1 / 20

Chapter 2 Equations and Inequalities in One Variable

Chapter 2 Equations and Inequalities in One Variable. Section 7 Problem Solving: Geometry and Uniform Motion. Section 2.7 Objectives. 1 Set Up and Solve Complementary and Supplementary Angle Problems 2 Set Up and Solve Angles of Triangle Problems 3 Use Geometry Formulas to Solve Problems

cillian-arvey
Download Presentation

Chapter 2 Equations and Inequalities in One Variable

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 2 Equations and Inequalities in One Variable Section 7 Problem Solving: Geometry and Uniform Motion

  2. Section 2.7 Objectives 1 Set Up and Solve Complementary and Supplementary Angle Problems 2 Set Up and Solve Angles of Triangle Problems 3 Use Geometry Formulas to Solve Problems 4 Set Up and Solve Uniform Motion Problems

  3. (90 – x)° x° complementary angles (180 – x)° x° supplementary angles Angles Two angles whose sum is 90° are called complementary angles. Each angle is called the complement of the other. Two angles whose sum is 180° are called supplementary angles. Each angle is called the supplement of the other.

  4. B A Solving Angle Problems • Example: • Angle A and angle B are complementary angles, and angle A is 21º more than twice angle B. Find the measure of both angles. Step 1: Identify This is complementary problem. We are looking for the measure of the two angles whose sum is 90°. Step 2: Name Let a represent the measure of angle A. Continued.

  5. Solving Angle Problems • Example continued: Step 3: Translate Angle A is 21° more than twice the measure of angle B. a = 21 + 2 ·m B a = 21 + 2 (90 – a) Step 4: Solve Solve the equation. a = 21 + 2 (90 – a) Distribute. a = 21 + 180 – 2a Combine like terms. a = 201 – 2a Continued.

  6. Solving Angle Problems • Example continued: a = 201 – 2a Add 2a to both sides. 3a = 201 Divide both sides by 3. a = 67 Step 5: Check The measure of  A is 67°. The measure of  B is 90° – a = 90° – 67° = 23°. 67° + 23° = 90°  Step 6: Answer the Question The two complementary angles measure 67° and 23°.

  7. C 84° 42° A B Solving Triangle Problems • Example: • Find the measure of Angle C. Remember that the sum of the measures of the interior angles of a triangle is 180°. Step 1: Identify This is an “angles of the triangle” problem. Step 2: Name Let c represent the measure of angle C. Continued.

  8. Solving Triangle Problems • Example continued: Step 3: Translate The three angles add up to 180°. 84 + 42 + c = 180 Step 4: Solve Solve the equation. 84 + 42 + c = 180 Combine like terms. 126 + c = 180 Subtract 126 from both sides. c = 54 Continued.

  9. C 84° 42° A B 54° Solving Triangle Problems • Example continued: Step 5: Check Is the sum of the three angles equal to 180°? 84° + 42° + 54°= 180° 180°= 180°  Step 6: Answer the Question The measure of Angle C is 54°.

  10. Solving Geometry Problems • Example: Julie is making cone-shaped candles. The mold for the candles is 4 in. in diameter and 7 in. high. How many cubic inches of wax does Julie need to buy if she wants to make 50 candles? Step 1: Identify This is a geometry volume problem. We want to find the volume of the cone-shaped candle to determine the amount of wax needed for 50 candles. Step 2: Name Let V represent the volume of one cone. Continued.

  11. Solving Geometry Problems • Example continued: Step 3: Translate We need to use the formula for the volume of a cone.   3.14; r = 2; h = 7 Step 4: Solve Solve the equation. Continued.

  12. Solving Geometry Problems • Example continued: This is the amount needed for one candle. This is the amount needed for 50 candles. 29.3 in.3 50  1465 in.3 Step 5: Check 29.3 in.3 50 = 1465 in.3  Step 6: Answer the Question Julie needs to buy approximately 1465 in.3 of wax to make 50 candles.

  13. Uniform Motion Objects that move at a constant velocity (speed) are said to be inuniform motion. Uniform Motion Formula If an object moves at an average speed r, the distance d covered in time t is given by the formula d = rt. The following table is helpful in solving motion problems.

  14. Uniform Motion Problem Example: Steve jogs at an average rate of 8 kilometers per hour. How long would it take him to jog 14 kilometers? Step 1: IdentifyThis is a uniform motion problem. We are looking for the length of time it would take Steve to jog 14 kilometers. Step 2: Name Let t represent the length of time it would take Steve to jog 14 kilometers. Continued.

  15. Uniform Motion Problem Example continued: Step 3: TranslateOrganize the information in a table. d = rt 14 = 8t Step 4: Solve Divide both sides by 8. Simplify. Continued.

  16. Uniform Motion Problem Example continued: Step 5: Check t = 1.75 represents the length of time. d = rt 14 = (8)(1.75) 14 = 14  Step 6: Answer the Question It takes Mark 1.75 hours (or 1 hour and 45 minutes) to run 14 kilometers.

  17. Uniform Motion Problem Example: Nina drove her car to Cleveland while Paula drove her car to Columbus. Nina drove 360 kilometers while Paula drove 280 kilometers. Nina drove 20 kilometers per hour faster than Paula on her trip. What was the average speed in kilometers per hour for each driver? Step 1: Identify Distance problems can be solved using the formula distance = rate × time (d = rt). Step 2: Name Let r = the rate of Paula’s car. Let r + 20 = the rate of Nina’s car. The time, t, for each driver was the same. Continued.

  18. d r Nina 360 r + 20 Paula 280 r Uniform Motion Problem Example continued: Step 3: Translate Step 4: Solve Since the time for each driver was the same, we can set the times equal to each other. Continued.

  19. Uniform Motion Problem Example continued: Multiply both sides by r(r + 20). Simplify. Distribute. Subtract 280r from each side. Divide each side by 80. Paula’s rate was 70 kilometers per hour. Nina’s rate was r + 20 = 90 kilometers per hour. Continued.

  20. Uniform Motion Problem Example continued: Step 5: Check  Step 6: Answer the Question Paula’s rate was 70 kilometers per hour. Nina’s rate was 90 kilometers per hour.

More Related