nearest year]? 25. How many solutions to the following systems of equations: y = 1 2x y = x 6

7 26. y = 2200x 700 y = 1300x t = 3 + 4w 12w + 3t + 9 = x = 5y 4y 3x = Two investments in high-technology companies total $1000. If one investment earns 10% annual interest and the other earns 20%. If the total interest earned for the year is $140, find the amount that was invested in the account earning 10% interest. 7