1. Copyright © 2013, 2009, 2005 Pearson Education, Inc. Section 1.4 Variables, Equations, and Formulas

2. Copyright © 2013, 2009, 2005 Pearson Education, Inc. Objectives Basic Concepts Modeling Data Square Roots and Cube Roots

3. Copyright © 2013, 2009, 2005 Pearson Education, Inc. Basic Concepts A variable is a symbol, such as x, y, or t, used to represent any unknown number or quantity. An algebraic expression can consist of numbers, variables, arithmetic symbols (+,,, ), exponents, and grouping symbols, such as parentheses, brackets, and square roots. Examples:

4. Copyright © 2013, 2009, 2005 Pearson Education, Inc. Basic Concepts An equation is a statement that two algebraic expressions are equal. Examples: A formula is an equation that can calculate one quantity by using a known value of another quantity.

5. Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example If a car travels at a constant speed of 65 miles per hour, write a formula that calculates the distance d that the car travels in t hours. Evaluate your formula when t = 2.5 and interpret the result. Solution The car will travel a distance of 65 miles in one hour. Evaluating for t = 2.5 After 2.5 hours the car has traveled 162.5 miles.

6. Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example Write a formula that does the following. a. Finds area of a circle with radius r. b. Calculates the pay P for working H hours at $12 per hour c. Converts Q quarts to G gallons Solution a. The area of a circle is A = r 2, where = 3.14. b. P = 12H c. There are 4 quarts in a gallon, so G = 4Q.

7. Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example Evaluate each formula for the given value(s) of the variable(s). a. A = r 2, r = 5 b. P = 2L + 2W, L = 12 and W = 6 Solution a.b.

8. Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example The data in the table can be modeled by the formula y = ax. Find a. xy 14 28 312 416 520 Solution Each value of y is 4 times the corresponding value of x, so a = 4.

9. Copyright © 2013, 2009, 2005 Pearson Education, Inc. Square Roots The number b is a square root of a number a if b 2 = a. For example, one square root of 16 is 4 because 4 2 = 16. The other square root of 16 is 4 because ( 4) 2 = 16.

10. Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example Evaluate each expression. a.b. c.

11. Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example Find the length of a side s for each geometric shape. a. A square with area 144 square feet b. A cube with volume 512 cubic inches Solution a. Squareb. Cube