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Warm Up Evaluate each expression. 1. –x2 for x = -5 2. 5x2 – x – 3x for x = -2 Simplify each expression. 3. -3(2x - y) 4. 4 - (x + y) Success Criteria: I can classify a variable I can graph numbers on a number line I can order real numbers I can use order of operations 1. 2. 3. 4. 5. 6. Do Now Check HW #1 Log on to pearson book Subscribe to calendar Start Calc Caching HW - Go through expression solving ppt attached to website Vocabulary • Pg 11 copy into the next section of your notebook with word, definition, and example. The diagram shows some important subsets of the real numbers. There are three different ways in which a basketball player can score points during a game. There are 1-point free throws, 2-point field goals, and 3-point field goals. An algebraic expression can represent the total points scored during a game. To translate a real-world situation into an algebraic expression, you must first determine the action being described. Then choose the operation that is indicated by the type of action and the context clues. Action Combine Combine equal groups Separate Separate into equal groups Operation Add Possible Context Clues How many total? Multiply How many altogether? Subtract How many more? How many remaining? Divide How many in each group? Example 1: Translating Words into Algebraic Expressions Write an algebraic expression to represent each situation. A. the number of apples in a basket of 12 after n more are added 12 + n Add n to 12. B. the number of days it will take to walk 100 miles if you walk M miles per day Divide 100 by M. C. Lucy’s age y years after her 18th birthday 18 + y Add y to 18. D. the number of seconds in h hours 3600h Multiply h by 3600. Shhh do this in your head! 20 ÷ 10 (2) + 3(2) ÷ 3 To evaluate an algebraic expression, substitute a number for each variable and simplify by using the order of operations. One way to remember the order of operations is by using the mnemonic PEMDAS. Order of Operations 1. 2. 3. 4. Parentheses and grouping symbols. Exponents. Multiply and Divide from left to right. Add and Subtract from left to right. Example 2A: Evaluating Algebraic Expressions Evaluate the expression for the given values of the variables. 2x – xy + 4y for x = 5 and y = 2 2(5) – (5)(2) + 4(2) Substitute 5 for x and 2 for y. 10 – 10 + 8 0+8 8 Multiply from left to right. Add and subtract from left to right. x2y – xy2 + 3y for x = 2 and y = 5. (2)2(5) – (2)(5)2 + 3(5) Substitute 2 for x and 5 for y. 4(5) – 2(25) + 3(5) 20 – 50 + 15 –15 Evaluate exponential expressions. Multiply from left to right. Add and subtract from left to right. Recall that the terms of an algebraic expression are separated by addition or subtraction symbols. Like terms have the same variables raised to the same exponents. Constant terms are like terms that always have the same value. Remember! Terms that are written without a coefficient have an understood coefficient of 1. x2 = 1x2 Example 3A: Simplifying Expressions YOU TRY! Simplify the expressions. 3x2 + 2x – 3y + 4x2 Identify like terms. 3x2 + 2x – 3y + 4x2 7x2 + 2x – 3y Combine like terms. 3x2 + 4x2 = 7x2 j(6k2 + 7k) + 9jk2 – 7jk 6jk2 + 7jk + 9jk2 – 7jk 15jk2 Distribute, and identify like terms. Combine like terms. 7jk – 7jk = 0 Check It Out! Example 4a A travel agent is selling 100 discount packages. He makes $50 for each Hawaii package and $80 for each Cancún package. Write an expression to represent the total the agent will make selling a combination of the two packages. Let h be the number of Hawaii packages. Then 100 – h is the remaining Cancun packages. 50h + 80(100 –h) = 50h + 8000 –80h Distribute 80. = 8000 – 30h Combine like terms. Check It Out! Example 4b How much will he make if he sells 28 Hawaii packages? Evaluate 8000 –30h for h = 28. 8000–30(28) = 8000–840 = 7160 He will make $7160. Assignment #2 Pg 22-24 #12 - 51 x3, 52, 53 Don’t forget syllabus Tuesday! #2 Pg 22-24 #12 - 51 x3 skip 45 (13 pts) Lesson Quiz: Part I Write an algebraic expression to represent each situation. 1. the number of cards in a 52-card deck after n cards are dealt. 52 – n 2. the number of days in W weeks 7W 3. Evaluate: rq2 + 3qr + r2 for r = 5 and q = 2. 75 4. Simplify: 5h2 + 4k + 7h – 4h2. h2 + 4k + 7h Lesson Quiz: Part II Jake has only nickels and dimes in his pocket. 5. Write and simplify an expression for the total value if Jake has 20 coins. Possible answer: $2 – ($0.05)N 6. How much does he have if he has 7 nickels? $1.65