Multiplying and Dividing Rational Expressions y y v 2 3 v 2-13v x z 25 x. n - 6 n 2-6n. 6x + 2 x 2. w y a 3 w.

Transcription

1 8- Multiplying and Dividing Rational Epressions Simplify each epression.. 9 a b 7 a b c. ( m n ) -8 m 5 n. 0 y + 5y 5 y - 5y. k - k - 5 k v v - v u y 5 z 5 5 u y 8. a + y y + a 9. n 5 n - n - n n 8 0. a - y w + n w - n y - a a 5 y w y a w 7 w 5 y. ( y w ) w a a + 5a + a - 5a y - y 7. s - 7s - 5 (s + ) ( + ) + + s - 0s + 5 s +. GEMETRY A right triangle with an area of - square units has a leg that measures + units. Determine the length of the other leg of the triangle.. GEMETRY A rectangular pyramid has a base area of square centimeters and a height of - centimeters. Write a rational epression to describe the volume of the rectangular pyramid. Chapter 8 8 Glencoe Algebra

2 8- Adding and Subtracting Rational Epressions Find the LCM of each set of polynomials.. y, y. a b c, abc. +, +. g -, g + g - 5. r +, r + r, r +., w +, w , , d + d + 9, (d - 9) Simplify each epression ab - 7 8a 5. y - 5 y. c d + c d. m mn a a m m m m 8. y - 5 y - y y y + y a. a - - a a + + a - 9 p - 0. p - 5p p y.. 5n n - y + r + r - r +. r + r + - y r + r 5. GEMETRY The epressions 5, 0 +, and 0 represent the lengths of the sides of a - triangle. Write a simplified epression for the perimeter of the triangle.. KAYAKING Mai is kayaking on a river that has a current of miles per hour. If r represents her rate in calm water, then r + represents her rate with the current, and r - represents her rate against the current. Mai kayaks miles downstream and then back to her starting point. Use the formula for time, t = d r, where d is the distance, to write a simplified epression for the total time it takes Mai to complete the trip. Chapter 8 Glencoe Algebra

3 8- Identify the asymptotes, domain, and range of each function.. f() = f() = + +. f() = f() - Graphing Reciprocal Functions f() f() Graph each function. State the domain and range.. f() = f() = f() = - + f() f() f() 7. RACE Kate enters a 0-mile bicycle race. Her basic rate is 0 miles per hour, but Kate will average miles per hour faster than that. Write and graph an equation relating (Kate s speed beyond 0 miles per hour) to the time it would take to complete the race. If she wanted to finish the race in hours instead of 5 hours, how much faster should she travel? t 0 8 Lesson Chapter 8 Glencoe Algebra

4 8- Graph each function. -. f() = - Graphing Rational Functions. f() = - -. f() = ( + ) f() f() f(). f() = f() 5. f() = f(). f() = f() 7. PAINTING Working alone, Tawa can give the shed a coat of paint in hours. It takes her father hours working alone to give the shed a coat of paint. The equation f() = + describes the portion of the job Tawa and her father working together can complete in hour. Graph f() = + for > 0, f() > 0. If Tawa s father can complete the job in hours alone, what portion of the job can they complete together in hour? What domain and range values are meaningful in the contet of the problem? 8. LIGHT The relationship between the illumination an object receives from a light source of I foot-candles and the square of the distance d in feet of the object from the source can be modeled by I(d) = 500. Graph the function I(d) = 500 for d 0 < I 80 and 0 < d 80. What is the illumination in foot-candles that the object receives at a distance of 0 feet from the light source? What domain and range values are meaningful in the contet of the problem? d I f() d Chapter 8 8 Glencoe Algebra

5 8-5 Variation Functions State whether each equation represents a direct, joint, inverse, or combined variation. Then name the constant of variation.. u = 8wz. p = s. L = 5 k. y =.5 5. C d.5 = π. d = mn 7. g = h 8. y = 9. If y varies directly as and y = 8 when =, find y when =. 0. If y varies directly as and y = - when =, find when y = -.. If y varies directly as and y = when =, find y when =.. If y varies directly as and y = 7 when =.5, find y when =.. If y varies jointly as and z and y = when = and z =, find y when is and z is.. If y varies jointly as and z and y = 0 when = and z =, find y when is and z is If y varies jointly as and z and y = when = - and z =, find y when is and z is -.. If y varies inversely as and y = when =, find y when =. 7. If y varies inversely as and y = when = 5, find when y = If y varies directly as z and inversely as and y = -8 and z = when =, find y when = 5 and z = If y varies directly as z and inversely as and y = 0 and z = 5 when =.5, find z when y = 7.5 and =. 0. GASES The volume V of a gas varies inversely as its pressure P. If V = 80 cubic centimeters when P = 000 millimeters of mercury, find V when P = 0 millimeters of mercury.. SPRINGS The length S that a spring will stretch varies directly with the weight F that is attached to the spring. If a spring stretches 0 inches with 5 pounds attached, how far will it stretch with 5 pounds attached?. GEMETRY The area A of a trapezoid varies jointly as its height and the sum of its bases. If the area is 80 square meters when the height is 0 meters and the bases are 8 meters and 0 meters, what is the area of a trapezoid when its height is 8 meters and its bases are 0 meters and 5 meters? Lesson 8-5 Chapter 8 5 Glencoe Algebra

6 8- Solve each equation or inequality. Check your solutions.. + =. p + 0 p - = p 5. 5 y - 5 = y Solving Rational Equations and Inequalities. - - = s. s + + s = 5s + 8 s + y = t < 9 8. t + h + 5 h = h - 9. w - = w + a < 7 a <. p + p < 5 5. g + g g - = g - 7. n + + n - = n - 9. k - + k - = 5 k - 7k + y. y y - 5 = y - y - 0 r. r + + r - = r + r y > 9 y. - = b. b + b - = - b - b - 8. c + c - = - c - c - v 0. v - - 5v v - = v - v = +. = a - a a BASKETBALL Kiana has made 9 of 9 free throws so far this season. Her goal is to make 0% of her free throws. If Kiana makes her net free throws in a row, the function f() = 9 + represents Kiana s new ratio of free throws made. How many 9 + successful free throws in a row will raise Kiana s percent made to 0%? Is this a reasonable answer? Eplain. 8. PTICS The lens equation p + q = relates the distance p of an object from a f lens, the distance q of the image of the object from the lens, and the focal length f of the lens. What is the distance of an object from a lens if the image of the object is 5 centimeters from the lens and the focal length of the lens is centimeters? Is this a reasonable answer? Eplain. Chapter 8 Glencoe Algebra