Solve a multi-step problem EXAMPLE 3 ELEVATORS The elevator that takes passengers from the lobby of the John Hancock Center in Chicago to the observation.

Slides:

Advertisements

Similar presentations

Write a ratio EXAMPLE 1 VOLLEYBALL A volleyball team plays 14 home matches and 10 away matches. a. Find the ratio of home matches to away matches. SOLUTION.

Advertisements

Solve an equation by multiplying by a reciprocal

Do Now Pass out calculators. Work on practice EOC Week # 8.

Solve a multi-step problem

Example 3 Each day, an elephant eats 5 pounds of food for every 100 pounds of its body weight. How much does a 9300 pound elephant eat per day? SOLUTION.

EXAMPLE 1 Find ratios of similar polygons Ratio (red to blue) of the perimeters a.a. Ratio (red to blue) of the areas b.b. In the diagram, ABC  DEF. Find.

EXAMPLE 5 Solve a vertical motion problem Juggling

Substitute 3 for x and 4 for y. Simplify. Write original equation. Check whether each ordered pair is a solution of the equation. SOLUTION Which ordered.

EXAMPLE 4 Solve a multi-step problem ICE SCULPTURES

Writing and Solving a Proportion EXAMPLE 3 STEP 1 Write a proportion. Let x represent the number of floors passed in 9 seconds. Empire State Building The.

Solving Multiplication and Division Equations. EXAMPLE 1 Solving a Multiplication Equation Solve the equation 3x = x = 15 Check 3x = 45 3 (15)

EXAMPLE 4 Solve proportions SOLUTION a x 16 = Multiply. Divide each side by 10. a x 16 = = 10 x5 16 = 10 x80 = x8 Write original proportion.

Use the cross products property EXAMPLE 1 Write original proportion = x 6 Solve the proportion =. 8 x 6 15 Cross products property Simplify. 120.

EXAMPLE 4 Solve a multi-step problem FOUNTAINS

Solve quadratic equations

Solve quadratic equations

EXAMPLE 2 Using the Cross Products Property = 40.8 m Write original proportion. Cross products property Multiply. 6.8m 6.8 = Divide.

Introduction All circles are similar; thus, so are the arcs intercepting congruent angles in circles. A central angle is an angle with its vertex at the.

Warm-up: Solve the proportion.

Standardized Test Practice

EXAMPLE 5 Find leg lengths using an angle of elevation SKATEBOARD RAMP You want to build a skateboard ramp with a length of 14 feet and an angle of elevation.

EXAMPLE 5 Find leg lengths using an angle of elevation SKATEBOARD RAMP You want to build a skateboard ramp with a length of 14 feet and an angle of elevation.

EXAMPLE 4 Solve a quadratic equation Solve 6(x – 4) 2 = 42. Round the solutions to the nearest hundredth. 6(x – 4) 2 = 42 Write original equation. (x –

Standardized Test Practice

EXAMPLE 4 Solve a multi-step problem CYCLING

EXAMPLE 4 Solve a multi-step problem CRAFTS You decide to use chalkboard paint to create a chalkboard on a door. You want the chalkboard to have a uniform.

Lesson Write Ratios and Solve Proportions

Solve a radical equation

EXAMPLE 1 Find ratios of similar polygons Ratio (red to blue) of the perimeters a.a. Ratio (red to blue) of the areas b.b. In the diagram, ABC  DEF. Find.

EXAMPLE 3 Solve a multi-step problem Many businesses pay website hosting companies to store and maintain the computer files that make up their websites.

SOLUTION RUNNING The distance d (in miles) that a runner travels is given by the function d = 6t where t is the time (in hours) spent running. The runner.

1.4 Graph Using Intercepts

EXAMPLE 4 Find a unit rate A car travels 110 miles in 2 hours. Find the unit rate. 110 miles 2 hours = 1 hour 55 miles 2 hours miles 2 = The unit.

EXAMPLE 3 Solve a right triangle

3-2 HW: Pg #4-34e, 38, 40, ) B 47.) C.

Use the sign shown. A gas station charges $.10 less per gallon of gasoline if a customer also gets a car wash. What are the possible amounts (in gallons)

10.4 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Use Square Roots to Solve Quadratic Equations.

1. √49 2. –√144 Lesson 4.5, For use with pages

SOLUTION Write an inverse variation equation EXAMPLE 5 x–5–34824 y2.44–3–1.5–0.5 Tell whether the table represents inverse variation. If so, write the.

SOLUTION Write a ratio EXAMPLE 1 VOLLEYBALL A volleyball team plays 14 home matches and 10 away matches. a. Find the ratio of home matches to away matches.

Warm-Up Exercises Solve the equation. 2. (6x + 3) = x =

EXAMPLE 6 Solve a multi-step problem A = 13, x 1 – 0.015x and T = x 1 – 0.016x The amount A (in millions of dollars) spent on all advertising.

EXAMPLE 3 Write the standard equation of a circle The point (–5, 6) is on a circle with center (–1, 3). Write the standard equation of the circle. SOLUTION.

EXAMPLE 1 Translate verbal phrases into expressions Verbal Phrase Expression a. 4 less than the quantity 6 times a number n b. 3 times the sum of 7 and.

2.6 Write Ratios and Proportions

Use the cross products property

Lesson 9-7 Pages Similar Triangles and Indirect Measurement Lesson Check 9-6 Lesson Check 9-5.

Multi Step Equations Copied from =ie7&rls=com.microsoft:en-us:IE- Address&ie=&oe=#hl=en&tbo=d&rls=com.microsoft:en-us:IE-

EXAMPLE 4 Solve a Multi-Step Problem SOLUTION STEP 1Find the amount of the tip. Your food bill at a restaurant is $24. You leave a 20% tip. The sales tax.

EXAMPLE 3 Solve a right triangle Solve the right triangle. Round decimal answers to the nearest tenth. SOLUTION STEP 1 Find m B by using the Triangle Sum.

3.5 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Write Ratios and Proportions.

Solve an inequality using multiplication EXAMPLE 2 < 7< 7 x –6 Write original inequality. Multiply each side by –6. Reverse inequality symbol. x > –42.

Identify properties of multiplication

SUBMERSIBLES Use a linear model EXAMPLE 5 A submersible designed to explore the ocean floor is at an elevation of –13,000 feet (13,000 feet below sea level.

EXAMPLE 4 Derive a trigonometric model Soccer Write an equation for the horizontal distance traveled by a soccer ball kicked from ground level (h 0 = 0)

EXAMPLE 2 Multiply by the LCD Solve. Check your solution. x – 2 x = SOLUTION x – 2 x = Multiply by LCD, 5(x – 2). 5(x – 2) x – 2 x 1 5.

Using Equivalent Ratios EXAMPLE 1 Sports A person burned about 210 calories while in-line skating for 30 minutes. About how many calories would the person.

EXAMPLE 5 Solve a vertical motion problem A juggler tosses a ball into the air. The ball leaves the juggler’s hand 4 feet above the ground and has an initial.

2.6 Write Ratios and Proportions You will find ratios and write and solve proportions. Essential Question: How do you find ratios and write and solve proportions?

Chapter 4 Section 10. EXAMPLE 1 Write a quadratic function in vertex form Write a quadratic function for the parabola shown. SOLUTION Use vertex form.

3-4 HW: Pg #4-24e, 28-44eoe, 49-50,

Solve a multi-step problem EXAMPLE 5 Forestry Use the diagram, which illustrates the growth of a giant sequoia, to find the average rate of change in the.

Solve the equation x = ANSWER (6x + 3) =

Do-Now 1. x = ANSWER (6x + 3) = ANSWER 3

Percents and Proportions

Solve an equation by multiplying by a reciprocal

Warm Up Lesson Presentation Lesson Quiz

Solve quadratic equations

Solve the equation x = ANSWER (6x + 3) =

EXAMPLE 4 Solve proportions Solve the proportion. ALGEBRA a x 16

Presentation transcript:

Solve a multi-step problem EXAMPLE 3 ELEVATORS The elevator that takes passengers from the lobby of the John Hancock Center in Chicago to the observation level travels 150 feet in 5 seconds. The observation level is located on the 94th floor, at 1029 feet above the ground. Find the time it takes the elevator to travel from the lobby to the observation level.

Solve a multi-step problem EXAMPLE 3 SOLUTION STEP 2 Solve the proportion. Write a proportion involving two ratios that compare the amount of time the elevator has ascended with the distance traveled. STEP 1 x 1029 = 5 Seconds 150 feet

Solve a multi-step problem EXAMPLE x 1029 = Write proportion =1029 x Multiply each side by = x Simplify = x Use a calculator. ANSWER The elevator travels from the lobby to the observation level in 34.3 seconds.

Solve a multi-step problem EXAMPLE 3 You can use a table to check the reasonableness of your answer. CHECK The solution, 34.3 seconds, is slightly less than 35 seconds, and 1029 feet is slightly less than 1050 feet. So, the solution is reasonable.

GUIDED PRACTICE for Example 3 WHAT IF ? In Example 3, suppose the elevator travels 125 feet in 5 seconds. Find the time it will take for elevator to travel from the lobby to the observation level. 6. ANSWER sec

GUIDED PRACTICE for Example 3 When two full moons appear in the same month. The second full moon is called a blue moon. On average, 2 blue moons occur every 5 years. Find the number of blue moons that are likely to occur in the next 25 years. 7. ASTRONOMY ANSWER 10 blue moons