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 Rectangles/577414: if the length of a rectangle is increased by 20% and the width is decreased by 20%then what will be the change in area and how much?1 solutions Answer 370271 by ankor@dixie-net.com(15652)   on 2012-02-24 21:21:33 (Show Source): You can put this solution on YOUR website!if the length of a rectangle is increased by 20% and the width is decreased by 20% then what will be the change in area and how much? : Multiplier for 20% increase = 1.2 Multiplier for 20% decrease = .8 : change in area: c = L * W - 1.2L*.8W c = 1LW - .96LW c = .04 which is a 4% change in area, how much will depend on the actual dimensions you're dealing with here :
 Geometry_Word_Problems/577617: I am a rectangular prism, so I have a height (h), a width (w) and a depth (d). Here are your clues to determining each of my dimensions...my depth is 3 more units than my width, my height is 1.5 units less than my depth, and the sum of my 3 dimensions is slightly > 25 units. Finally, my volume is 595 cubic units while my surface area is 429 square units. What are my 3 dimensions? List the depth, height and width 1 solutions Answer 370260 by ankor@dixie-net.com(15652)   on 2012-02-24 20:20:33 (Show Source): You can put this solution on YOUR website!I am a rectangular prism, so I have a height (h), a width (w) and a depth (d). : Write an equation for each statement: : " depth is 3 more units than my width," d = w + 3 or w = (d-3) : "height is 1.5 units less than my depth," h = (d-1.5) : "the sum of my 3 dimensions is slightly > 25 units." h + w + d > 25 : " volume is 595 cubic units" h*w*d = 595 : "surface area is 429 square units." 2(h*w) + 2(h*d) + 2(w*d) = 429 : Replace h and w in the sum equation h + w + d > 25 (d-1.5) + (d-3) + d > 25 3d - 4.5 > 25 3d > 25 + 4.5 3d > 29.5 d > 29.5/3 d > 9.833 d = 10 is the depth then w = 10-3 w = 7 is the width and h = 10-1.5 h = 8.5 is the height : Find vol with these values 8.5 * 7 * 10 = 595, checks out : Check the surface area 2(8.5*7) + 2(8.5(10) + 2(7*10) = 119 + 170 + 140 = 429 : Summarize: h = 8.5; w = 7; d = 10
 test/577384: The time (t) of travel of an automobile trip varies inversely as the speed (v). At an average speed of 65mph, a trip took 4h. The return trip took 5h. Find the average speed of the return trip.1 solutions Answer 370247 by ankor@dixie-net.com(15652)   on 2012-02-24 19:13:42 (Show Source): You can put this solution on YOUR website!The time (t) of travel of an automobile trip varies inversely as the speed (v). At an average speed of 65mph, a trip took 4h. The return trip took 5h. Find the average speed of the return trip. : Let s = the speed on the return trip ; the distance there and back is the same : Write a distance equation; dist = speed * time : 5s = 4(65) 5s = 260 s = 260/5 s = 52 mph on the return trip : : check solution by finding the distances, should be the same 65 * 4 = 260 52 * 5 = 260
 Exponents-negative-and-fractional/577373: Simplify to a normal looking fraction of whole numbers: (16/25)^-3/2.1 solutions Answer 370240 by ankor@dixie-net.com(15652)   on 2012-02-24 18:22:58 (Show Source): You can put this solution on YOUR website!(16/25)^-3/2. The reciprocal gets rid of the neg exponent 1/2 exponent is the square root of: : = []^3 = = =
 Expressions-with-variables/127778: Find the width and length of the rectangle so that it has the given perimeter: P = 60 inches, width is x, and length is 3x – 5. 1 solutions Answer 370223 by ankor@dixie-net.com(15652)   on 2012-02-24 17:10:02 (Show Source): You can put this solution on YOUR website!Find the width and length of the rectangle so that it has the given perimeter: P = 60 inches, width is x, and length is 3x – 5. : The perimeter equation: 2(3x-5) + 2x = 60 6x - 10 + 2x = 60 6x + 2x = 60 + 10 8x = 70 x = x = 8.75 is the width then 3(8.75) - 5 = 26.25 - 5 = 21.25 is the length : : Check the perimeter 2(21.25) + 2(8.75 = 42.5 + 17.5 = 60
 Quadratic_Equations/5549: the width of a rectangle is 3 inches less than its length. The area of the rectangle is 340 square inches. What are the length and widthof the rectangle?1 solutions Answer 370196 by ankor@dixie-net.com(15652)   on 2012-02-24 13:35:29 (Show Source): You can put this solution on YOUR website!he width of a rectangle is 3 inches less than its length. The area of the rectangle is 340 square inches. What are the length and width of the rectangle? : We know the Area is: L * W = 340 Given that,"The width of a rectangle is 3 inches less than its length." W = L - 3 Replace W with (L-3) in the area equation L * (L-3) = 340 L^2 - 3L = 340 L^2 - 3L - 340 = 0; a quadratic equation factors to (L-20)(L+17) = 0 The positive solution L = 20 inches is the Length then w = 20 - 3 = 17 inches is the width : : Check by finding the area: 20 * 17 = 340
 Travel_Word_Problems/577439: A man calculated that if his speed had been increased by 4km/h he would have completed his 48km journey 1 hour sooner.determine his speed. 1 solutions Answer 370170 by ankor@dixie-net.com(15652)   on 2012-02-24 08:14:48 (Show Source): You can put this solution on YOUR website!A man calculated that if his speed had been increased by 4km/h he would have completed his 48km journey 1 hour sooner. determine his speed. : Let s = his speed then (s+4) = his faster speed : Write a time equation: time = dist/speed : normal time - faster time = 1 hr - = 1 Multiply by s(s+4) s(s+4)* - s(s+4)* = 1s(s+4) cancel the denominators 48(s+4) - 48s = s^2 + 4s 48s + 192 - 48s = s^2 + 4s 0 = s^2 + 4s - 192 = 0 Factors to (s-12)(s+16) = 0 the positive solution s = 12 mph his speed : : Check this by finding the actual times 48/12 = 4 hrs 48/16 = 3 hrs --------------- diff is 1 hr
 Rectangles/576912: The length of a rectangle is 3cm less than twice the width. The perimeter of the rectangle is 72cm. Find the length and width of the rectangle. I need help setting up the correct formula to find the answer, I tried a couple and my answer is still wrong.1 solutions Answer 370154 by ankor@dixie-net.com(15652)   on 2012-02-23 21:49:06 (Show Source): You can put this solution on YOUR website!The length of a rectangle is 3cm less than twice the width. The perimeter of the rectangle is 72cm. Find the length and width of the rectangle. : The perimeter 2L + 2W = 72 : It say's,"The length of a rectangle is 3cm less than twice the width.". therefore: L = 2W - 3 : Replace L in the 1st equation with (2W-3) 2(2W-3) + 2W = 72 Mult what's inside the brackets 4W - 6 + 2W = 72 4W + 2W = 72 + 6 6W = 78 W = W = 13 : Now you should be able to find L. Then check the perimeter with those values
 Numbers_Word_Problems/576705: the sum of the two numbers is 380. the difference between the two numbers is 138. what is the smaller number and what is the greater number.1 solutions Answer 370153 by ankor@dixie-net.com(15652)   on 2012-02-23 21:39:49 (Show Source): You can put this solution on YOUR website!the sum of the two numbers is 380. the difference between the two numbers is 138. what is the smaller number and what is the greater number. : A good problem for the elimination method a + b = 380 a - b = 138 ---------------adding eliminates b, find a. Then find b, It's easy
 Exponential-and-logarithmic-functions/576749: The half-life of a radioactive substance is the time it takes for half of the substance to decay. The half-life if carbon-14 is 5700 years. A.) write a exponential function to model the decay of a 240-my sample. B.) explain what each value in the function model represents. C.) to the nearest hundredth, find the amount of carbon-14 remaining after 2353 years. Explain how you found this amount.1 solutions Answer 370013 by ankor@dixie-net.com(15652)   on 2012-02-23 08:42:10 (Show Source): You can put this solution on YOUR website!The half-life of a radioactive substance is the time it takes for half of the substance to decay. The half-life if carbon-14 is 5700 years. : The radioactive decay formula: A = Ao*2^(-t/h) where A = amt after t time Ao = initial amt (t=0) t = time of decay h = half-life of the substance : A.) write a exponential function to model the decay of a 240-my sample. A = 240(2^(-t/5700) : B.) explain what each value in the function model represents. see above : C.) to the nearest hundredth, find the amount of carbon-14 remaining after 2353 years. A = 240(2^(-2353/5700) A = 240(2^(-.4128)) using a calc A = 240*75116 A = 180.3 grams remain after 2,353 yrs
 Quadratic_Equations/576831: 3(x^2-3) = 35x + 19 please use the quadratic formula thankssss1 solutions Answer 370011 by ankor@dixie-net.com(15652)   on 2012-02-23 08:22:06 (Show Source): You can put this solution on YOUR website!3(x^2-3) = 35x + 19 put the equation in the standard form: ax^2 + bx^2 + c = 0 3x^2 - 9 - 35x - 19 = 0 3x^2 - 35x - 28 = 0 : the quadratic formula : a=3, b = -35; c = -28 : : Two solutions x = x = 12.42 and x = x = -.75 : : You can confirm this by replacing x in the original equation with these values
 Triangles/576714: what is the base of a right triangle with a height of 5 and a hypotenuse of 8? 1 solutions Answer 370009 by ankor@dixie-net.com(15652)   on 2012-02-23 08:00:22 (Show Source): You can put this solution on YOUR website!what is the base of a right triangle with a height of 5 and a hypotenuse of 8? : Got old Pythagoras out of bed for this one: a^2 + b^2 = c^2 5^2 + b^2 = 8^2 25 + b^2 = 64 b^2 = 64 - 25 b^2 = 39 b = b ~ 6.245 is the base : : You can check this on your calc: enter
 Graphs/576690: Please help me solve this equation. 3/5 (3x-3) > 91 solutions Answer 369968 by ankor@dixie-net.com(15652)   on 2012-02-22 21:53:30 (Show Source): You can put this solution on YOUR website!(3x-3) > 9 Get rid of that annoying fractions, multiply both sides by 5, results 3(3x-3) > 5(9) multiply what's inside the brackets 9x - 9 > 45 9x > 45 + 9 9x > 54 x > x > 6
 Mixture_Word_Problems/576674: Plese help me solve this problem: erika wants to dilute a 12% salt solution with water to make 36 ounces of 8% salt solution. How much water and how much 12% salt solution should she mix together?1 solutions Answer 369966 by ankor@dixie-net.com(15652)   on 2012-02-22 21:45:04 (Show Source): You can put this solution on YOUR website!dilute a 12% salt solution with water to make 36 ounces of 8% salt solution. How much water and how much 12% salt solution should she mix together? ; Let x = amt of 12% solution required the resulting amt is to be 36 oz, therefore (36-x) = amt of water required : Write an amt of salt equation, the amt of salt remains the same only the percent changes : .12x = .08(36) .12x = 2.88 x = x = 24 oz of 12% solution then 36 - 24 = 12 oz of water
 Human-and-algebraic-language/576539: The second of three numbers is 3 times the first. The third is 5 more than the second. If the second is decreased by twice the third. The result is 5. What are the three numbers? The greater of two numbers is 3 more than the smaller. If twice the smaller is added to the greater, the result is 30. What are the numbers? 1 solutions Answer 369955 by ankor@dixie-net.com(15652)   on 2012-02-22 21:20:26 (Show Source): You can put this solution on YOUR website!Let the three number be a, b, c : The second of three numbers is 3 times the first. b = 3a : The third is 5 more than the second. c = b+5 : If the second is decreased by twice the third, the result is 5. b - 2c = 5 From the above we can replace c with (b+5) b - 2(b+5) = 5 b - 2b + 10 = 5 -b = 5 - 10 -b = -5 b = 5 then c = 5 + 5 c = 10 and b = 3a 5 = 3a a = : What are the three numbers?: , 5, 10 : : The greater of two numbers is 3 more than the smaller. a = b+3 : If twice the smaller is added to the greater, the result is 30. a + 2b = 30 Replace a with (b+3) (b+3) + 2b = 30 3b = 30 - 3 3b = 27 b = b = 9 then a = 9 + 3 a = 12 : What are the numbers? 12 and 9
 Travel_Word_Problems/576301: Two airplanes depart simultaneously from an airport. One flies due south; the other flies due east at a rate 30 mph faster than that of the first airplane. After 3 hours, radar indicates that the airplanes are 450 miles apart. What is the ground speed of each airplane1 solutions Answer 369902 by ankor@dixie-net.com(15652)   on 2012-02-22 19:20:30 (Show Source): You can put this solution on YOUR website!Two airplanes depart simultaneously from an airport. One flies due south; the other flies due east at a rate 30 mph faster than that of the first airplane. After 3 hours, radar indicates that the airplanes are 450 miles apart. What is the ground speed of each airplane. : let s = speed of the southbound airplane then (s+30) = speed of the eastbound : dist = time * speed, therefore 3s = distance traveled by the southbound plane and 3(s+30) = distance traveled by the eastbound plane : This is a right triangle problem: a^2 + b^2 = c^2, where a = 3s b = 3(s+30) c = 450 : (3s)^2 + (3(s+30))^2 = 450^2 9s^2 + (3s+90)^2 = 202500 9s^2 + 9s^2 + 270s + 270s + 8100 - 202500 = 0 18s^2 + 540s - 194400 = 0 simplify, divide by 18 s^2 + 30s - 10800 = 0 you can use the quadratic formula to find s, but this will factor to: (s+120)(s-90) = 0 the positive solution is all we want here s = 90 mph, speed of the southbound plane then 90+30 = 120 mph, speed of the eastbound : : Check this out on your calc: enter results 450
 Miscellaneous_Word_Problems/576244: what numbers have a sum of 36 and difference of 81 solutions Answer 369860 by ankor@dixie-net.com(15652)   on 2012-02-22 16:59:16 (Show Source): You can put this solution on YOUR website!what numbers have a sum of 36 and difference of 8 a + b = 36 a - b = 8 --------------addition eliminates b, find a, then find b
 Travel_Word_Problems/576213: Mrs. Sanchez ran 3/5 of a mile. Mrs. Fritz ran 2/3 as far as Mrs. Sanchez. How far did Mrs. Fritz run? How much farther than Mrs. Fritz did Mrs. Sanchez run? Show work.1 solutions Answer 369857 by ankor@dixie-net.com(15652)   on 2012-02-22 16:53:52 (Show Source): You can put this solution on YOUR website!Mrs. Sanchez ran 3/5 of a mile. Mrs. Fritz ran 2/3 as far as Mrs. Sanchez. How far did Mrs. Fritz run? * = reduces to mi by Fritz (you could have just canceled the 3's) : How much farther than Mrs. Fritz did Mrs. Sanchez run? - = mi further
 Age_Word_Problems/576434: I am desperately trying to help my niece with homework while her parents are out of town. I am not a math guru. Here is the word problem: Joe is 2 years older than his brother. The sum of their ages is 12. How old is his brother? She knows the answers are ages 5 and 7 (5+7=12) but I do not know how to help her figure out the mathematical equation. Can you PLEASE HELP????1 solutions Answer 369856 by ankor@dixie-net.com(15652)   on 2012-02-22 16:46:23 (Show Source): You can put this solution on YOUR website!Let j = Joe's age Let b = his brother's age ; Write an equation for each statement : "Joe is 2 years older than his brother." j = b + 2 : "The sum of their ages is 12." j + b = 12 In first equation we know that j = (b+2), replace j with (b+2) in the above equation (b+2) + b = 12 add the b's 2b + 2 = 12 subtract 2 from both sides 2b = 12 - 2 2b = 10 Divide both sides by 2 b= 10/2 b = 5 yrs is brothers age. : Use the 1st equation to find Joes age : Check your solutions in the 2nd equatiion
 Probability-and-statistics/575827: travis is talking out a loan for \$35,000. it is a 10-year loan with an APR of 8.5% . what will his monthly payment be?1 solutions Answer 369713 by ankor@dixie-net.com(15652)   on 2012-02-21 21:56:08 (Show Source): You can put this solution on YOUR website!\$433.95 a month
 Age_Word_Problems/575980: Three siblings have a combines age of 108 yrs. The oldest is 8 years older than the youngest. what are the ages of the siblings?1 solutions Answer 369709 by ankor@dixie-net.com(15652)   on 2012-02-21 21:41:14 (Show Source): You can put this solution on YOUR website!Three unknowns, two equations, calls for some reasoning here. Three siblings have a combined age of 108 yrs. a + b + c = 108 ; The oldest is 8 years older than the youngest. a = c + 8 : a + b + c = 108 (c+8) + b + c = 108 2c + b = 108 - 8 2c = b = 100 b = -2c + 100 we know b is < 8 and > 1 yr more than c c = 31 b = -2(31) + 100 b = 38 or c = 32 b = -2(32) + 100 b = 36 and c = 33 b = -2(33) + 100 b = 34 : So we have three possibilities: a = 39 b = 38 c = 31 or a = 40 b = 36 c = 32 or a = 41 b = 34 c = 33
 Volume/576042: What is the volume of a cylinder whose radius is 2 1/6 and the height is 1 1/2?1 solutions Answer 369704 by ankor@dixie-net.com(15652)   on 2012-02-21 21:09:53 (Show Source): You can put this solution on YOUR website!What is the volume of a cylinder whose radius is 2 1/6 and the height is 1 1/2? Chance 2 1/6 to 13/6 and 1 1/5 to 1.5 : V = *1.5 V = 22.12 cu/units
 Word_Problems_With_Coins/575781: how do you write one more than twice as many is three?1 solutions Answer 369701 by ankor@dixie-net.com(15652)   on 2012-02-21 21:04:00 (Show Source): You can put this solution on YOUR website!how do you write one more than twice as many is three? 2x + 1 = 3
 Polynomials-and-rational-expressions/576034: Factor Completely: (please provide steps) x^4y-81y^5 thanks for your help1 solutions Answer 369697 by ankor@dixie-net.com(15652)   on 2012-02-21 20:59:27 (Show Source): You can put this solution on YOUR website! Factor out y The difference of squares will factor to one more difference of squares
 Travel_Word_Problems/575977: a bus travels 1800m from your school to the first stop.the entire trip takes 2 minutes what is the average speed of the bus in meters per second?1 solutions Answer 369693 by ankor@dixie-net.com(15652)   on 2012-02-21 20:50:58 (Show Source): You can put this solution on YOUR website!a bus travels 1800m from your school to the first stop.the entire trip takes 2 minutes what is the average speed of the bus in meters per second? : Change 2 min to 120 sec : = 15 m/sec
 Percentage-and-ratio-word-problems/575934: If it takes 4 hours for 3 paint mixers to mix a fixed amount of paint.The number of hours varies inversely as the number of paint mixers used. How long would it take 8 paint mixers to do the same job?1 solutions Answer 369691 by ankor@dixie-net.com(15652)   on 2012-02-21 20:44:16 (Show Source): You can put this solution on YOUR website!If it takes 4 hours for 3 paint mixers to mix a fixed amount of paint. Find how many man-hours to do the job 3 * 4 = 12 man-hrs to complete the job : How long would it take 8 paint mixers to do the same job? let h = no. of hrs to do it with 6 men 8h = 12 h = 12/8 h = 1.5 hrs for 8 men to do it
 Quadratic_Equations/575890: A rain gutter is to be made of a sheet that is 10in wide by turning up the edges 90 degrees. I have developed the formula for the cross sectional area by letting x define the unknown quantity of depth that is to be the independent value. my formula is f(x)= 2x^2 + 10x My question is, what happens to the cross sectional area as depth size increases? What x and y values make sense for this problem? (restricted domain and range)1 solutions Answer 369690 by ankor@dixie-net.com(15652)   on 2012-02-21 20:40:06 (Show Source): You can put this solution on YOUR website!A rain gutter is to be made of a sheet that is 10in wide by turning up the edges 90 degrees. : Using the depth as x, then (10-2x) = the width of the gutter ; y = the cross sectional area : y = depth * width y = x(10-2x) y = -2x^2 + 10x or f(x) = -2x^2 + 2x : Graphing this would make it clear You can see the domain is >0 to < 5, with max area when x= 2.5
 Average/576018: Show me how one arrive at the answer 77 for this problem. A total of 50 juniors and seniors were given a mathematics test. The 35 juniors attained and average score of 80 while the 15 seniors attained an average of 70. What was the average score for all 50 students who took the test? I know the answer is 77. I'm just not sure how to arrive at this answer. Is there a algebra formula that one can use to solve this problem and if so would you show me how to solve it using the algebra formula? My e-mail is zippor21@gmail.com1 solutions Answer 369688 by ankor@dixie-net.com(15652)   on 2012-02-21 20:28:48 (Show Source): You can put this solution on YOUR website!A total of 50 juniors and seniors were given a mathematics test. The 35 juniors attained and average score of 80 while the 15 seniors attained an average of 70. What was the average score for all 50 students who took the test? : av =
 Age_Word_Problems/575757: In 55 years, William will be 6 times as old as he is right now. How old is he right now?1 solutions Answer 369687 by ankor@dixie-net.com(15652)   on 2012-02-21 20:25:28 (Show Source): You can put this solution on YOUR website!In 55 years, William will be 6 times as old as he is right now. How old is he right now? : Let w = his age now : w + 55 = 6w 55 = 6w - w 55 = 5w w = 55/5 w = 1 yrs is his present age
 Money_Word_Problems/575970: What Number increased by 12% and then decreased by 12% = 86.7328 I can't set up the equation properly, Thanks in advance for your help. 1 solutions Answer 369685 by ankor@dixie-net.com(15652)   on 2012-02-21 20:18:50 (Show Source): You can put this solution on YOUR website!What Number increased by 12% and then decreased by 12% = 86.7328 : an increase of 12%, the multiplier is 1.12 a decrease of 12%, the multiplier is .88 : .88(1.12x) = 86.7328 .9856x = 86.7328 x = x = 88
 Rate-of-work-word-problems/575909: You have a rectangular pool that is 20 ft by 10 ft and a depth of 8ft. How do I solve and find out how much water you need to fill the pool? Also i would like to know how I can use pythagoreans theorem to solve it.1 solutions Answer 369672 by ankor@dixie-net.com(15652)   on 2012-02-21 19:27:11 (Show Source): You can put this solution on YOUR website!You have a rectangular pool that is 20 ft by 10 ft and a depth of 8ft. How do I solve and find out how much water you need to fill the pool? : you don't need Pythag for this, just know that 1 cu/ft of water = 7.481 gallons : 20 * 10 * 8 * 7.481 = 11,969.6 gallons