AT100 - Introductory Algebra. Chapter 2 Section 5: Formulas. interest = principal rate time OR i= profit = revenue - cost OR p = r c

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1 Chapter Section 5: Formulas In this section, we will Use formulas to solve word problems Solve a formula for a given variable.5 Formulas We will use the followg formulas from busess: terest = prcipal rate time OR i= prt profit = revenue - cost OR p = r c simple terest formula Don t forget to change your percent to a decimal before usg it a formula! retail price = cost + markup OR r = c+ m We will use the followg formulas from science: distance = rate time OR d = rt 5( F ) C = 9 Where C and F are the temperature degrees Celsius and Fahrenheit respectively. Example: Fd the markup on a CD player whose wholesale cost is $19 and whose retail price is $95. Example: After expenses of $55.15 were paid, a Rotary Club donated $ proceeds from a pancake breakfast to a local health clic. How much did the breakfast gross? AT100 - Introductory Algebra

45% annually, a depositor withdrew the $,48 terest earned. How much money was left the account?

2 Example: Cryobiologists freeze livg matter to preserve it for future use. o They can work with temperatures as low as 70 C. Change this to degrees Fahrenheit. Example: Three years after openg an account that paid 6.45% annually, a depositor withdrew the $,48 terest earned. How much money was left the account? Example: Rose Parade floats travel down the 5.5 mile-long parade route at a rate of.5 miles per hour. How long will it take a float to complete the parade if there are no delays?

3 Rectangle or Perimeter = l+ w Rectangular Box Volume = l w h Area = l w Triangle Parallelogram 1 Area = bh Area = bh For these formulas: The height meets the base-side at a 90-degree angle Trapezoid a+b Area = h Circle Circumference f = π d Area = π r π π 7 *To mimize roundgerrors we will use the π button on our TI

volume) should be used and which unit of measurement (,, ) would be appropriate.

4 base Pyramid Volume = hb 1 * B is the area of the base * Cone Volume = π 1 rh Sphere Volume = π r 4 Cylder Volume = π rh Example: For each of the followg scenarios, dicate which geometric concept (perimeter, circumference, area or volume) should be used and which unit of measurement (,, ) would be appropriate. The amount of storage a freezer The distance around the outside of a buildg lot The amount of land makg up the Sahara Desert How far a bike tire rolls one revolution

) Example: Fd the perimeter and area of the truss below: 6 ft 16 ft perimeter: area: Example: Fd the amount of space the hamster tube below.

5 Example: A horse trots a perfect circle around its traer at the end of a 8 foot-long rope. How far does the horse travel as it circles the traer once? (Round your answer to the nearest tenth.) Example: Fd the perimeter and area of the truss below: 6 ft 16 ft perimeter: area: Example: Fd the amount of space the hamster tube below. Round your answer to the nearest tenth. Example: Fd the exact area of the square road sign below: 1 Example: Fd the volume of a spherical-shaped pumpk that has a diameter of 9 ches. Round your answer to the nearest hundredth. AT100 - Introductory Algebra

$the variable by g the operations: Isolate Solvg Lear Equations One Variable: 1. If the equation contas fractions, multiply both sides by the magic number (LCM of the denomators) to clear fractions.$

6 the variable by g the operations: Isolate Solvg Lear Equations One Variable: 1. If the equation contas fractions, multiply both sides by the magic number (LCM of the denomators) to clear fractions. Use the Distributive Property to remove the parentheses (then combe the like-terms on each side of the equation) {. Use the Addition and Subtraction Properties to get all of the variables on one side of the equation together (and all of the numbers on the other side of the equation) 4. Use the Multiplication and Division Properties to make the undog{ coefficient of the variable equal to 1 Remember that solvg an equation means that we isolate the variable we are solvg for!.5 Solve a Formula for a Given Variable Example: Solve each formula for the given variable. d = rt for t I = prt for r.5 Solve a Formula for a Given Variable Example: Solve each formula for the given variable. P = l+ w for l K = mv m 1 for.5 Solve a Formula for a Given Variable

7 Example: Solve each formula for the given variable. 5y 5 = x for y 6y+ 1= 5 x for y We will need to have this skill for chapters and 7..5 Solve a Formula for a Given Variable Independent Practice You learn math by dog math. The best way to learn math is to practice, practice, practice. The assigned homework examples provide you with an opportunity to practice. Be sure to complete every assigned problem (or more if you need additional practice). Check your answers to the odd-numbered problems the back of the text to see whether you have correctly solved each problem; rework all problems that are correct. Read pp Homework: pp #1-51 odds, 57, 59, 65, 67, 69, 7, 75.5 Formulas AT100 - Introductory Algebra

Ex: Determine if the following are true or false. Ex: Determine whether 4 is a solution of x + 6 = 10

2.1 Solving Equations Using Properties of Equality True and False Equations Ex: Determine if the following are true or false. 1) 3 + 4 = 7 2) 3 + 4 = 8 3) x + 6 = 10 Ex: Determine whether 4 is a solution