10-2 Simplifying Radical Expressions. Simplify each expression. SOLUTION: 4. SOLUTION: SOLUTION: SOLUTION: 10. MULTIPLE CHOICE Which expression is
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1 2. Simplify each expression. 10. MULTIPLE CHOICE Which expression is equivalent to? A B 4. C D The correct choice is D. Simplify each expression. esolutions Manual - Powered by Cognero Page 1
2 Simplify each expression esolutions Manual - Powered by Cognero Page 2
3 CCSS PRECISION When fighting a fire, the velocity v of water being pumped into the air is modeled by the function, where h represents the maximum height of the water and g represents the acceleration due to gravity (32 ft/s 2 ). a. Solve the function for h. b. The Hollowville Fire Department needs a pump that will propel water 80 feet into the air. Will a pump advertised to project water with a velocity of 70 feet per second meet their needs? Explain. c. The Jackson Fire Department must purchase a pump that will propel water 90 feet into the air. Will a pump that is advertised to project water with a velocity of 77 feet per second meet the fire department s need? Explain. a. 38. A pump with a velocity of 77 feet per second will pump water to a maximum height of 92.6 feet. Therefore, this pump will meet the fire department s need. Simplify each expression. 40. b. To determine the height of the water, substitute 70 for v in the function. A pump with a velocity of 70 feet per second will pump water only to a maximum height of 76.6 feet. Therefore, this pump will not meet the fire department s need. c. To determine the height of the water, substitute 77 for v in the function. esolutions Manual - Powered by Cognero Page 3
4 esolutions Manual - Powered by Cognero Page 4
5 50. KINETIC ENERGY The speed v of a ball can be determined by the equation, where k is the kinetic energy and m is the mass of the ball. a. Simplify the formula if the mass of the ball is 3 kilograms. b. If the ball is traveling 7 meters per second, what is the kinetic energy of the ball in Joules? a. If the mass of the ball is 3 kilograms, substitute m = 3 into the equation. 52. CCSS STRUCTURE Explain how to solve. To solve an equation of equal ratios, first find the equal cross products and then solve for the variable. Use the conjugate of denominator. to rationalize the b. Substitute V = 7 in the equation. So, the solution is. 54. REASONING Marge takes a number, subtracts 4, multiplies by 4, takes the square root, and takes the reciprocal to get. What number did she start with? Write a formula to describe the process. Let x = a number. The kinetic energy of the ball is 73.5 Joules. esolutions Manual - Powered by Cognero Page 5
6 56. CHALLENGE Use the Quotient Property of Square Roots to derive the Quadratic Formula by solving the quadratic equation ax 2 + bx + c = 0. (Hint: Begin by completing the square.) 60. The expression is equivalent to which of the following? A B C D So, the correct choice is C. 58. Jerry s electric bill is $23 less than his natural gas bill. The two bills are a total of $109. Which of the following equations can be used to find the amount of his natural gas bill? A g + g = 109 B g = 109 C g 23 = 109 D 2g 23 = Graph each function. Compare to the parent graph. State the domain and range. x y Let g = Jerry s natural gas bill. Jerry s electric bill is $23 less than his natural gas bill, so the electric bill is g 23. The two bills are a total of $109. So, the correct choice is D. The parent function is multiplied by a value greater than 1 and is subtracted by the value 1, so the graph is a vertical stretch of followed by a translation 1 unit down. The domain is {x x 0}, and the range is {y y -1}. esolutions Manual - Powered by Cognero Page 6
7 64. x y Determine the domain and range for each function. 68. f (x) = 2x 5 Since f (x) cannot be negative, the minimum point of the graph is where f (x) = 0. This graph is the result of a vertical stretch of the graph of y = followed by a translation 2 units left. The domain is {x x 2}, and the range is {y y 0}. Make a table of values. x f (x) x y The domain is all real numbers, and the range is {y y 0}. This graph is the result of a vertical stretch of the graph of followed by a reflection across the x-axis, and then a translation 3 units right. The domain is {x x 3}, and the range is {y y 0}. esolutions Manual - Powered by Cognero Page 7
8 70. This is a piecewise-defined function. Make a table of values. Be sure to include the domain values for which the function changes r 2 + r 14 = 0 For this equation, a = 2, b = 1, and c = 14. x g(x) Notice that both functions are linear. The solutions are 2.9 and z 2 z = 3 The domain is all real numbers, and the range is {y y 1}. Solve each equation by using the Quadratic Formula. Round to the nearest tenth if necessary. 72. r = 0 For this equation, a = 1, b = 0, and c = 25. Rewrite the equation in standard form. For this equation, a = 11, b = 1, and c = 3. The solutions are 0.5 and 0.6. There are no real positive square roots of 100. Therefore, the solution to this equation is ø. esolutions Manual - Powered by Cognero Page 8
9 Factor each polynomial, if possible. If the polynomial cannot be factored, write prime a 2 Write the prime factorization of each number x 4 2y The number 31 is prime. So, the prime factorization of 31 is x 3 3x 2 9x TOMATOES There are more than 10,000 varieties of tomatoes. One seed company produces seed packages for 200 varieties of tomatoes. For how many varieties do they not provide seeds? Let t be the number of varieties of tomatoes for which the seed company does not produce. Since the seed company produces packages for 200 varieties, the total number of varieties can be expressed as: t Since there are more than 10,000 varieties of tomatoes: t > 10,000. Solving, we get: t > 10, t > 9,800 esolutions Manual - Powered by Cognero Page 9
10-2 Simplifying Radical Expressions. Simplify each expression. 1. SOLUTION: 2. SOLUTION: 3. SOLUTION: 4. SOLUTION: 5. SOLUTION:
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