6. Carolyn has 9 quarters, 4 dimes, 7 nickels, and 2 pennies. Write and evaluate the expression to determine how much money she has. 7. Mr. Martinez orders 250 key chains printed with his athletic team’s logo and 500 pencils printed with their Web address. If k represents the cost of each key chain and p represents the cost of each pencil, write an expression that represents the cost of the order. 8. Jocelyn babysat for 25 hours and worked at the grocery store for 15 hours in a week. Let b be the amount she earns per hour babysitting and g be the amount she earns per hour at the grocery store. Write an algebraic expression that represents the total amount she earned. If Jocelyn earns $10 an hour babysitting and $8.25 an hour working at the grocery store, find the total amount she earned that week. 9. A certain smartphone family plan costs $55 per month plus additional usage costs. It costs $2 per each extra megabyte used. Let x represent the number of megabytes of data used above the plan. Interpret the following expressions: 2x 2x + 55 Algebra 1 Section 1.5 Notes: Equations Warm-up Use the distributive property to rewrite the expression without parentheses. 1.) 8(x + 5) 2.) 4(y – 7) 3.) (x – 4)(2) 4.) –6(r – 1) 5.) (m – 7)( –3) 6.) –12(n + 3) 7.) (x)(x + 3) 8.) (–a)(a + 3) 9.) (2x + 1)(5x) Open Sentence: a mathematical statement with one or more . Equation: a mathematical sentence that contains an . Solving an open sentence: Finding a for the that results in a true sentence or an that results in a true statement when substitute into the equation.
Example 4: Solve Example 5: a) Dalila pays $16 per month for a gym membership. In addition, she pays $2 per Pilates class. Write and solve an equation to find the total amount Dalila spent this month if she took 12 Pilates classes. b) Amelia drives an average of 65 miles per hour. Write and solve an equation to find the time it will take her to drive 36 miles. Algebra 1 Section 1.5 Worksheet Find the solution of each equation if the replacement sets are a = and b = {3, 3.5, 4, 4.5, 5}. 1. a + = 1 2. 4b – 8 = 6 3. 6a + 18 = 27 4. 7b – 8 = 16.5 5. 120 – 28a = 78 6. + 9 = 16 Solve each equation. 7. x = 18.3 – 4.8 8. w = 20.2 – 8.95 9. = d 10. = k 11. y = 12. = p
22. TRAVEL The cost for cars entering President George Bush Turnpike at Beltline road is given by the relation x = 0.75, where x is the dollar amount for entrance to the toll road and y is the number of passengers. Determine if this relation is a function. Explain. 23. CONSUMER CHOICES Aisha just received a $40 paycheck from her new job. She spends some of it buying music online and saves the rest in a bank account. Her savings is given by f(x) = 40 – 1.25x, where x is the number of songs she downloads at $1.25 per song. a. Graph the function. b. Find f(3), f(18), and f(36). What do these values represent? c. How many songs can Aisha buy if she wants to save $30? 1.7 Textbook Homework Algebra 1 Section 1.8 Notes: Interpreting Graphs of Functions Warm-up Determine whether each relation is a function. 1. 2. 3. 4. If , find . 5. The graph of is shown. What is the approximate solution if ? y-intercept: the of a point where a graph crosses the y – axis. x-intercept: the of a point where a graph crosses the x – axis. Example 1: The graph shows the cost at a community college y as a function of the number of credit hours taken x. a) Identify the function as linear or nonlinear. b) Estimate and interpret the intercepts of the function.
15. Is the function linear or nonlinear (circle one)? 16. Estimate the intercepts. Explain what they represent. 17. Does the function have symmetry? 18. What is the x-coordinate of any relative extrema? What does it represent? 19. Estimate and interpret where the function is positive, negative, increasing, and decreasing. 20. Interpret the end behavior of the function CHAPTER 2
b. If Pietra walked 9 miles during the week, how many miles did Deanna walk? c. If Pietra walked 11 miles during the week, how many miles did the two girls walk together? 16. HOUSES The area of the Hartstein’s kitchen is 182 square feet. This is 20% of the area of the first floor of their house. Let F represent the area of the first floor. Write an equation to represent the situation. 17. FAMILY Katie is twice as old as her sister Mara. The sum of their ages is 24. Write a one-variable equation to represent the situation. 18. GEOMETRY The formula F + V = E + 2 shows the relationship between the number of faces F, edges E, and vertices V of a polyhedron, such as a pyramid. Write the formula in words. 19. WIRELESS PHONE Spinfrog wireless phone company bills on a monthly basis. Each bill includes a $29.95 service fee for 1000 minutes plus a $2.95 federal communication tax. Additionally, there is a charge of $0.05 for each minute used over 1000. Let m represent the number of minutes over 1000 used during the month. Write an equation to describe the cost p of the wireless phone service per month. 20. TEMPERATURE The table below shows the temperature in Fahrenheit for some corresponding temperatures in Celsius. Celsius Fahrenheit –20° –4° –10° 14° 0° 32° 10° 50° 20° 68° 30° 86° a. Write a formula for converting Celsius temperatures to Fahrenheit temperatures. b. Find the Fahrenheit equivalents for 25ºC and 35ºC. 2.1 Textbook Homework
Example 5: Standardized test practice. a) Find the value of h so that the figures have the same area. A. 1 B. 3 C. 4 D. 5 b) Find the value of x so that the figures have the same perimeter. F. 1.5 G. 2 H. 3.2 J. 4 Algebra 1 Section 2.4 Worksheet Solve each equation. Check your solution. 1. 5x – 3 = 13 – 3x 2. –4r – 11 = 4r + 21 3. 1 – m = 6 – 6m 4. 14 + 5n = –4n + 17 5. k – 3 = 2 – k 6. (6 – y) = y 7. 3(–2 – 3x) = –9x – 4 8. 4(4 – w) = 3(2w + 2) 9. 9(4b – 1) = 2(9b + 3) 10. 3(6 + 5y) = 2(–5 + 4y) 11. –5x – 10 = 2 – (x + 4) 12. 6 + 2(3j – 2) = 4(1 + j) 13. t – t = 3 + t 14. 1.4f + 1.1 = 8.3 – f 15. x – = x + 16. 2 – k = k + 9 17. (3g – 2) = 18. (n + 1) = (3n – 5) 19. (5 – 2h) = 20. (2m – 16) = (2m + 4) 21. 3(d – 8) – 5 = 9(d + 2) + 1 22. 2(a – 8) + 7 = 5(a + 2) – 3a – 19