Monday we covered Multiplying polynomials. Remember to always combine like terms and to distribute to EVERYTHING in the parentheses.
P. 327 Numbers 2-38 even
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1. alternate interior angles
2. skew lines 3. transversal 4. point-slope form 5. rise; run 6. possible answer: DE and BC 7. AB || DE 8. AD is perpendicular to DE 9. plane ABC || plane DEF 10. L is the transversal; alternate interior angles. 11. N is the transversal; corresponding angles 12. L is the transversal; same-side interior angles 13. M is the transversal; alternate exterior angles 14. m<WYZ = 90 degrees 15. m<KLM = 100 degrees 16. m<DEF = 79 degrees 17. m<QRS = 76 degrees 18. <4 is congruent to <6 so c || d by the converse of the alternate interior angles theorem. 19. m<1 = 107 degrees; and m<5 = 107 degrees, so <1 is congruent to <5. c||d by the converse of the corresponding angles postulate. 20. m<6 = 66 degrees, m<3 = 114 degrees, and 66+114=180 degrees. So <6 and <3 are supplementary. c||d by the converse of the same side interior angles theorem. 21. m<1 = 99 degrees, and m<7 = 99 degrees, so <1 is congruent to <7. c||d by the converse of the alternate exterior angles theorem. 25. m = -1/7 26. m = 5/3 27. neither. 28. Parallel 29. Perpendicular 30. y = -4/9x + 11/3 31. y = 2/3x - 2 32. y - 0 = 2(x - 1) 33. parallel 34. intersect 35. same line. or coincide. Today in Geometry we are reviewing for our Ch 3 Test on Monday.
In Math for College Readiness we are taking our Chapter four test. Which means that next week we will be going on to chapter 5. I apologize for my absence on my website and i will be more diligent in posting notes and assignments for all classes. Thanks and have a great 3 day weekend! biconditional statement: a statement that can be written in the form "p if and only if Q". that means "if p then q" AND "if q then p". A biconditional statement is the combination of a conditional statement and its converse. p <--> q
For a biconditional to be true, both the conditional and the converse must be true. if either the conditional or the converse is false then the biconditional statement is false. A definition is a statement that describes a mathematical object and can be written as a true biconditional. Ex. conditional: IF a figure has 3 or more sides and is closed, THEN it is a polygon. converse: IF a figure is a polygon, THEN it has 3 or more sides and it is closed. both of these are true so we can form a biconditional statement. Biconditional: A figure is a polygon IF AND ONLY IF it has 3 or more sides and is a closed figure. because the conditional and converse are both true, the biconditional is also true. Today we covered Deductive Reasoning.
Deductive Reasoning- the process of using logic to draw conclusions from given facts definitions and properties. Law of detachment: If P -> Q is a true statement and P is a true statement and P is true, then Q is true. Law of Syllogisms: If P -> Q and Q -> R are true statements then P -> R is a true statement. Previously this week we covered Inductive Reasoning and Conditional Statements. Inductive reasoning- the process of reasoning that a rule or statement is true because specific cases are true. Conjecture- a statement that you believe to be true based on inductive reasoning. How to use inductive reasoning: 1. look for a pattern. 2. make a conjecture. 3. prove the conjecture or find a counterexample. counterexample- an example that shows that a conjecture is false. Conditional Statement- a statement that can be written in the form " if P then Q." P -> Q Hypothesis- the part P of a conditional statement following the word "if" Conclusion- the part Q of a conditional statement following the word "then" Truth Value- a statement is either True or False. Converse- the statement formed by exchanging the hypothesis and conclusion. Q -> P Inverse- the statement formed by negating the hypothesis and the conclusion -P -> - Q Contrapositive- the statement formed by both exchanging and negating the hypothesis and the conclusion. -Q -> -P |
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