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miller_introductory_algebra_3e_ch1_3

Section 1.1 Introduction to Algebra and the Set of Real Numbers 47 b. To calculate the maximum recommended heart rate for a 45-year-old, substitute 45 for a in the expression. 220 a 220 ( ) When substituting a number for a variable, use parentheses. 220 (45) Substitute a 45. 175 Subtract. The maximum recommended heart rate for a 45-year-old is 175 beats per minute. Computing the Area of a Rectangle The area of a rectangle is the product of the length, l, and the width, w.The area of a rectangle can be computed by evaluating the given algebraic expression for values of l and w. Area lw Compute the area of a rectangle that is 12.5 ft long and 8 ft wide. Solution: lw ( )( ) When substituting numbers for variables, use parentheses for each variable. (12.5 ft)(8 ft) Substitute l 12.5 and w 8. 100 ft2 Multiply. The area of the rectangle is 100 ft2. 2. The Set of Real Numbers Typically, the numbers represented by variables in an algebraic expression are all part of a set of real numbers. These are the numbers that we work with on a day-to-day basis. The real numbers encompass zero, all positive, and all negative numbers, including those represented by fractions and decimal numbers. The set of real numbers can be represented graphically on a horizontal number line with a point labeled as 0. Positive real numbers are graphed to the right of 0, and negative real numbers are graphed to the left of 0. Zero is neither positive nor negative. Each point on the number line corresponds to exactly one real number. For this reason, this number line is called the real number line (Figure 1-1). 1 2 3 4 5 5 4 3 2 1 0 Negative numbers Positive numbers Figure 1-1 Example 2 Skill Practice 3. The perimeter of a triangle 12 with sides 12 a, b, and c can be represented by Perimeter a b c Compute the perimeter of a triangle whose sides measure 2 cm, 6 cm, and 4 cm. Classroom Example: p. 56, Exercise 14 Answer 3. 13 cm


miller_introductory_algebra_3e_ch1_3
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