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4.1 1. Simplify your answer, use a comma to separate the answers as needed 3/5 + ½ = 1/x 10/11 2. Simplify your answer, use a comma to separate the answers as needed 3/7v + 7/v = 1 52/7 3. Simplify your answer, use a comma to separate the answers as needed 4/(x+5) = 6/x -15 4. Simplify your answer, a comma to separate the answers as needed. Type an exact answer, using radicals as needed. (x-3)/(x+1) = (x+5)/(x+3) -7/3 5. x=? 2/(x-1) + 3/(x+1)=3x/(x^2-1) 1/2 6. a=? 5-[(a-8)/(a+4)]=(a^2-4)/(a+4) 8 7. Solve. Simplify your answer; use a comma to separate the answers as needed (2a-1)=(a+17)/(a+1) -3, 3 8. One dude does job for 5 hrs, another dude the same job for 4 hrs. How long will it take them to do it together? 2 2/9 hours 9. One thing is 8 mph faster than another; it travels 310 miles in the same time it takes another to travel 270 miles. What’s the speed of each? 54 mph, 62 mph 10. A thing travels 132 miles for a walk in one direction in snow. The return trip in rain was finished at double the speed and took 3 hrs faster. Find the speed going. 22 mph 11. (Answered). 12. 2 lbs of muscle for every 7 lbs of body weight of an animal. For a 189 lbs animal, how much of the weight is muscle? 54 lbs 13. 10cm^3 of a normal specimen of human blood contains 1.2 g of hemoglobin. How many grams does 31 cm^3 of the same blood contain? 3.72 g 14. It is known that making 1 lb of honey requires 20,000 trips by bees to flowers to gather nectar. How many lbs of honey would 25,000 trips produce?1.25 lbs 15. Last season, Rockies player got 80 hits in 200 times at bat. If he expects to bat 600 times in whole season with the same ratio, how many hits can the player expect to have? 240 hits 16. Hat sizes are determined by measuring the circumference of one’s head in inches or cm’s. Use ration and proportion to complete the following table. Hat size Head Circumference Head Circumference (to nearest 1/5 inch) (to nearest cm) 6 7/8 21 3/5 55 7¾ 24 2/5 62 17. A sample of 129 firecrackers contained 9 duds. How many duds would you expect in a sample of 1419 firecrackers? 99 18. For the pair of similar triangles, find the value for x. X G Y Z F H Between X Z is 12 and between G and H is 4. (To solve this, some more data is required and is missing. Please clarify.) 19. Find the variation constant and an equation of variation where y varies directly as x and y =40 when x =4. k = 10, y = 10x 20. The number N of aluminum cans used each year varies directly as the number of people P using the cans. If 51 people use 14,484 cans in one year, how many cans are used in a city which has population of 1,954,000? 554,936,000 cans 21. Hooke’s Law. The distance d when a spring is stretched by a hanging object varies directly as the weight w of the object. If the distance is 30 cm when the weight is 2 kg what is the distance when the weight is 7 kg? 105 cm 22. Find the variation constant and an equation of variation where y varies inversely as x and y=10 when x=19. k = 190, y = 190/x 23. It takes 9 hrs for 5 cooks to prepare the food for a wedding rehearsal dinner. How long will it take 8 cooks to prepare the dinner? (a) What kind of variation applies to this situation: direct or inverse? Inverse (b) Solve the problem. 5 5/8 hours 24. The stopping distance d of a car after the breaks are applied varies directly as the square of the speed r. If a car traveling 70 mph can stop in 270 ft, how many feet will it take the same car to stop when it is traveling 30mph? 49.59 ft 4(2). 1. What is the principle square root of 6400? 80 2. Find the square root that is a real number: √-81= Square root is not a real number 3. Find each function value, if it exist f(t)=√t^2+1, f(0)= 1 4. Find the following. Assume that variable can be any real number: √(a+3)^2= |a + 3| 5. Simplify: 3√-27x^3 -3x 4 6. 10000 10 7. 4 (5a) ^4= 5a 8. Rewrite without exponents: x^1/3= 3x 9. Rewrite with rational exponents, simplify: 3 xy^2z x^(1/3) y^(2/3) z^(1/3) 10. Simplify completely: 8^-4/3 1/16 11. Use the laws of exponents to simplify: (6.5^5/4)/(6.5^6/7)= (6.5)^(11/28) 12. Rewrite using only rational positive exponents, simplify: (x^5/4)^-4/7= 1/[x^(5/7)] 13. Use rational exponents to simplify 6 x ^ 42 = x^-7 14. Use rational exponents to simplify: x^6 y^8 = x^3 y^4 15. Use rational exponents to rewrite: x^1/6*y^1/5*z^1/3= 30 (x^5 y^6 z^10) 16. Simplify by factoring, an exact answer using radicals as needed: 108 x ^ 4 = 6x^2 3 17. Simplify by factoring, an exact answer using radicals as needed: 4 810 = 3 410 18. Multiply and simplify. Assume that all expressions represent nonnegative numbers: 5x ^3 30 x 5x^2 6 19. Multiply and simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers: 3 y ^4 3 81y^5 = 81 y^4 y 20. Simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers: 4 48x^8 y ^10 = 2x^2 y^2 4(3y^2) 21. Simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers: 5 224x^17 y^20 = 2x^3 y^4 5(7x^2) 22. Multiply and simplify by factoring, an exact answer using radicals as needed: 80 * 90 = 602 23. Multiply and simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers: 5b ^3 55c ^ 4 = 5bc^2 (11b) 24. Divide. Then simplify by taking roots, if possible. Assume that all expressions under radicals represent positive numbers: 15aa = 5 3 25. Divide. Then simplify by taking roots, if possible. Assume that all expressions under radicals represent positive numbers: 3 32 a ^ 7b ^ 2 : 3 4a ^5b ^1 = 2a (2b) 26. Divide and simplify. Assume that all expressions under radicals represent nonnegative numbers: 4 3x : 7 x 28(2187x^3) 27. Simplify by taking roots of the numerator and the denominator. Assume that all 243x^3 expressions under radicals represent positive numbers: 5 = y ^ 20 (3/ y^4) 5(x^3) 28. Add or subtract. Simplify by collecting like radical items, if possible. Simplify, type exact answer using radicals as needed: 6*√3-4*√3+7*√3= 93 29. Add. Simplify by collecting like radical terms if possible. Simplify to exact answer: 7*√50+2*√18= 412 30. Add. Simplify by collecting like radical terms if possible, assuming that all expressions under radicals represent nonnegative numbers, an exact answer using radicals as needed: 2a +4* 8a ^3 = (1 + 8a) (2a) 31. Multiply, simplify, an exact answer using radicals as needed: √6*(9-10*√6)= 96 - 60 32. Multiply, simplify, an exact answer using radicals as needed: 3 a *( 3 3a ^ 2 + 3 81a ^ 2 )= 4a 33 33. Multiply, simplify, an exact answer using radicals as needed: (2+√5)(2-√5)= -1 34. Multiply. ( 5 4 - 5 2 )( 5 125 + 5 8 )= 5500 - 5250 + 2 - 516 35. Rationalize the dominator: (10*√3)/(3*√5)= (2/3) 15 36. Rationalize the dominator. Assume that all expressions under radicals represent positive numbers: 3 3y ^4 : 3 6x ^ 4 = (y/ 2x^2) 3(4x^2 y) 37. Rationalize the dominator. Assume that all expressions under radicals represent positive numbers: (2-√a)/(3+√a)= (6 - 5a + a)/(9 - a) 38. Rationalize the dominator. Assume that all expressions under radicals represent positive numbers, an exact answer using radicals as needed: (√a-√b)/(√a+√b)= [a + b - 2(ab)]/(a -- b).

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