Homework, Page 253 Solve the equation algebraically. Support your answer numerically and identify any extraneous solutions. 1.

Homework, Page 253 Solve the equation algebraically. Support your answer numerically and identify any extraneous solutions. 5.

Homework, Page 253 Solve the equation algebraically and graphically. Check for extraneous solutions. 9.

Homework, Page 253 Solve the equation algebraically. Check for extraneous solutions. Support your answer graphically. 13.

Homework, Page 253 Solve the equation algebraically. Check for extraneous solutions. Support your answer graphically. 17.

Homework, Page 253 21. Both are extraneous. Two possible solutions to the equation f (x) = 0 are listed. Use the given graph of y = f (x) to decide which, if any are extraneous. 21. Both are extraneous.

Homework, Page 253 Solve the equation. 25.

Homework, Page 253 Solve the equation. 29.

Homework, Page 253 33. Mid Town Sports Apparel has found that it needs to sell golf hats at $2.75 each to be competitive. It costs $2.12 to produce each hat, and weekly overhead is $3,000. a. Let x be the number of hats produced each week. Express the average cost (including overhead) of producing one hat as a function of x. b. Solve algebraically to find the number of golf hats that must be sold each week to make a profit. Support your answer graphically. c. How many golf hats must be sold to make a profit of $1,000 in one week. Explain your answer.

Homework, Page 253 33. a. Let x be the number of hats produced each week. Express the average cost (including overhead) of producing one hat as a function of x. b. Solve algebraically to find the number of golf hats that must be sold each week to make a profit.

Homework, Page 253 33. c. How many golf hats must be sold to make a profit of $1,000 in one week. Explain your answer. To break even, 4,762 hats must be sold. After breaking even, a profit of $0.63 is made on each hat sold, so selling a total of 6,350 hats will yield a $1,000 profit.

Homework, Page 253 37. Drake Cannery will pack peaches in 0.5-L cylindrical cans. Let x be the radius of the can in cm. a. Express the surface area of the can S as a function of x.

Homework, Page 253 37. b. Find the radius and height of the can if the surface area is 900 cm2.

Homework, Page 253 41. Drains A and B are used to empty a swimming pool. Drain A alone can empty the pool in 4.75 h. Let t be the time it takes for drain B alone to empty the pool. a. Express as a function of t the part D of the drainage that can be done in 1 h with both drains open at the same time. b. Find graphically the time it takes for drain B alone to empty the pool if both drains, when open at the same time, can empty the pool in 2.6 h. Confirm algebraically.

Homework, Page 253 41. a. Express as a function of t the part D of the drainage that can be done in 1 h with both drains open at the same time.

Homework, Page 253 41. b. Find graphically the time it takes for drain B alone to empty the pool if both drains, when open at the same time, can empty the pool in 2.6 h. Confirm algebraically.

Homework, Page 253 45. True – False An extraneous solution of a rational equation is also a solution of the equation. Justify your answer. False. An extraneous solution is a solution of an equation obtained by multiplying or dividing each term of a rational equation by an expression containing a variable. The extraneous solution is a solution of the resulting equation, but not of the original equation.

Homework, Page 253 49. Which of the following are solutions of the equation a. b. c. d. e. There are no solutions.

Homework, Page 253 Solve for x. 53.

Solving Inequalities in One Variable 2.8 Solving Inequalities in One Variable

What you’ll learn about Polynomial Inequalities Rational Inequalities Other Inequalities Applications … and why Designing containers as well as other types of applications often require that an inequality be solved.

Polynomial Inequalities

Example Finding where a Polynomial is Zero, Positive, or Negative

Example Solving a Polynomial Inequality Analytically

Example Solving a Polynomial Inequality Graphically

Example Creating a Sign Chart for a Rational Function

Example Solving an Inequality Involving a Rational Function

Example Solving an Inequality Involving a Radical

Example Solving an Inequality Involving an Absolute Value

Homework Review Section 2.8 Page 264, Exercises: 1 – 69 (EOO) Quiz next time