12) 13) 14) (5x)2/3. 16) x5/8 x3/8. 19) (r1/7 s1/7) 2

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1 DMA 080 WORKSHEET # (8.-8.2) Name Find the square root. Assume that all variables represent positive real numbers. ) 6 2) 8 / 2) 9x8 ) -00 ) / Use a calculator to approximate the square root to decimal places. Check to see that the approximation is reasonable. 4) 8 4) (5x)2/ Find the cube root. 5) -64 Write with positive exponents. Simplify if possible. 5) 6-/2 6) 25x6 Simplify. Assume that all variables represent any real number. 7) (-)2 Use the properties of exponents to simplify the expression. Write with positive exponents. 6) x5/8 x/8 8) 49x2 7) y /4 y/4 Evaluate. 9) If f(x) = 2x + 9, find the value of f(5). 8) (b) 2/ 0) If f(x) = x + 4, find the value of f(-2). Use radical notation to write the expression. Simplify if possible. ) 00/2 9) (r/7 s/7) 2

2 Use rational exponents to simplify the following. 20) 2 x7 2) 4 256x2 22) 2 y2z2 Use rational exponents to write as a single radical expression. 2) 4 x x 24) 4 x x2 25) 8 y 9 y 2

3 DMA 080 WORKSHEET #2 (8., 8.4, 8.5) Name Use the product rule to multiply. Assume all variables represent positive real numbers. ) 8 2 8) 40a 5b6 5a 2 2) 5 25 Find the distance between the pair of points. 9) (-5, -2) and (, 2) Use the quotient rule to divide and simplify. ) 27x2y 25 Add or subtract. Assume all variables represent positive real numbers. 0) ) 54x 2x ) Simplify the radical expression. Assume that all variables represent positive real numbers. 2) 4 xy0 + 2xy 8y7 5) p 6) 8k7q8 Multiply, and then simplify if possible. Assume all variables represent positive real numbers. ) 2( ) 7) -8a8b0 4) ( + )( - )

4 5) ( 2 + 9)( 2 + 4) 2) ) ( 7 - ) 2 7) x ) ) Find the area of the rectangle. 2) a + a w 8 ft 4 8 ft Rationalize the numerator and simplify. Assume all variables represent positive real numbers. 24) 2 x y Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. 9) 20) 4 9 2

5 DMA 080 WORKSHEET # (8.6, 8.8) Name ) x - 4 = 4 Use the Pythagorean theorem to find the unknown side of the right triangle. 7) 2) x = ) 2x = 0 8) ) x = x + 2 5) x2-2x + 6 = x + 5 9) A balloon is secured to rope that is staked to the ground. A breeze blows the balloon so that the rope is taut while the balloon is directly above a flag pole that is 50 feet from where the rope is staked down. Find the altitude of the balloon if the rope is 20 feet long. 6) When an object is dropped to the ground from a height of h meters, the time it takes for the object to reach the ground is given by the h equation t =, where t is measured in 4.9 seconds. If an object falls 44. meters before it hits the ground, find the time it took for the object to fall. Use the quadratic formula to solve the equation. 0) x2 + 6x + 6 = 0

6 ) 5x2 + 2x = - 6 Given the graph on the calculator screen of a quadratic equation of the form y = f(x), find the number of real number solutions of the related equation f(x) = 0. 8) 2) z 2 2 = z Use the quadratic formula and a calculator to approximate the solution to the nearest tenth. ) x2 + 6x - 2 = 0 9) 4) A ball is thrown upward with an initial velocity of 28 meters per second from a cliff that is 40 meters high. The height of the ball is given by the quadratic equation h = -4.9t2 + 28t + 40 where h is in meters and t is the time in seconds since the ball was thrown. Find the time it takes the ball to hit the ground. Round your answer to the nearest tenth of a second. 20) Use the discriminant to determine the number and type of solutions of the equation. 5) x2 + 7x + 6 = 0 2) The base of a triangle is 8 more than twice its height. If the area of the triangle is 22 square centimeters, find its base and height. 6) x2 + 2x + = 0 7) x2 + x + 8 = 0 2

7 DMA 080 Review for Final Name Find the square root. Assume that all variables represent positive real numbers. ) 6x2 Use a calculator to approximate the square root to decimal places. Check to see that the approximation is reasonable. 2) 480 Find the cube root. ) -8x24y6 Simplify. Assume that all variables represent any real number. 4) 5 (-0)5 Evaluate. 5) If f(x) = x -, find the value of f(4). Use radical notation to write the expression. Simplify if possible. 6) (-4x2) / 7) (x + 2)2/9 Write with positive exponents. Simplify if possible. 8) x-8/9 Use the properties of exponents to simplify the expression. Write with positive exponents. 9) z-2/5 z/5 0) (-2x /5) 5 x-/5 Use rational exponents to simplify the following. ) 42 y8z5 Use the product rule to multiply. Assume all variables represent positive real numbers. 2) 27m 25m

8 Use the quotient rule to divide and simplify. 00 ) 5 Simplify the radical expression. Assume that all variables represent positive real numbers. 4) p Find the distance between the pair of points. 5) (6, ) and (-7, -5) Add or subtract. Assume all variables represent positive real numbers. 6) ) Find the perimeter of the triangle. Simplify. 2 m 08 m 2 m 8) Find the area of the rectangle. 8 ft 4 8 ft Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. 7 9) 20) - 9 x + 8 2

9 2) The maximum number of volts, E, that can be placed across a resistor is given by the formula E = PR, where P is the number of watts of power that the resistor can absorb and R is the resistance of the resistor in ohms. If a -watt resistor has a resistance of 52 ohms, find the largest number of volts of electricity that could be placed 8 across the resistor. 22) A balloon is secured to rope that is staked to the ground. A breeze blows the balloon so that the rope is taut while the balloon is directly above a flag pole that is 20 feet from where the rope is staked down. Find the length of the rope if the altitude of the balloon is 80 feet. Use the quadratic formula to solve the equation. 2) (x - 9)(x - ) = 22 24) The revenue for a small company is given by the quadratic function r(t) = t2 + 8t where t is the number of years since 998 and r(t) is in thousands of dollars. If this trend continues, find the year after 998 in which the company's revenue will be $225 thousand. Round to the nearest whole year. 25) The hypotenuse of a right triangle is 9 feet long. One leg of the triangle is 5 feet longer then the other leg. Find the perimeter of the triangle.