Section 1 8 Using Substitution to Evaluate Algebraic

Section 1. 8 Using Substitution to Evaluate Algebraic Expressions and Formulas Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc.

Evaluating Algebraic Expressions The order of operations is used to evaluate variable expressions. When we replace a variable by a particular value, we say we have substituted the value for the variable. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 2

Example Evaluate 3 x – 2 for x = 8. 3 x – 2 = 3( 8) – 2 = – 24 – 2 = – 26 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 3

Example Evaluate for x = 3. a. b. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 4

Example Evaluate 5 x 2 – 3 x + 4 y for x = 2 and y = 6. 5 x 2 – 3 x + 4 y = 5(2)2 – 3(2) + 4( 6) = 5(4) – 3(2) + 4( 6) = 20 – 6 – 24 = – 10 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 5

Geometry Review A formula can be evaluated by substituting values for the variables. The perimeter (P) is the distance around a figure. A A The area (A) is the measure of the amount of surface in a region. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 6

Common Geometric Formulas Parallelogram Rectangle Square a c b w l s A = ab P = 2 b + 2 c A = lw P = 2 l + 2 w A = s 2 P = 4 s Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 7

Common Geometric Formulas a Triangle Trapezoid d b b 1 a e A = ab P = sum of all three sides A = a(b 1 + b 2) P = sum of all four sides A = πr 2 (π = 3. 14) C = πd b 2 Circle r d =2 r r is the radius d is the diameter Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 8

Example Find the perimeter of the parallelogram. 11 m 7 m P = 2 l + 2 w = 2(11) + 2(7) 7 m 11 m = 22 + 14 = 36 The perimeter of the parallelogram is 36 m. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 9

Example Find the area of the trapezoid. 6 mm 5. 5 mm 8 mm The area of the trapezoid is 38. 5 mm 2. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 10

Example Find the area of the triangle. 40. 1 in 36. 8 in The area of the triangle is 737. 84 in 2. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 11

Example Find the circumference and area of a circle whose radius is 15 feet. The diameter is 15 twice the radius. The circumference is approximately 94. 2 ft and the area is approximately 706. 5 ft 2. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 12