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1 Math 00 Final Review Questions In problems 6, perform the indicated operations and simplif if necessar ( i) ( 4 i) 4. (8 i). ( 9 i)( 7 i) 6. ( i)( i) In problems 7-, solve the following applications. Define the variable(s), state the equation(s), solve the equation(s), and state the solution in a complete sentence. 7. On a freewa a car travels 0 miles in the same time that a truck travels miles. If the rate of the car is 8 miles per hour faster than the rate of the truck, find both rates. 8. Mr. Ngen wants to diversif is portfolio b investing a total of $,000 in two accounts, one is high risk paing 4% simple annual interest and the other is low risk paing % simple annual interest. If he wants to earn $0 annual interest, how much should he invest at each rate? 9. At a concession stand, three hot dogs and four hamburgers cost $.; four hot dogs and three hamburgers cost $.00. Find the cost of one hot dog and one hamburger.. Amie plans to use one-fourth the area of her 48-foot-b-0-foot rectangular back ard to plant a garden. Find the perimeter of the garden if the length is to be 40 feet greater than the width.. If the length of each side of a square is increased b 4 inches, the area of the larger square becomes 9 times greater than the area of the original square. Find the perimeter of the original square a. State the values of that are not in the domain of this rational function. f () = b. State the domain of the rational function. f () = + +. How is f( ) pronounced and what does it reall mean? 4. If. If f ( ) 6 and g( ) 4, find f(7) g(7). f ( ) 6, find f ( ) and f( a ). For problems 6 7, find the inverse of the given function; find f 6. ( ). f( ) ( ) 7. f( ) 8. Graph f() = 9. Graph 4 Last modified Spring 06

2 Math 00 Final Review Questions 0. Graph 6. Graph f( ) f(). Graph f() = + +. Graph f() = ( + ) State the Domain and Range State the Domain and Range f() f() 4. Find the equation of a line passing through points (-,) and (, -4). Write our final answer in both Slope- Intercept form and Standard form.. Find the equation of a line passing through point (,) and perpendicular to the line with equation =. Write our final answer in both Point-Slope form and Standard form. 6. Solve the sstem of equations b graphing. 4 4 Last modified Spring 06

3 Math 00 Final Review Questions In problems 7 8, solve the sstems of equations. One must be b the elimination (ie. addition) method and the other b substitution method Graph 0. Graph Simplif. Use onl positive eponents in the reduced answer. 7 ( ) ( ) 4 ( ) ( ) - For problems -4, perform the indicated operations and simplif if necessar. 4.. (a 7 b) 6 4. a 6ab 9b a b 4a 6b a 4ab For problems -6, factor completel.. 0 4t 6. (n + ) + (n + ) For problems 7-9, solve the following equations b factoring (4 ) 7(4 ) 0 Solve b completing the square = 0 For problems 4-4, solve the following equations that are quadratic in form. 4. z 4 z + 6 = 0 4. For problems 4-4, solve using the method of our choice ( ) Last modified Spring 06

4 Math 00 Final Review Questions For problems 46-48, solve the equations for. If the solutions are comple, write them in a bi form ( ) Solve problems 4- and state the solution in interval notation Sketch 9 ( ) and find: verte -intercept(s) -intercept equation ais of smmetr - 4. Sketch f ( ) 6 and find: verte - -intercept(s) -intercept equation ais of smmetr - For problems -60, solve the equations for = Simplif the epression. Assume all variables represent positive real numbers. Rationalize the denominator in our final answer. 4t u 9 6. Simplif the epression. Write the final answer with positive eponents. 8 7 Last modified Spring 06

5 Math 00 Final Review Questions For problems 6-6, simplif the comple fractions. 6. k k 4k 66. If 4, evaluate the epression For problems 67-69, solve the equations. Round the answer to the nearest hundredth where appropriate e Rewrite the following epressions as a single logarithm. 70. log log 7. ln ln Write each logarithm as a sum and/or difference of logarithms. Simplif where possible. e 7. log ( ab) 7. ln Solve the following equations for : if necessar, answer as a simplified fraction. 74. log 6 ( ) 7. log 76. Using a calculator, approimate the following values to decimal places a) ln 6 b) log c) d) log If a ship leaves port and sails east 6.7 miles and then turns south and sails for.9 miles, how far is the ship from port? Round the answer to the nearest tenth of a mile. 78. Solve the given triangle. Round each answer to the nearest tenth of a unit. B 6.0 cm 7.0 cm C b A 79. Use a calculator to find the value of to the nearest tenth of an inch. 7 in. 80. A ver old white pine tree casts a shadow 40 feet long on the flat ground on a nice sunn da. Suppose the angle formed from the tip of the shadow on the ground to the top of the tree is 6. Use a calculator to find the height of the tree rounded to the nearest tenth of a foot. Last modified Spring 06

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