Algebraic Expressions

Transcription

1 CHAPTER Algebraic Expressions Simplify each expression.. [(x ) ] 8x. 8m [.m (..m)] m. 8 p p 0. b ab a Factor each expression.. y y x. 0t 0b 0 7. (y ) x 8. x x y Write an expression for the measure of each figure. Sho your ork. 9. Find the area of the trapezoid. 8 cm x cm x cm 9 0 Chapter Algebraic Expressions

2 0. The area of the triangle is x (x ) square centimeters. Find the perimeter. (x ) cm x cm Solve. Sho your ork.. Elle is years younger than Felicia. Marta is tice as old of Felicia. Given that Marta is years old, a) find the age difference beteen Marta and Elle. b) rite an expression that shos the three girls average age.. A rectangle measures 0 inches by ( y) inches. If the length and the idth of the rectangle both increase by 0%, by ho much does the area of the rectangle increase? Enrichment Course

3 . Some oranges, apples, and grapes are used in a produce display. The ratio of the eight of oranges to the eight of apples is :. The ratio of the eight of apples to the eight of grapes is :. If the grapes eigh pounds, ho much do the oranges eigh?. A faucet is used to fill an empty rectangular tank. Water flos out of the faucet at a rate of cubic centimeters per second. After running the faucet for x seconds, the volume of ater in the tank is cubic centimeters more than of the capacity of the tank. a) Write an expression to represent the capacity of the tank, y, in cubic centimeters. b) Ho many seconds does it take to fill the empty tank to capacity? Chapter Algebraic Expressions

4 . There are q students ho attend a certain community college. The number of male students exceed the number of female students by %. One out of five male students and to out of three female students take a Spanish course. Write an expression that can be used to determine the number of students ho do not take a Spanish course.. A piggy bank contains some quarters, dimes, and nickels. The total value of the coins is $8. The bank has x number of dimes. The ratio of nickels to quarters in the bank is :. a) Ho many quarters are in the bank? b) Ho many nickels are in the bank? Enrichment Course

5 b) 9 mi gal 78 mi 9? 78 9? Darren needs 8 gallons of gas to travel 78 miles.. a) Difference beteen nickel and mercury, (7.89),88.89 Difference beteen nickel and helium, (8),09 Difference beteen nickel and copper,,98..8 Difference beteen mercury and helium 7.89 (8) 0. Difference beteen mercury and copper,98. (7.89),0. Difference beteen helium and copper,98. (8),. So, mercury and helium have melting points that are closest in values ith a difference of 0. F. b) Total, (7.89) (8),98.,9. F Average,9.,0.9 F. Loest temperature recorded in Colorado 7 F F F The record lo temperature in Colorado as F.. Brain@Work Let a, b, and c. a bc ()() 0 (a b)(a c) ( ) ( ) (7)(8) Since a bc is not equivalent to (a b)(a c) for a, b, and c, the distributive property is not true for addition over multiplication.. Brain@Work Actual eight of all the barrels (0)(0) () 9() () (8), The actual eight of all the barrels is 9 pounds. Chapter. 8m [.m (..m)] m 8m (.m.) m 8m.m 0 m.m. p 8 p 0 p p 0 p. [(x ) ] 8x [x ] 8x [x ] 8x x 9 8x x 9. b ab a 8 b ab a a a b b a b ( a b). [y (y ) x]. 0(t b ) 7. (y x) 8. x x y x 9x y ( x 9x) y [x (x 9) y] 9. Area of trapezoid x x i i 8 x 8 ( ) x cm Enrichment Course

6 0. Area of triangle x (x ) (base)(height) x (x ) (base)(x) x (x ) base x ( x ) x x base x Perimeter (x ) x (x ) x x. a) Elle Marta Felicia 7 x cm x Marta s age Elle s age b) Average age:. Ne length ( ) i 0 in. Ne idth 0 ( y) 00 ( y) ( y) y 0 0 0y y 0 0 y in. 0 Increase in area of rectangle Ne area Original area y i 0 (0)( y) y 0 0 (0 0y) y y 0 y 0 0 ( y ) in 0. units pounds units pounds So, eight of apples is pounds. units pounds units pounds So, eight of oranges is pounds.. a) Let y represent the capacity of tank. b) x y y x y (x ) cm ( x ) (x ) s. Brain@Work Males %; Females 7% Number of males 00 q Number of females 7 00 q Number of students ho do not take Spanish q 7 q q q q q q,00 87 q, 00 Ansers

7 . a) Let y represent the number of quarters. Total value $8 800 cents y() y() x(0) 800 b) Number of nickels y Chapter 80 ( x) 7 80 x 7 y 0x 800 y 80 ( x) 7. a (7 a) 9( a) a a 8 9a a 8 9a a 8 9a a 9a a 9a 9a 9a a a a. m ( m) m m m m m m m m m m m m m m m. ( p ) ( p) p p 7 p p 7 p p 8 p p 8 p p p p 8 p 8 p p.. ( m). ( m m) 7.. m. 7 ( m ).. m. m 7... m. m. m7.. m. m m m m 0. m m 0.. x x x x x x x x x x x x 0 x 0 8 x x 8 x Enrichment Course