Warm-up 10/14/2010

1. Warm-up 10/14/2010 Simplify. • 1.) 5(7x – 12) • 2.) (–3 – 4p)(3) • 3.) 4 - 2(–6y + 2)

2. Algebra 1 Chapter 3 Sections 1-5 PE: A1.1.B Solve Problems that can be represented by linear functions, equations, and inequalities.

3. Vocabulary • Equivalent: has the same value, “is equal” • Inverse Operations: operations that undo each other. • Linear Equation: An equation where the variable (or variables) are raised to the first power, do not occur in the denominator, inside a square root, or inside absolute value symbols. • Example: 3x-2=27 is a linear equation

4. Linear or Not? Are the following Linear Equations? Why? x + 5 = 9 yes x2 + 5 = 9 no -4 + n = 2n - 6 yes |x + 3| = 7 no

5. ( ) distribute • • Can you combine like terms on the LHS? ____ (do it!) • • Can you combine like terms on the RHS? ____ (do it!) • • If variables are on both sides, then make one go away. • • What side of the new equation is the variable on? ____ • • Is there a number being added or subtracted to THAT side? ___ (get rid of it! Do the opposite.) • • Is there a number “next to” the variable? _____ (get rid of it! DIVIDE.)

6. Examples • Solve x - 5 = -13 for x.

7. Examples • Solve -8 = n - (-4)

8. Entry Task 10/20/2011 Simplify. • 1.) -5(6x – 11) • 2.) (3 – 7p)(-2) • 3.) 4 - 2(–7y - 2)

10. Exit Task • Solve x – 7 = 13 for x. • Solve 3 – (-x) = 12 for x.

11. Entry Task 10/24/2011 • Solve using multiplication and division • 1.) 2.) • 3.) 4x = 12 4.)

12. Exit Task • Classify the following numbers as Real, Irrational, Rational, Integers, whole numbers , or natural • 1.) 4 2.) ¾ 3.) -2

13. Chapter 2 test Get out your math notebook Get out your knowledge folder Make sure there is at lease 1 foot between you and your neighbor. Make sure you have a pencil, calculator and eraser to take the quiz.

14. Entry Task 10/26/2011 Simplify. • 1.) Solve 2.) 3.)

15. Exit Task • The usual rate for taking and projecting professional movies is 24 frames per second. Find the total number of frames in a movie that is 90 minutes long.

16. Entry Task 10/27/2011 • Simplify: • 1.) 2.) • 3.) 4.) • 5.)

17. Entry Task 10/28/2011 • Simplify the following: • 1.) -6(x+5) 2.) (r-3)(-4) • 3.) m(m-1) 4.) (-2a)(a+3) • 5.) Write an expression for the perimeter of the trapezoid shown below and simplify it

18. Homework Questions?

19. Homework • Pg. 148 #1-9, 11-35odd, due 10/21 • Extra Credit Pg. 148 # 10-36 even, 57-61

20. Entry Task 11/01/2011 • Simplify: • 1.) 2.) • Determine whether the given number is a solution to the equation or inequality. 3.) 8+r2 = 16; 4 4.) 2(5y-4)=14; 7.5 5.)

21. Entry Task 11/02/2011 • Evaluate the following for x=2 1.) 2x+7 2.) 5x2 + 2 3.) 3[(x-2)+x] 4.) 3(x-8)x • Determine whether the given number is a solution to the equation or inequality. 5.) 8+r2 = 16; 2 6.) 2(5y-4)=14; 2.2

22. Entry Task 11/03/2011 1.) 2.) 3.) 4.) 5.) 6.)

23. Chapter 2 test retake (again) Get out your math notebook Get out your knowledge folder Make sure there is at lease 1 foot between you and your neighbor. Make sure you have a pencil, calculator and eraser to take the quiz.

24. Number of Solutions Equations can have zero, one or many solutions. Equations with one solution can be worked out to equal one number.

25. NO Solution • If the variables cancel out and the numbers left are not equal there are no solutions

26. Many solutions • If the variables cancel out and the two sides of the equal sign are equal then there are many solutions, in fact x would be all real numbers.

27. Homework Questions?

28. Entry Task 11/14/2011 • Evaluate the following for x=5 1.) 2x+7 2.) 5x2 + 2 3.) 3[(x-2)+x] 4.) 3(x-8)x • Determine whether the given number is a solution to the equation or inequality. 5.) 8+r2 = 16; 5 6.) 2(5y-4)<14; 2 Solve. 7.) 8.)

29. Section 3.7 • Objective: Solve a formula for one of its variables.

30. Solving Formulas • The formula for the area of a rectangle is A=lw • Find a formula for l in terms of A and w.

31. Rewriting an Equation in Function Form • Rewrite the equation so that x is a function of y

32. Entry Task 11/15/2011 • Simplify: • 1.) 2.) • 3.) 4.) • Solve: • 5.) • 6.)

33. Entry Task 11/16/2011 1.) 2.) 3.) 4.) 5.) 6.)

34. Entry Task 11/28/2012 • Solve using multiplication and division • 1.) 2.) • 3.) 4x = 12 4.) • 5.) Decide if the following are functions, state the domain and range if they are. Input Output 2 4 5 InputOutput 1 2 3 4 5 7 9 1 2 3 4

35. Entry Task 11/18/2011 • Simplify: • 1.) 2.) • 3.) 4.) • Solve: • 5.) • 6.)

36. Identifying functions A relation is any set of ordered pairs. A Function is a relation where for every input there is exactly one output. f(x) is read “f of x” or “the value of f at x”. It Does not mean f times x f(x) is called function notation. Write y = 3x + 2 in function notation

37. Function notation f(x) is read “f of x” or “the value of f at x”. It Does not mean f times x f(x) is called function notation. Write y = 3x + 2 in function notation

38. Examples a.) b.)

39. Examples a.) b.)

40. Examples a.) b.)

41. Entry Task 10/22/2010 • Solve: • 1.) 2.)

42. Homework Questions?

43. Agenda for today • Quiz • When finished with Quiz quietly work on: Pg. 157#1-11, 19-250dd Extra Credit pg. 157 #12-40 even, 47=49

44. Entry Task 10/25/2010 • Solve: • 1.) 2.)

45. Section 3.5 • Objective: Solve problems using linear equations

46. Example GAZELLE AND CHEETAH A gazelle can run 73 feet per second for several minutes. A cheetah can run faster (88 feet per second) but can only sustain its top speed for about 20 seconds before it is worn out. How far away from the cheetah does the gazelle need to stay for it to be safe?

47. Example A pate of your school yearbook is 8 ½ inches by 11 inches. The left margin is ¾ inch and the space to the right of the pictures is 2 7/8 inches. The space between pictures is 3/16 inch. How wide can each picture be to fit three across the width of the page?

48. Homework • Pg. 163 #1-5 • Extra Credit pg. 163 #18-21, 27

49. Entry Task 10/27/2010 • Solve: • 1.) 2.)

50. Section 3.5 • Objective: Solve problems using linear equations