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Reviewing What We Have Learned August 30/31 Using Linear Models ALGEBRA 2 LESSON 2-4 Pages 81–84 Exercises 1. d = 62.5h + 15 3. h = 8x + 60 5. y = 0.5x + 0.75; 3.25 lb 2-4 Using Linear Models ALGEBRA 2 LESSON 2-4 7. y = 1.75x + 1.75; $8.40 9. 13. a. Linear model is reasonable; models may vary. Sample: y = 2.6x – 0.6 11. Answers may vary. Sample: y = 125x + 975 not reasonable 2-4 Using Linear Models ALGEBRA 2 LESSON 2-4 19. a. y = 29.95 b. y = 2.95x; slope = 2.95, y-intercept = 0 c. Answers may vary. Sample: Either way, you will average the same costs over the long run. 2-4 Using Linear Models ALGEBRA 2 LESSON 2-4 21. a. population b–c. d. 2 million e. Answers may vary. Sample: Strong; the points fall close to a straight line. 2-4 Absolute Value Functions and Graphs ALGEBRA 2 LESSON 2-5 Pages 88–90 Exercises 1–9. Tables may vary. Samples are given. 1. 5. 3. 2-5 Absolute Value Functions and Graphs ALGEBRA 2 LESSON 2-5 11. 7. 9. 2-5 Absolute Value Functions and Graphs ALGEBRA 2 LESSON 2-5 15. 19. 17. 13. 2-5 Absolute Value Functions and Graphs ALGEBRA 2 LESSON 2-5 21. 25. 27. 23. 2-5 Let’s Review • This will be turned in as a HW grade • NO CALCULATORS TODAY • We need to learn how to do stuff without a calculator • Once we know how, calculators can then be used to speed up our process and check for errors • No decimals or mixed numbers today • We are going to get used to putting everything as an “improper” fraction • Once you get to the very end, then you can convert it So…a few concepts to review We are going to do problems with these ideas later today. But let’s first cover them in generalities When a problem tells us to “solve” the equation, what are we trying to do? In an equation, when we do something to one side, what must we do to the opposite side? In an inequality, if we divide or multiply by a negative number, what must we do to the inequality sign? If something is written as f(x)=whatever, we know that it is ___________ Let’s Review—You will turn this in as a HW grade simplify 1. 15+3 2. 15-3 3. -15-3 4. -15+3 5. 15/3 6. -15/3 7. 15/-3 8. -15/-3 Simplify | 4 |, |–9.2|, |3 – 8|, and |-22+8| Algebraic Expressions ALGEBRA 2 LESSON 1-2 Evaluate (k – 18)2 – 4k for k = 6. (k – 18)2 – 4k = (6 – 18)2 – 4(6) Substitute 6 for k. = (–12)2 – 4(6) Subtract within parentheses. = 144 – 4(6) Simplify the power. = 144 – 24 Multiply. = 120 Subtract. 1-2 Algebraic Expressions ALGEBRA 2 LESSON 1-2 8 The expression – 100y 2 + 3y models the percent increase of Hispanic voters in a town from 1990 to 2000. In the expression, y represents the number of years since 1990. Find the approximate percent of increase of Hispanic voters by 1998. Since 1998 – 1990 = 8, y = 8 represents the year 1998. −8 −8 –100y2 + 3y = –100(8)2 + 3(8) −8 = –100(64) + 24= Substitute 8 for y 512 − 100+24 = 512 2400 -100+ 100 = 1888 =18.88 100 The number of Hispanic voters had increased by about 19%. 1-2 Solving Equations ALGEBRA 2 LESSON 1-3 Solve 4(m + 9) = –3(m – 4). 4(m + 9) = –3(m – 4) 4m + 36 Property = –3m + 12 7m + 36 7m m 24 7 Distributive = 12 Add 3m to each side. = –24 =– Subtract 36 from each side. Divide each side by 7. 1-3 Solving Equations ALGEBRA 2 LESSON 1-3 x Solve a + 8 = b for x. Find any restrictions on a and b. x a +8 a(ax ) + a(8) x + 8a x =b = ab Multiply each side by the least common denominator (LCD), a. = ab Simplify. = ab – 8a Subtract 8a from each side. The denominator cannot be zero, so a =/ 0. 1-3 Solving Equations ALGEBRA 2 LESSON 1-3 A plane takes off from an airport and flies east at a speed of 350 mi/h. Thirty-five minutes later, a second plane takes off from the same airport and flies east at a higher altitude at a speed of 400 mi/h. How long does it take the second plane to overtake the first plane? Relate: distance first plane travels = distance second plane travels. Define: Let t = the time in hours for the second plane. Then t + 35 = the time in hours for the first plane. 60 Write: 7 400t = 350 (t + 12 ) 400t = 350t + 1225 Distributive Property 6 1-3 Solving Equations ALGEBRA 2 LESSON 1-3 (continued) 50t = 1225 Solve for t. 6 1 t = 4 12 h or about 4 h 5 min Check: Is the answer reasonable? In 4 h, the second plane travels 1600 mi. In 4 2 h, the first plane travels about 1600 mi. The answer is 3 reasonable. 1-3 Solve the following inequalities: 1. −2𝑥 < 3(𝑥 − 5) 2. 7𝑥 < 7 2 + 𝑥 3. 14𝑥 > 7(4 + 2𝑥) Solve: 1. 4 − 2 𝑥 + 9 = −5 2. −2 𝑥 + 1 + 5 ≥ −3 3. 5 𝑥 + 3 > 10 Find f(3) and f(-3) for each function: 1. 𝑓 𝑥 = −𝑥 2 + 1 2. 𝑓 𝑥 = 3𝑥 2 3. 𝑓 𝑥 = 1−𝑥