EXAMPLE 5 Solve a multi-step problem BANNER DIMENSIONS You are making banners to hang during school spirit week. Each banner requires 16.5 square feet.

Slides:

Advertisements

Similar presentations

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

Advertisements

EXAMPLE 4 Solve a multi-step problem ICE SCULPTURES

Do Now Pass out calculators. Pick up a homework answer key from the back table and correct your homework that was due on last week on Friday (pg. 586 #

( ) EXAMPLE 3 Solve ax2 + bx + c = 0 when a = 1

EXAMPLE 6 Solve a multi-step problem TERRARIUM

Do Now: Pass out calculators. Complete EOC Review Week # 17. Have your homework out ready to check.

EXAMPLE 3 Use a ratio of areas Cooking SOLUTION First draw a diagram to represent the problem. Label dimensions and areas. Then use Theorem If the.

EXAMPLE 1 Solve quadratic equations Solve the equation. a. 2x 2 = 8 SOLUTION a. 2x 2 = 8 Write original equation. x 2 = 4 Divide each side by 2. x = ±

Solve an equation with variables on both sides

EXAMPLE 1 Solve a quadratic equation having two solutions Solve x 2 – 2x = 3 by graphing. STEP 1 Write the equation in standard form. Write original equation.

Solve an absolute value equation EXAMPLE 2 SOLUTION Rewrite the absolute value equation as two equations. Then solve each equation separately. x – 3 =

EXAMPLE 3 Use a ratio of areas Then use Theorem If the area ratio is a 2 : b 2, then the length ratio is a:b. Cooking A large rectangular baking.

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.

Solve an equation using subtraction EXAMPLE 1 Solve x + 7 = 4. x + 7 = 4x + 7 = 4 Write original equation. x + 7 – 7 = 4 – 7 Use subtraction property of.

Standardized Test Practice

Standardized Test Practice

Divide each side by 2. Write original equation. Write 3x + 2y = 8 so that y is a function of x. EXAMPLE 2 Rewrite an equation Subtract 3x from each side.

EXAMPLE 1 Collecting Like Terms x + 2 = 3x x + 2 –x = 3x – x 2 = 2x 1 = x Original equation Subtract x from each side. Divide both sides by x2x.

Standardized Test Practice

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.

EXAMPLE 3 Solve an equation by factoring Solve 2x 2 + 8x = 0. 2x 2 + 8x = 0 2x(x + 4) = 0 2x = 0 x = 0 or x + 4 = 0 or x = – 4 ANSWER The solutions of.

Standardized Test Practice

EXAMPLE 2 Write a rule for the nth term a. 4, 9, 14, 19,... b. 60, 52, 44, 36,... SOLUTION The sequence is arithmetic with first term a 1 = 4 and common.

Solve a radical equation

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.

Subtract b from each side. Write original equation. Solve ax + b = c for x. STEP 1 SOLUTION Solve ax +b = c for x. Then use the solution to solve 2x +

Find the product. 1. (x + 6)(x – 4) ANSWER x2 + 2x – 24

Solving Radical Equations

2.9 Warm Up 1. Solve 2x2 + 11x = , –7 ANSWER 2

EXAMPLE 2 Rationalize denominators of fractions Simplify

Warm-Up Exercises 1. Simplify –2 (9a – b). ANSWER –18a + 2b ANSWER r3s4r3s4 2. Simplify r 2 s rs 3.

3.6 Solving Quadratic Equations

5.3 Solving Quadratic Equations by Finding Square Roots.

Warm-ups Find each product. 1. (x + 2)(x + 7)2. (x – 11)(x + 5) 3. (x – 10) 2 Factor each polynomial. 4. x x x 2 + 2x – x 2.

2.8 Warm Up Factor. 1.8x² + 26x x² + 15x x² - 18x - 8.

1. Solve 2x2 + 11x = 21. ANSWER 3 2 , –7 2. Factor 4x2 + 10x + 4.

EXAMPLE 2 Rewrite a formula with three variables SOLUTION Solve the formula for w. STEP 1 P = 2l + 2w P – 2l = 2w P – 2l 2 = w Write perimeter formula.

Literal Equations. ANSWER 2a + 3 = Write an equation for “ 3 more than twice a is 24. ” ANSWER 64 ft 2 2.A square has a side length of 8 feet. Find.

EXAMPLE 3 Standardized Test Practice A = lw 63 = 9w 63 = = w Write area formula. Substitute values. Divide each side by 9. Simplify. ANSWERThe.

EXAMPLE 1 Find a positive slope Let (x 1, y 1 ) = (–4, 2) = (x 2, y 2 ) = (2, 6). m = y 2 – y 1 x 2 – x 1 6 – 2 2 – (–4) = = = Simplify. Substitute.

Factoring to Solve Quadratic Equations ALGEBRA 1 LESSON 10-5 (For help, go to Lessons 2-2 and 9-6.) Solve and check each equation n = 22. – 9 =

2.5Solve Equations in Factored FormVocabulary Let a and b be real numbers. If ab = 0, then = 0 or = 0. Zero-Product Property a b.

Solve an equation using addition EXAMPLE 2 Solve x – 12 = 3. Horizontal format Vertical format x– 12 = 3 Write original equation. x – 12 = 3 Add 12 to.

Example 1 Solving Two-Step Equations SOLUTION a. 12x2x + 5 = Write original equation. 112x2x + – = 15 – Subtract 1 from each side. (Subtraction property.

Use the substitution method

4 = 4 Solve each equation. Check your answers. a. x – 5 = 4 x – 5 = 4

4.4 Solving Multi-step Inequalities. 4.4 – Solving Multi-step Inequal. Goals / “I can…”  Solve multi-step inequalities with variables on one side  Solve.

EXAMPLE 3 Use the quadratic formula y = 10x 2 – 94x = 10x 2 – 94x – = 10x 2 – 94x – 300 Write function. Substitute 4200 for y. Write.

9.2 Multiply Polynomials I can…multiply polynomials

CONFIDENTIAL 1 Algebra1 Solving Radical Equations.

SOLUTION EXAMPLE 6 Standardized Test Practice The dimensions of a rectangle are x + 3 and x + 2. Which expression represents the area of the rectangle.

EXAMPLE 1 Rewrite a formula with two variables Solve the formula C = 2πr for r. Then find the radius of a circle with a circumference of 44 inches. SOLUTION.

EXAMPLE 4 Solve an equation with an extraneous solution Solve 6 – x = x. 6 – x = x ( 6 – x ) = x – x = x 2 x – 2 = 0 or x + 3 = 0 0 = x + x – 6 2.

Holt Algebra Solving Radical Equations Warm Up(Add to Hw) Solve each equation. 1. 3x +5 = x + 1 = 2x – (x + 7)(x – 4) = 0 5. x 2.

1. Simplify –2 (9a – b). ANSWER –18a + 2b 2. Simplify r2s rs3. ANSWER

Warm Ups Term 2 Week 6.

Rewrite a formula with three variables

EXAMPLE 2 Rationalize denominators of fractions Simplify

EXAMPLE 1 Finding Area and Perimeter of a Triangle

Solve a literal equation

Solve an equation by multiplying by a reciprocal

Dividing by a number is the inverse of multiplying by that number

Solve a quadratic equation

Factor x2 + bx + c Warm Up Lesson Presentation Lesson Quiz.

EXAMPLE 3 Use a ratio of areas Cooking

Factoring to Solve Quadratic Equations

Multiply Polynomials Warm Up Lesson Presentation Lesson Quiz.

Solve an equation by combining like terms

Warm Up Solve each equation

Presentation transcript:

EXAMPLE 5 Solve a multi-step problem BANNER DIMENSIONS You are making banners to hang during school spirit week. Each banner requires 16.5 square feet of felt and will be cut as shown. Find the width of one banner. STEP 1 Draw a diagram of two banners together. SOLUTION

EXAMPLE 5 Solve a polynomial equation STEP 2 Write an equation using the fact that the area of 2 banners is 2(16.5) = 33 square feet. Solve the equation for w. Formula for area of a rectangle A = l w Substitute 33 for A and (4 + w + 4) for l. Simplify and subtract 33 from each side. 0 = w 2 + 8w – 33 Factor right side. 0 = (w + 11)(w – 3) Zero-product property w + 11 = 0 or w – 3 = 0 33 = (4 + w + 4) w Solve for w. w = – 11 ANSWER The banner cannot have a negative width, so the width is 3 feet. w = 3 or

GUIDED PRACTICE for Example 5 WHAT IF ? In example 5, suppose the area of a banner is to be 10 square feet. What is the width of one banner ? 9. ANSWER 2 feet