SALTWATER AQUARIUM EXAMPLE 4 Solve a multi-step problem Write a direct variation equation that relates w and s. How many tablespoons of salt should be.

Slides:

Advertisements

Similar presentations

EXAMPLE 1 Standardized Test Practice SOLUTION Substitute several values of h into the equation C = h and solve for C.Then identify the table that.

Advertisements

Solve a multi-step problem

EXAMPLE 3 Standardized Test Practice SOLUTION

Solve an equation with variables on both sides

EXAMPLE 5 Solve a multi-step problem LIBRARY

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 2 Graph direct variation equations Graph the direct variation equation. a.a. y = x 2 3 y = –3x b.b. SOLUTION a.a. Plot a point at the origin. The.

EXAMPLE 5 Write a joint variation equation The variable z varies jointly with x and y. Also, z = –75 when x = 3 and y = –5. Write an equation that relates.

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 EXAMPLE 4 ANSWER The correct answer is B. DCBA Simplify the expression 4(n + 9) – 3(2 + n). 4(n + 9) – 3(2 + n) = Distributive.

Standardized Test Practice

EXAMPLE 5 Solve a multi-step problem Recording Studio

Do Now Pass out calculators. Solve the following system by graphing: Graph paper is in the back. 5x + 2y = 9 x + y = -3 Solve the following system by using.

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 1 Write an equation of a circle Write the equation of the circle shown. The radius is 3 and the center is at the origin. x 2 + y 2 = r 2 x 2 +

Tell whether the equation represents direct variation.

Write and graph a direct variation equation

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.

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.

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.

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

4-6 Direct Variation Direct Variation: y = kx k=constant of variation = SLOPE Ex: y = 2x the constant of variation=2 All equations of form y=kx have.

3.6 Model Direct Variation

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.

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.

Lesson: 3.6 Model Direct Variation Essential Question: How do you write and graph direct variation equation? Warm-up: Rewrite the equation so.

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

Solve a two-step inequality EXAMPLE 1 3x – 7 < 8 Write original inequality. 3x < 15 Add 7 to each side. x < 5 Divide each side by 3. ANSWER The solutions.

Solving Quadratic Equations – Quadratic Formula The following shows how to solve quadratic equations using the Quadratic Formula. A quadratic equation.

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.

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 Solve by equating exponents Rewrite 4 and as powers with base Solve 4 = x 1 2 x – 3 (2 ) = (2 ) 2 x – 3x – 1– 1 2 = 2 2 x– x + 3 2x =

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

EXAMPLE 1 Solve a two-step equation Solve + 5 = 11. x 2 Write original equation. + 5 = x – 5 = x 2 11 – 5 Subtract 5 from each side. = x 2 6 Simplify.

Warm Up Solve. 1. 3x = = z – 100 = w = 98.6 x = 34 y = 225 z = 121 w = 19.5 y 15.

Use the substitution method

EXAMPLE 4 Solve a system using substitution Marketing The marketing department of a company has a budget of $30,000 for advertising. A television ad costs.

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

Solve Linear Systems by Substitution Students will solve systems of linear equations by substitution. Students will do assigned homework. Students will.

Lesson 4.6 Model Direct Variation Word Problems Essential Question: How do you write and graph direct variation equations?

Direct Variation odd, even, 3-9 odd, even, 23-25, #31 He was seized by the fidgets, Grab ONE sheet of graph paper.

EXAMPLE 4 Solve linear systems with many or no solutions Solve the linear system. a.x – 2y = 4 3x – 6y = 8 b.4x – 10y = 8 – 14x + 35y = – 28 SOLUTION a.

Solve a two-step equation by combining like terms EXAMPLE 2 Solve 7x – 4x = 21 7x – 4x = 21 Write original equation. 3x = 21 Combine like terms. Divide.

EXAMPLE 1 Write an equation of a circle Write the equation of the circle shown. SOLUTION The radius is 3 and the center is at the origin. x 2 + y 2 = r.

Warm-Up Exercises Lesson x – 2y = –8 2. –9x + 3y = 21 ANSWER y = 2x + 4 Rewrite the equation so y is a function of x. y = 3x + 7.

Model Direct Variation

EXAMPLE 2 Rationalize denominators of fractions Simplify

Solve a literal equation

Solve an equation by multiplying by a reciprocal

Solve a quadratic equation

3-2: Solving Systems of Equations using Substitution

Solve a system of linear equation in two variables

3-2: Solving Systems of Equations using Substitution

Solving Systems of Equations using Substitution

3-2: Solving Systems of Equations using Substitution

Solve an equation by combining like terms

Solving One and Two Step Equations

Standardized Test Practice

Quadratics Review and VDOE SOL Practice

Solve an inequality using subtraction

3-2: Solving Systems of Equations using Substitution

3-2: Solving Systems of Equations using Substitution

3-2: Solving Systems of Equations using Substitution

3-2: Solving Systems of Equations using Substitution

3-2: Solving Systems of Equations using Substitution

Presentation transcript:

SALTWATER AQUARIUM EXAMPLE 4 Solve a multi-step problem Write a direct variation equation that relates w and s. How many tablespoons of salt should be added to a 30 gallon saltwater fish tank ? The number s of tablespoons of sea salt needed in a saltwater fish tank varies directly with the number w of gallons of water in the tank. A pet shop owner recommends adding 100 tablespoons of sea salt to a 20 gallon tank.

SOLUTION EXAMPLE 4 Solve a multi-step problem Write a direct variation equation. Because s varies directly with w, you can use the equation s = aw. Also use the fact that s = 100 when w = 20. s = aw Write direct variation equation. 100 = a(20) Substitute. 5 = a Solve for a. ANSWER A direct variation equation that relates w and s is s = 5w. STEP 1

EXAMPLE 4 Solve a multi-step problem Find the number of tablespoons of salt that should be added to a 30 gallon saltwater fish tank. Use your direct variation equation from Step 1. s = 5 w Write direct variation equation. s = 5(30) Substitute 30 for w. s = 150 Simplify. ANSWER You should add 150 tablespoons of salt to a 30 gallon fish tank. STEP 2

GUIDED PRACTICE for Example 4 6. WHAT IF? In Example 4, suppose the fish tank is a 25 gallon tank. How many tablespoon of salt should be added to the tank ? ANSWER 125 tbsp