Transcript Expressions
Warm Up Ella purchased 2 DVDs and 3 CDs from Tyler’s Electronics at the prices listed below. After taxes, her total cost increased by $5.60. Item Cost ($) CD c DVD d 1. How can you write the cost of 2 DVDs as an algebraic expression? 2. How can you write the cost of 2 DVDs and 3 CDs as an algebraic expression? 3. How can you write the cost of 2 DVDs and 3 CDs, increased by $5.60 for taxes, as an algebraic expression? EXPRESSIONS Vocabulary • Algebraic Expression: a mathematical statement that includes numbers, operations, and variables to represent a number or quantity • Variables: a letter used to represent a value or unknown quantity that can change or vary • Term: a number, a variable, or the product of a number and variable(s) • Factors: one of two or more numbers or expressions that when multiplied produce a given product • Coefficient: the number multiplied by a variable in an algebraic expression • Constant: a quantity that does not change Expression Terms Factors Coefficient Constants 𝟒𝒙𝟐 + 𝟑𝒙 + 𝟕 • Like Terms: terms that contain the same variables raised to the same power 5x + 3x – 9 What are the like terms? Example 1: Identify each term, coefficient, constant, and factor 2(3 + x) + x(1 – 4x) + 5 Terms: Coefficients: Constants: Factors: Example 2: A smartphone is on sale for 25% off its list price. The sale price of the smartphone is $149.25. What expression can be used to represent the list price of the smartphone? Identify each term, coefficient, constant, and factor of the expression described. Terms: Coefficients: Constants: Factors: Example 3: Helen purchased 3 books from an online bookstore and received a 20% discount. The shipping cost was $10 and was not discounted. Write an expression that can be used to represent the total amount Helen paid for 3 books plus the shipping cost. Identify each term, coefficient, constant, and factor of the expression described. Terms: Coefficients: Constants: Factors: Try on your own: Tara and 2 friends had dinner at a Spanish tapas restaurant that charged $6 per tapa, or appetizer. The three of them shared several tapas. The total bill included taxes of $4.32. What are the terms, factors, and coefficients of the algebraic expression that represents the number of tapas ordered, including taxes? Warm Up At the beginning of the school year, Javier deposited $750 in account that pays 3% of his initial deposit each year. He left the money in the bank for 5 years. 1. How much interest did Javier earn in 5 years? 2. After 5 years, what is the total amount of money that Javier has? Example 1: A new car loses an average value of $1,800 per year for each of the first six years of ownership. Which Nia bought her new car, she paid $25,000. The expression 25,000 – 1,800y represents the current value of the car, where y represents the number of years since Nia bought it. What effect, if any, does the change in number of years since Nia bought the car have on the original price of the car? Example 2: To calculate the perimeter of an isosceles triangle, the expression 2s + b is used, where s represents the length of the two congruent sides and b represents the length of the base. What effect, if any, does increasing the length of the congruent sides have on the expression? • Base: the factor being multiplied together in an exponential expression • Exponent: the number of times a factor is being multiplied together in an exponential expression Example 3: Money deposited in a bank account earns interest on the initial amount deposited as well as any interest earned as time passes. The compound interest can be described by the expression 𝑃(1 + 𝑟)𝑛 where P represents the initial amount deposited, r represents the interest rate, and n represents the number of months that pass. How does a change in each variable affect that value of the expression? Example 4: Austin plans to open a savings account. The amount of money in a savings account can be found using the equation 𝑠 = 𝑝 ∙ (1 + 𝑟)𝑡 , where p is the principal, r is the rate of interest, and t is the amount of time. Austin is considering two savings accounts. He will deposit $1000 as the principal into either account. In Account A, the interest rate will be 0.015 per year for 5 years. In Account B, the interest rate will be 0.02 per year for 3 years. 1. What is the total amount in Account A? 2. What is the total amount in Account B? 3. Which account has more money at the end of the term? 4. If he could, would it be wise for Austin to leave his money in the account that has less savings for an addition year?