Math 1 Chapter 3 notes.notebook. October 22, Examples

Transcription

1 Chapter 3 SOLVING LINEAR EQUATIONS!! Lesson 3 1 Solve one step equations Key Vocab: Inverse operations: are two operations that undo each other. Addition and subtraction Multiplication and division equivalent equations: Equations that have the same solution reciprocal: examples: Examples Example 4: Example 5 Example 6: In the 2004 Olympics, Shawn Crawford won the 200 meter dash. His winning time was seconds. Find his average speed to the nearest meter per second. USE YOUR 4 STEPS Assign: pg odd 1

2 Lesson 3-2 Solve two-step equations Key vocab: Like terms: terms that have the exact same variable parts input: DOMAIN, INDEPENDENT, X Output: RANGE, DEPENDENT, Y To solve an equation you are getting the variable by itself. You do the opposite of what is happening to x ORDERS OF OPERATION BACKWARDS!! Example 1: example 2: You have to add like terms first before you can solve Example 3: lets go back to input and output write an equation then solve The output of a function is 3 less than 5 times the input. Find the input when the output is 17 Example 4: As a scuba diver descends into deeper water, the pressure of the water on the diver's body steadily increases. the pressure at the surface of the water is 2117 pounds per square foot. The pressure increases at a rate of 64 pounds per square foot for each foot the diver descends. Find the dept at which a diver experiences a pressure of 8517 pounds per square foot. USE YOUR FOUR STEPS 2

3 Lesson 3-3 Solve Multi-step equations Getting the variable by itself... UNDO what is happening to it Key Vocab: Like terms: terms that have the exact same variable parts Distributive property: reciprocal: two numbers whose product is 1 Example 1 and 2 SOLVE AND CHECK: CRT test PREP!!! * ******** Which equation represents Step 2 in the solution process? Step 1 Step 2 Step 3 Step 4 A. C. B. D. Example 4 Solve and Check Example 5: A flock of cranes migrates from Canada to Texas. The cranes take 14 days (336 hours) to travel 2500 miles. The cranes fly at an average speed of 25 miles per hour. How many hours of the migration are the cranes not flying? 4 STEPS Assign: pg EOO (EVERY OTHER ODD) 1, 5, 9, 13 ect #38 3

4 Lesson 3 4 Solve equations with variables on both sides Key vocab: identity: Example 1 and 2: Example 3: A car dealership sold 78 new cars and 67 used cars this year. The number of new cares sold by the dealership has been increasing by 6 cars each year. the number of used cars sold by the dealership has been decreasing by 4 cars each year. If these trends continue, in how many years will the number of new cars sold be twice the number of used cars? 4 STEPS!! Example 4 4

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7 Math 1 Chapter 3 notes.notebook October 22, 2012 Lesson 3 5 Write Ratios and Proportions Key Vocab Ratio Proportion simplest form RATIO A ratio uses division to divide two quantities Each Ratio is read "the ratio of a to b" Example 1: Capital Volleyball has 8 home matches and 10 away matches. Find the ratio of home matches to away matches Find the ratio of home matches to all matches Proportion: Is an equation that states 2 ratios are equal Example 2: Setting up a proportion: EXAMPLE A recipe for tomato salsa calls for 30 tomatoes to make 12 pints of salsa. How many tomatoes are needed to make 4 pints of salsa? example 3: SET UP A PROPORTION The elevator that takes passengers from the lobby of the John Hancock Center in Chicago to the observation level travels 150 feet in 5 seconds. The observation level is located on the 94th floor, at 1029 feet above the ground. Find the time it takes the elevator to travel from the lobby to the observation level. MAKE SURE YOU SHOW YOUR 4 STEPS 1. Write down the information and define your varibable 2. Write your proportion 3. solve 4. Write out answer and make sure it makes sense 7

8 Lesson 3 6 Solving proportions using cross products: Key Vocab: Cross Products: Scale drawing: Scale Model: Scale: Cross Multiply (products) Property: Example 1 and 2 Example 3: Each day, the seals at an aquarium are each fed 8 pounds of food for every 100 pounds of their body weight. A seal at the aquarium weighs 280 pounds. How much food should the seals be fed per day? 4 steps 1 3/8 in example 4: use the metric ruler and the map of Ohio to estimate the distance between Cleveland and Cincinnati 3.6 cm 8

9 EXTENSION pg. 174: Congruent figures: If they have the same shape and size Similar figures: If the have the same shape but not necessarily the same size. Corresponding parts: The sides or angles that have the same relative position within 2 figures Example 1 Example 2 Percent of Change on page 182 The percent of Change, p% is the ratio of the amount of increase or decrease to the original amount Example 1 identify the percent of change as an increase or a decrease. THEN FIND the percent of change Example 2 FINDING A NEW AMOUNT if you know the original amount and the percent of change you can find the new amount Find the sale price of the pair of jeans described in the table pg pg

10 Lesson 3 7 Solving percent problems Percent: PER 100 Proportion: What ----> x is > = of > times (mulitiply) % > per 100 move decimal 2 places Example 1: What percent of 20 is 15? What number is 30% of 90 What percent of 25 is 17? Example 2: What percent of 136 is 51? What number is 15% of 88? What number is 140% of 50 What percent of 56 is 49? What percent of 55 is 11? Example 4: 20 is 12.5% of what number? 50 is 125% of what number 65 is 62.5% of what number Example 5: 10

11 Lesson 3 8 Rewrite Equations and Formulas Key vocab: Literal equation: Formula: Remember solving an equation is simply getting the variable by itself!!! it is the same thing here DON'T panic Example 1 and 2 a. a. Can you use part a to help you solve part b b. b. REWRITING AN EQUATION: in terms of another equation, all you have to do is get that variable by itself!! Example 2 and 3 This formula is solved for A. Now I want you to solve it for h in terms of A and b ALL YOU have to do is get h by itself. Undo what is happening to it. Now substitute 64.4 for A and 14 for b then find the height. Solve for y, so that y is a function of x... Simply get y by itself Example 4 11

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13 Attachments Online book chapter 3