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Estimating Algebra 2 Enrollment at LHS and Understanding Linear Equations

This content focuses on estimating the number of students enrolled in Algebra 2 at LHS based on data from the last seven years, with a particular emphasis on a misplaced year. Additionally, it introduces the concepts of solving linear equations, properties of equality, and practical applications such as converting temperatures and solving real-world problems. Examples, including car rental calculations and temperature conversions, provide a clear understanding of how to apply these mathematical concepts effectively.

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Estimating Algebra 2 Enrollment at LHS and Understanding Linear Equations

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  1. 7 minutes Warm-Up The table below shows the number of juniors enrolled in Algebra 2 at LHS in six of the last 7 years. The number for the third year has been misplaced. Estimate the number of students enrolled in Algebra 2 in the third year.

  2. y y y x x x Correlation and Prediction no reliable correlation perfect positive correlation perfect negative correlation r = -1 r = 0 r = 1

  3. 1.6 Intro to Solving Equations Objectives: Write and solve a linear equation in one variable Solve a literal equation for a specified variable

  4. Division If a = b, then , where c  0. a b = c c Properties of Equality Reflexive a = a Symmetric If a = b, then b = a. Transitive If a = b and b = c, then a = c. Addition If a = b, then a + c = b + c. Subtraction If a = b, then a – c = b – c. Multiplication If a = b, then ac = bc.

  5. Example 1 The relationship between the Celsius temperature, C, and the Fahrenheit temperature, F, is given by . Find the Celsius temperature that is equivalent to 1220F. 500C

  6. Example 2 Solve. 3x – 8 = 5x - 20 3x – 8 = 5x - 20 -3x -3x -8 = 2x - 20 + 20 + 20 12 = 2x 2 2 6 = x CHECK: 3(6) – 8 = 5(6) - 20 18 – 8 = 30 - 20 10 = 10

  7. Example 3 Selene rented a car for one day. The rate was $30 per day plus $0.20 per mile. She paid a total of $84. How many miles did she drive? x = number of miles that Selene drove 0.2x + 30 = 84 0.2x = 54 x = 270

  8. Example 4 Solve 5.02x – 3.02 = -1.76x + 8.75 by graphing. 1) Rewrite as a pair of equations y = 5.02x – 3.02 y = -1.76x + 8.75 2) Graph the two equations on the same screen 3) Find the point of intersection

  9. A Solve P = for n. 1+ ni A – P Pi n = Divide by Pi. Example 5 P(1 + ni) = A Multiply by (1+ ni). P + Pni = A distributive property Pni = A – P Subtract P.

  10. Homework p.40 #22 p.49 #13,23,31,35,37,41,43,47,51,53,59,69

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