Using Substitution to Evaluate Algebraic Expressions and Formulas Section 1.8 Using Substitution to Evaluate Algebraic Expressions and Formulas

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.

Example Evaluate 3x – 2 for x = 8. 3x – 2 = 3(8) – 2 = –24 – 2 = –26

Example Evaluate for x = 3. a. b.

Example Evaluate 5x2 – 3x + 4y for x = 2 and y = 6. 5x2 – 3x + 4y = 5(2)2 – 3(2) + 4(6) = 5(4) – 3(2) + 4(6) = 20 – 6 – 24 = –10

Geometry Review A formula can be evaluated by substituting values for the variables. The perimeter (P) is the distance around a figure. The area (A) is the measure of the amount of surface in a region. A A

Common Geometric Formulas Parallelogram A = ab P = 2b + 2c Rectangle A = lw P = 2l + 2w Square A = s2 P = 4s a c b w l s

Common Geometric Formulas Triangle A = ab P = sum of all three sides Trapezoid A = a(b1 + b2) P = sum of all four sides Circle A = πr2 (π = 3.14) C = πd a b d a b2 e b1 d =2r r r is the radius d is the diameter

Example Find the perimeter of the parallelogram. P = 2l + 2w = 2(11) + 2(7) = 22 + 14 = 36 11 m 7 m The perimeter of the parallelogram is 36 m.

Example Find the area of the trapezoid. 8 mm 5.5 mm 6 mm The area of the trapezoid is 38.5 mm2.

Example Find the area of the triangle. The area of the triangle is 737.84 in2.

Example Find the circumference and area of a circle whose radius is 15 feet. The diameter is twice the radius. 15 The circumference is approximately 94.2 ft and the area is approximately 706.5 ft2.