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Name: ____________________________________ 1.3.4 Rearranging Formulas – Day 1 (p.109) Date __________ Algebra 1 Essential Question: How can we alter a formula to make algebra easier? Introduction: * Formulas that relate two or more variable symbols such as 𝐴 = 𝑙𝑤, 𝐷 = 𝑟𝑡, and 𝑎2 + 𝑏 2 = 𝑐 2 arise in different applications of mathematics, science, and other areas of study. These formulas have meaning based on a situation. * However, even without an applied setting, formulas can stand on their own as a relationship between variables. * You can use the equation-solving techniques from earlier lessons to rearrange formulas and solve for a specific variable symbol. Exercise 1: Exercise 2: Compare your work in parts (a) through (c) above. Did you have to do anything differently to solve for x in part (c)? Exercise 3: Solve the equation 𝑎𝑥 − 𝑏 = 𝑐 for a. The variable symbols x, b, and c represent numbers. Key points: *Variables are placeholders for numbers and as such have ________________________. *When solving an equation with several variables, you _______________________________ _______________________________________________________________________. This type of equation is a LITERAL EQUATION (an equation with two or more variables). Formulas are types of literal equations. Example 1: Rearranging Familiar Formulas The area A of a rectangle is 25 in2. The formula for the area is 𝐴 = 𝑙𝑤. A = 25 in2 l a) If the width is 10 inches, what is the length, l ? w b) If the width is 15 inches, what is the length, l ? c) Rearrange the area formula to solve for l. d) Verify that the area formula, solved for l will give the same results for l as having solved for l in the original area formula. e) Now, solve for the length if A = 10 and w = 8 3 Exercise 4: Solve each problem two ways. First, substitute the given values and solve for the given variable. Then, solve for the given variable and substitute the given values. a) The perimeter formula for a rectangle is p = 2(l + w) where p represents the perimeter, l represents the length, and w represents the width. Calculate l when p = 70 and w = 15. 1 2 b) The area formula for a triangle is 𝐴 = 𝑏ℎ, where A represents the area, b represents the length of the base, and h represents the height. Calculate b when A = 100 and h = 20. Exercise 5: Rearrange each formula to solve for the specified variable. Assume no variable is equal to 0. a. Given 𝐴 = 𝑃(1 + 𝑟𝑡) i. Solve for P ii. Solve for t 1 2 b. Given 𝐾 = 𝑚𝑣 2 i. Solve for m ii. Solve for v