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 test/285928: If log a=2 and log b=3, what is the numerical value of log?1 solutions Answer 207354 by ankor@dixie-net.com(16527)   on 2010-03-27 20:05:31 (Show Source): You can put this solution on YOUR website!If log a=2 and log b=3, what is the numerical value of log? : We know that if: log a=2; then a=100 and log b=3; then b=1000 : Write it: log = log = -8
 Rate-of-work-word-problems/285946: what equation would be used to find the value of 3 consecutive integers such that twice the smallest is twelve more than than the largest?1 solutions Answer 207348 by ankor@dixie-net.com(16527)   on 2010-03-27 19:48:21 (Show Source): You can put this solution on YOUR website!what equation would be used to find the value of 3 consecutive integers such that twice the smallest is twelve more than than the largest? : How about: 2x = (x+2) + 12 : Where the three integers are x, (x+1), (x+2)
 Linear-equations/285659: Life Span Some scientists believe there is a limit to how long humans can live.* One supporting argument is that during the last century, life expectancy from age 65 has increased more slowly than life expectancy from birth, so eventually these two will be equal, at which point, according to these scientists, life expectancy should increase no further. In 1900, life expectancy at birth was 46 yr, and life expectancy at age 65 was 76. In 2000, these figures had risen to 76.9 and 82.9, respectively. In both cases, the increase in life expectancy has been linear. Using these assumptions and the data given, find the maximum life expectancy for humans.1 solutions Answer 207169 by ankor@dixie-net.com(16527)   on 2010-03-26 21:15:29 (Show Source): You can put this solution on YOUR website!Some scientists believe there is a limit to how long humans can live. One supporting argument is that during the last century, life expectancy from age 65 has increased more slowly than life expectancy from birth, so eventually these two will be equal, at which point, according to these scientists, life expenctancy should increase no further. In 1900, life expectancy at birth was 46yr, and life expectancy at age 65 was 76. In 2000, these figures had risen to 76.9 and 82.9 , respectively. IN both cases, the increase in life expectancy has been linear. Using these assumptions and the data given, find the maximum life expectancy for humans. : Let x = number of yrs from 1900 (1900 = 0 and 2000 = 100) : Let y = yrs of life expected : Determine the "from birth" equation x1 = 0; y1 = 46 x2 = 100; y2 = 76.9 : Find the slope: m = (y2-y1)/(x2-x1) m = (76.9 - 46)/(100-0) = 30.9/100 = .309 is the slope : Find the equation using y - y1 = m(x-x1) y - 46 = .309(x - 0) y = .309x + 46 : : Determine the "from age 65" equation (green): x1 = 0; y1 = 76 x2 =100; y2 = 82.9 : Find the slope: m = (82.9-76)/(100 - 0) = 6.9/100 = .069 is the slope Find the equation: y - 76 = .069(x - 0) y = .069x + 76 : Max life expectancy is said to occur when these two lines intersect: Age = vertical axis, year = horizontal : : To solve, put equations into the standard form to solve: -.309x + y = 46 -.069x + y = 76 -----------------subtracting eliminates y -.24x = -30 x = -30/-.24 x = 125 yrs, (the year 2025) : Find the actual age this occurs, find y: -.069(125) + y = 76 -8.625 + y = 76 y = 76 + 8.625 y = 84.625 max age :
 Travel_Word_Problems/279456: A student begins to walk along a straight road at the rate of 3 km/h to the next town which is 18 km away. After 10 minutes a car picks him up and in 15 more minutes he is in town. How fast was the car traveling? (the time is in minutes which throws me for a loop)1 solutions Answer 203215 by ankor@dixie-net.com(16527)   on 2010-03-10 21:46:27 (Show Source): You can put this solution on YOUR website!A student begins to walk along a straight road at the rate of 3 km/h to the next town which is 18 km away. After 10 minutes a car picks him up and in 15 more minutes he is in town. How fast was the car traveling? : Let's put all the times in hrs and see what we have 10/60 = hr : 15/60 = hr : Let s = the speed the car is traveling : Write a dist equation: dist = speed * time : Walk dist + ride dist = 18 km 3* + s = 18 3 cancels into six so we have + s = 18 Multiply by 4 to get rid of the denominators; results: 2 + s = 4(18) : s = 72 - 2 s = 70 km/hr is the speed of the car ; ; Check solution by finding the total dist 3* + (70) = .5 + 17.5 = 18 : : Did this straighten things out for you?
 Travel_Word_Problems/279459: A cross country skier walks 3000m up a mountain road, rests for 10 minutes and then skis down the road. he returns a half hour after he started. if he skis four times as fast as he walks, at what rate does he ski? ( having a hard time grasping these word problems and what dictates a constant factor and how to build the equation.1 solutions Answer 203204 by ankor@dixie-net.com(16527)   on 2010-03-10 21:20:10 (Show Source): You can put this solution on YOUR website!A cross country skier walks 3000m up a mountain road, rests for 10 minutes and then skis down the road. he returns a half hour after he started. if he skis four times as fast as he walks, at what rate does he ski? : Change half hour to 30 min : Let w = his walking speed (in meters/minute) then 4w = his skiing speed : Write a time equation: time = dist/speed : up time + 10 min + down time = 30 min + 10 + = 30 Multiply by 4W,results 4(3000) + 4w(10) + 3000 = 4w(30) : 12000 + 40w + 3000 = 120w : 12000 + 3000 = 120w - 40w : 15000 = 80w w = w = 187.5 m/min; his walking speed and 4(187.5) = 750 m/min is his skiing speed : That would be: = 45 km/hr : : Check solution by finding the times 3000/187.5 = 16 min resting time:10 min 3000/750.0 = 4 min --------------------- total time = 30 min; confirms our solution
 Travel_Word_Problems/279305: A plane flying the 3020-mile trip from City A to City B has a 60-mph tailwind. The flight's point of no return is the point at which the flight time required to return to City A is the same as the time required to continue to City B. If the speed of the plan in still air is 430 mph, how far from City A is the point of no return? 1 solutions Answer 203162 by ankor@dixie-net.com(16527)   on 2010-03-10 20:01:59 (Show Source): You can put this solution on YOUR website!A plane flying the 3020-mile trip from City A to City B has a 60-mph tailwind. The flight's point of no return is the point at which the flight time required to return to City A is the same as the time required to continue to City B. If the speed of the plan in still air is 430 mph, how far from City A is the point of no return? : Determine the speeds 430+60 = 490 mph toward city B (with the wind) 430-60 = 370 mph back to city A (against the wind) : Let d = distance from City A to the point of no return then (3020-d) = distance from city B to this point : At this point the travel time to each city will be the same Write a time equation; Time = dist/speed : Time to return against the wind = time to continue with the wind = Cross multiply 490d = 370(3020-d) : 490d = 1117400 - 370d : 490d + 370d = 1117400 : 860d = 1117400 d = d = 1299.3 miles from A : : You can prove this: 3020 - 1299.3 = 1720.7 to city B Time back to A: 1299.3/370 = 3.511 hrs Time on to B: 1720.7/490 = 3.511 hrs also : Did this make sense to you?
 Expressions-with-variables/279277: Tallest candle is 16 centimeters. For each hour it burna, the candle loses 2.5 centimeters its height. The shortest candle is 12 centimeters and it loses 1.5 centimeter its height for each hour it burns. Determine whether these 2 candles would ever reach the same height it allows to burn the same length of time. Also, what height the 2 candles would be at that time. if it is possible why it could not happen and what would it need to be true in order for them to be able to reach the same height. Please use the multiple representation and justify the results and explain your thinking. Thank you.1 solutions Answer 203104 by ankor@dixie-net.com(16527)   on 2010-03-10 15:26:17 (Show Source): You can put this solution on YOUR website!Tallest candle is 16 centimeters. For each hour it burns, the candle loses 2.5 centimeters its height. The shortest candle is 12 centimeters and it loses 1.5 centimeter its height for each hour it burns. Determine whether these 2 candles would ever reach the same height it allows to burn the same length of time. Also, what height the 2 candles would be at that time. if it is possible why it could not happen and what would it need to be true in order for them to be able to reach the same height. Please use the multiple representation and justify the results and explain your thinking. : Let t = no. hrs for the two candles to be equal : 16-2.5t = 12-1.5t 16 - 12 = -1.5t + 2.5t 4 = t, will the same height in 4 hrs : what height the 2 candles would be at that time. 16 - 2.5(4) = 6 cm check the smaller candle 12 - 1.5(4) = 6 cm also
 Square-cubic-other-roots/279187: sqrt(x+11)=sqrt(x) +1 im not sure how to solve for this1 solutions Answer 203060 by ankor@dixie-net.com(16527)   on 2010-03-10 11:15:43 (Show Source): You can put this solution on YOUR website!sqrt(x+11) = sqrt(x) +1 Square both sides x + 11 = (sqrt(x) + 1)^2 FOIL the right side x + 11 = x + sqrt(x) + sqrt(x) + 1 : x + 11 = x + 2sqrt(x) + 1 ; x - x + 11 - 1 = 2sqrt(x) : 10 = 2sqrt(x) Square both sides 100 = 4x x = 100/4 x = 25 : You can check solution in original problem
 Pythagorean-theorem/279050: Ok, there is a problem in my worksheet that gives me the following information: Perimeter of the Rectangle: 68cm Area of the Rectangle: 144sq. cm and its asking for the length of the diagonal, how do i solve this? it does not give any dimensions (Width, Height) If you can help me, id love it. Thank You 1 solutions Answer 202972 by ankor@dixie-net.com(16527)   on 2010-03-09 21:50:37 (Show Source): You can put this solution on YOUR website!gives me the following information: : Start by using L for Length, W for width : Perimeter of the Rectangle: 68cm 2L + 2W = 68 Simplify, divide by 2 L + W = 34 or W = (34-L) : Area of the Rectangle: 144sq. cm L * W = 144 Substitute (34-L) for W L * (34-L) = 144 34L - L^2 = 144 Arrange as a quadratic equation -L^2 + 34L - 144 = 0 We have to solve this using the quadratic formula In this equation: x=L; a=-1; b=34; c=-144 : : Two solutions L = L = +4.958 and L = L = +29.0415 : the larger 29.0415 cm is the length the smaller 4.958 cm is the width : Check our solution by finding the perimeter with a calc 2(29.0415) + 2(4.958) = 67.999 ~ 68 : and its asking for the length of the diagonal, now we have the dimensions: Use pythag for this: c = , : c = c = 29.462 is the diagonal
 Linear_Equations_And_Systems_Word_Problems/279020: This word problem came out of the quadratic section. The length of a rectangle is 2 ft longer than the width. If the area is 16ft^2, then what are the length and the width? Thank you so much.1 solutions Answer 202965 by ankor@dixie-net.com(16527)   on 2010-03-09 21:20:38 (Show Source): You can put this solution on YOUR website!The length of a rectangle is 2 ft longer than the width. L = (W+2) : If the area is 16ft^2, then what are the length and the width? L * W = 16 : Substitute (W+2) for L (W+2)*W = 16 W^2 + 2W = 16 W^2 + 2W - 16 = 0; a quadratic equation use the quadratic formula: In this equation: x=W; a=1; b=2; c=-16 : : We want the positive solution here W = W = 3.123 ft is the width then 3.123 + 2 = 5.123 ft is the length ; Check solution by finding the area: 3.123 * 5.123 = 15.999 ~ 16
 Miscellaneous_Word_Problems/278864: The resistance, R, in ohms varies directly as its length, L, in feet and inversely as the square of the diameter, d, in inches of the wire. Write an equation that expresses this variation1 solutions Answer 202962 by ankor@dixie-net.com(16527)   on 2010-03-09 20:57:59 (Show Source): You can put this solution on YOUR website!The resistance, R, in ohms varies directly as its length, L, in feet and inversely as the square of the diameter, d, in inches of the wire. Write an equation that expresses this variation : R =
 Age_Word_Problems/278836: Paul's father is 2 years older than his mother. Paul's age is one third his father's age. When Paul was born, the sum of his parent's age was 42. How old are Paul's parents now?1 solutions Answer 202942 by ankor@dixie-net.com(16527)   on 2010-03-09 19:16:25 (Show Source): You can put this solution on YOUR website!Paul's father is 2 years older than his mother. Paul's age is one third his father's age. When Paul was born, the sum of his parent's age was 42. How old are Paul's parents now? : Let f = father's present age Let m = mother's present age Let p = paul's present age : "Paul's father is 2 years older than his mother." f = m - 2 or m = f + 2 : "Paul's age is one third his father's age." p = f : " When Paul was born, the sum of his parent's age was 42." (f-p) + (m-p) = 42 : In the above equation, replace p with f and m with (f+2) (f - f) + (f+2) - (f) = 42 : f + f + 2 - f = 42 ; f + f - f = 42 - 2 : f + f - f = 40 : f + f = 40 multiply by 3: 2f + 2f = 3(40) 4f = 120 f = f = 30 yrs and m = 32 : Father is 30, mother is 32 ; : Check solution by finding P's age (30) = 10 yrs is Paul,s age : Check solution in the statement: "" When Paul was born, the sum of his parent's age was 42." (30-10) + (32-10) = 42
 Volume/278750: A large fish tank has a rectangular base that is 6 ft. by 4 ft. The tank currently contains water at a height of 21/2 ft. What volume of water (in cubic ft.) must be added to the tank to make the water level measure 3 ft. deep? 1 solutions Answer 202784 by ankor@dixie-net.com(16527)   on 2010-03-09 08:16:33 (Show Source): You can put this solution on YOUR website!What exactly is 21/2 ft? Does that mean 10.5 ft? 6 by 3 by 10.5 then?
 real-numbers/278778: i must simplify (2+3i)(2-3i) i think the answer is 4-9i is that correct1 solutions Answer 202782 by ankor@dixie-net.com(16527)   on 2010-03-09 08:10:51 (Show Source): You can put this solution on YOUR website!i must simplify (2+3i)(2-3i) i think the answer is 4-9i is that correct : If you FOIL this you have: 4 - 6i + 6i - 9(i^2) : 6i's cancel and i^2 = -1 so you have: 4 - 9(-1) : 4 + 9 = 13 is the solution
 Travel_Word_Problems/278671: Frank rides his bike 12 miles an hour faster than he walks. He can bike from home to work in the same amount of time it takes him to walk from home to the park. If the distance from Frank's home to work is 9 miles, and the distance from his home to the park is 3 miles, what is Franks walking speed?1 solutions Answer 202741 by ankor@dixie-net.com(16527)   on 2010-03-08 21:57:03 (Show Source): You can put this solution on YOUR website!Frank rides his bike 12 miles an hour faster than he walks. He can bike from home to work in the same amount of time it takes him to walk from home to the park. If the distance from Frank's home to work is 9 miles, and the distance from his home to the park is 3 miles, what is Franks walking speed? : Let w = walking speed then (w+12) = biking speed : Write a time equation; time = dist/speed : time to work = time to park = cross multiply 9w = 3(w+12) : 9w = 3w + 36 : 9w - 3w = 36 " 6w = 36 w = w = 6 mph is his walking speed : : Check solution by finding the times, should be equal 9/18 = .5 hr 3/6 = .5 hrs also
 Age_Word_Problems/278577: Molly's age is twice Anitas. If the sum of the squares of thier ages is 80, then what are their ages?1 solutions Answer 202731 by ankor@dixie-net.com(16527)   on 2010-03-08 21:26:02 (Show Source): You can put this solution on YOUR website!Molly's age is twice Anitas. If the sum of the squares of their ages is 80, then what are their ages? : m = 2a : m^2 + a^2 = 80 : Replace m with 2a (2a)^2 + a^2 = 80 : 4a^2 + a^2 = 80 : 5a^2 = 80 : a^2 = a^2 = 16 a = 4 then m = 8 : : Check 4^2 + 8^2 = 80
 Rectangles/278642: PLEASE HELP ME ANSWER THIS: a rectangle with length 16 and width 4 has the same area as a square. what is the length of a side of the square?1 solutions Answer 202723 by ankor@dixie-net.com(16527)   on 2010-03-08 21:12:09 (Show Source): You can put this solution on YOUR website!a rectangle with length 16 and width 4 has the same area as a square. what is the length of a side of the square : Let s = side of the square s = : s = 8
 Travel_Word_Problems/278605: Angelina drove at an average rate of 80 kph and then stopped 20 minutes for gas. After the stop, she drove at an average rate of 100kph. Altogether she drove 250km in a total trip of 3 hours including the stop. Which equation could be used to solve for the time T in hours that she drove before her stop?1 solutions Answer 202721 by ankor@dixie-net.com(16527)   on 2010-03-08 21:07:54 (Show Source): You can put this solution on YOUR website!Angelina drove at an average rate of 80 kph and then stopped 20 minutes for gas. After the stop, she drove at an average rate of 100kph. Altogether she drove 250km in a total trip of 3 hours including the stop. Which equation could be used to solve for the time T in hours that she drove before her stop? : Change 20 min to 20/60 = 1/3 hr : Let T = time driving at 80 km/hr then (3-T-) = driving time at 100 km/hr : write a distance equation; Dist = speed * time : 80T + 100(3-T-) = 250 80T + 100(2.67-T) = 250 : 80T + 267 - 100t = 250 80T - 100T = 250 - 267 -20T = -17 T = T = +.85 hrs at 80 km/hr
 Word_Problems_With_Coins/278456: I subscribe to the Comic-of-the- Month Club. Each month I can buy any number of the 48 titles offered by the club. The first month I bought five comics for \$3.07. The second month I bought two comics for \$1.72. The next month I bought six of the club offerings for \$3.52. In May I bought three more for \$2.17. The club charges a fee for each comic and a handling fee for the entire order. How much would it have cost to buy all 48 titles at the same time? I need to solve using a guess and check table.1 solutions Answer 202708 by ankor@dixie-net.com(16527)   on 2010-03-08 20:02:44 (Show Source): You can put this solution on YOUR website!I subscribe to the Comic-of-the- Month Club. Each month I can buy any number of the 48 titles offered by the club. The first month I bought five comics for \$3.07. The second month I bought two comics for \$1.72. The next month I bought six of the club offerings for \$3.52. In May I bought three more for \$2.17. The club charges a fee for each comic and a handling fee for the entire order. How much would it have cost to buy all 48 titles at the same time? : Let c = cost of each comic including the fee Let h = handling fee per order : Write equation for the 1st two transactions 5c + h = 3.07 2c + h = 1.72 ----------------subtraction eliminates h, find c 3c = 1.35 c = c = .45 for each comic : Find h 5(.45) + h = 3.07 2.25 + h = 3.07 h = 3.07 - 2.25 h = .82 is the handling fee : Confirm this by checking it in the 3rd transaction 6(.45) + .82 = 3.52 2.70 + .82 = 3.52 : All 48 comics 48(.45) + .82 = \$22.42
 Travel_Word_Problems/278560: Mrs. Casey is in charge of making sandwiches in the lunchroom. She can make 4 sandwiches in 2 minutes. One Monday, she must make 400 sandwiches by 12:00 noon. What time does she need to start? Please provide step by step instruction, I am helping my child.1 solutions Answer 202704 by ankor@dixie-net.com(16527)   on 2010-03-08 19:21:28 (Show Source): You can put this solution on YOUR website!Mrs. Casey is in charge of making sandwiches in the lunchroom. She can make 4 sandwiches in 2 minutes. One Monday, she must make 400 sandwiches by 12:00 noon. What time does she need to start? : Find out how many sandwiches per minute = 2 sandwiches per minute : Find number minutes to make 400 sandwiches = 200 minutes : Change minutes to hrs = 3 hrs or 3 hrs 20 min : Find the time 12 - 3 = 8 hrs or 8:40, she needs to start : : You can check this by finding number of minutes from 8:40 to 12:00 3(60) + 20 = 200 min * 2 = 400 sandwiches
 Travel_Word_Problems/278558: an aircraft flew 2 hours with the wind. the return trip took 3 hours against the wind. if the speed of the plane in still air is 164 miles per hour more than the speed of the wind, find the wind speed and the speed of the plane in still air1 solutions Answer 202692 by ankor@dixie-net.com(16527)   on 2010-03-08 19:05:00 (Show Source): You can put this solution on YOUR website!an aircraft flew 2 hours with the wind. the return trip took 3 hours against the wind. if the speed of the plane in still air is 164 miles per hour more than the speed of the wind, find the wind speed and the speed of the plane in still air : (164 + w) = aircraft speed in still air then 164 = aircraft speed against wind and (164 + 2W) = aircraft speed with the wind : The two trips are equal distance, write a distance equation : 2(164+2W) = 3(164) 328 + 4W = 492 4W = 492 - 328 4W = 164 W = W = 41 mph is the speed of the wind then 164 + 41 = 205 mph is speed of the plane : : Check solutions by finding the distance, they should be equal 2(205+41) = 492 mi 3(205-41) = 492
 Travel_Word_Problems/278495: a train leaves a station at 1pm travelling at 40mph. Another train leaves the same station at 2pm travelling at 60mph. What time will it be when the two trains first meet?1 solutions Answer 202684 by ankor@dixie-net.com(16527)   on 2010-03-08 17:48:17 (Show Source): You can put this solution on YOUR website!a train leaves a station at 1pm traveling at 40mph. Another train leaves the same station at 2pm traveling at 60mph. What time will it be when the two trains first meet? : Let t = travel time of the 60 mph train then (t+1) = travel time of the 50 mph train : When one train overtakes the other train, they will have traveled the same distance : Write a distance equation: dist = speed * time 60t = 50(t+1) 60t = 50t + 50 60t - 50t = 50 10t = 50 t = 5 hrs : 2 PM + 5 hrs = 7 PM : : Confirm solution by finding the distances 60(5) = 300 50(6) = 300 mi
 Rectangles/278450: A rectangular field 15 feet wide is enclosed by a fence. If the area of the field is 360 square feet, how many feet of fencing are used to enclose the field?1 solutions Answer 202661 by ankor@dixie-net.com(16527)   on 2010-03-08 15:51:24 (Show Source): You can put this solution on YOUR website!A rectangular field 15 feet wide is enclosed by a fence. If the area of the field is 360 square feet, how many feet of fencing are used to enclose the field? : Find the length of the field, L * W = 360; therefore L = L = 24 ft is the length ; Find the perimeter to find the amt of fence required P = 2L + 2W P = 2(24) + 2(15) P = 48 + 30 P = 78 ft of fence
 Graphs/278441: I have to sketch the graph of each line y=-1/5x-21 solutions Answer 202658 by ankor@dixie-net.com(16527)   on 2010-03-08 15:45:48 (Show Source): You can put this solution on YOUR website!Assume the problem is : y = x - 2 : Choose two convenient values for x, and find y x = 0; y = -2 and x = 5; y = -3 : Plot these two points, should look like this:
 Miscellaneous_Word_Problems/278506: The current I in an electrical conductor varies inversely as the resistance R of the conductor. If the current is 0.5 amperes when the resistance id 240 ohms, What is the current when the resistance is 960 ohms?1 solutions Answer 202656 by ankor@dixie-net.com(16527)   on 2010-03-08 15:36:17 (Show Source): You can put this solution on YOUR website!The current I in an electrical conductor varies inversely as the resistance R of the conductor. If the current is 0.5 amperes when the resistance id 240 ohms, What is the current when the resistance is 960 ohms? : Find the volts (E) E = I*R E = .5 * 120 E = 120 volts : Find current when resistance = 960 0hms I = I = I = .125 amps
 Rate-of-work-word-problems/278501: A swimming pool can be filled in 12 hours if water enters through a pipe alone, or in 28 hours if water enters through a hose alone. If the water is entering through both the pipe and the hose, how long will it take to fill this pool?1 solutions Answer 202655 by ankor@dixie-net.com(16527)   on 2010-03-08 15:28:48 (Show Source): You can put this solution on YOUR website!A swimming pool can be filled in 12 hours if water enters through a pipe alone, or in 28 hours if water enters through a hose alone. If the water is entering through both the pipe and the hose, how long will it take to fill this pool? : Let t = time required when both are used : Let the completed job (a full pool) = 1 : A typical mixture equation + = 1 Multiply equation by 84 to clear the denominators, results 7t + 3t = 84 t = t = 8.4 hrs working together ; : Check solution + = .7 + .3 = 1
 Numbers_Word_Problems/278465: Emily has nickels, dimes, and quarters in her piggy bank. She has twice as many dimes as nickels and 12 fewer quarters than dimes. The total value of the coins is \$9.00. How many of each coin type does Emily have? This has had me confused for an hour. Can I get an explanation also? Thanks! 1 solutions Answer 202645 by ankor@dixie-net.com(16527)   on 2010-03-08 14:15:14 (Show Source): You can put this solution on YOUR website!Emily has nickels, dimes, and quarters in her piggy bank. She has twice as many dimes as nickels and 12 fewer quarters than dimes. The total value of the coins is \$9.00. How many of each coin type does Emily have? : Write an equation for each phrase : "She has twice as many dimes as nickels " d = 2n or divide both sides by 2 and you have: n = .5d : "12 fewer quarters than dimes. " q = (d - 12) : "The total value of the coins is \$9.00." .05n + .10d + .25q = 9.00 : In the above equation, replace n with .5d, and replace q with (d-12) .05(.5d) + .10d + .25(d-12) = 9.00 : .025d + .10d + .25d - 3 = 9.00 : .375d = 9 + 3 d = d = 32 dimes then n = .5d n = .5(32) n = 16 nickels and q = d - 12 q = 32 - 12 q = 20 quarters ; : Check all this in the total\$ equation .05(16) + .10(32) + .25(20) = .80 + 3.20 + 5.00 = 9.00 : How about this? Did we eliminate some confusion about this? The trick on these problems is to get all three unknowns in terms of one the unknowns, d in this case.
 Travel_Word_Problems/278452: Hilary went riding in the hills. At one point, however, her horse stumbled and was hurt. Hilary left the horse and walked back home to call her vet. Hilary figures the horse walks about twice as fast as she does. If her horse was hurt about 8 miles into her ride and her whole trip took 4 hours total, how fast does Hilary walk?1 solutions Answer 202642 by ankor@dixie-net.com(16527)   on 2010-03-08 13:59:06 (Show Source): You can put this solution on YOUR website! Hilary figures the horse walks about twice as fast as she does. If her horse was hurt about 8 miles into her ride and her whole trip took 4 hours total, how fast does Hilary walk? : Let s = rate of H's walk then 2s = rate of horses walk : Write a time equation, time = dist/rate : ride time + walk time = 4 hrs + = 4 Multiply by 2s 8 + 2(8) = 4(2s) 8 + 16 = 8s 8s = 24 s = 3 mph H walks ; : Check solution by finding the times 8/6 = 1.33 8/3 = 2.67 -------------- total 4 hrs
 logarithm/278305: A population doubles in size every 15 years. Assuming exponential growth, find the annual growth rate and and continuous growth rate. Thank you! :D1 solutions Answer 202640 by ankor@dixie-net.com(16527)   on 2010-03-08 13:34:35 (Show Source): You can put this solution on YOUR website!A population doubles in size every 15 years. Assuming exponential growth, find the annual growth rate and and continuous growth rate. : Assume an initial amt of 1, then results are 2 : Let x = per cent in decimal form growth rate per year 1(1+x)^15 = 2 ln((1+x)^15) = ln(2) 15*ln(1+x) = .693 ln(x+1) = ln(x+1) = .04621 find the antilog (e^x on calc) x+1 = 1.0473 x = 1.0473 - 1 x = .0473 or 4.73 % annual growth rate : Check on a calc: enter 1.0473^15 = 2.000 : : Continuous growth rate 1*e^(15x) = 2 ln(e^15x) = ln(2) 15x*ln(e) = ln(2) ln(e) = 1 so we have 15x = .693 x = x = .0462 or 4.62 % growth continuously ; Check on a calc: enter e^(.0462*15) = 1.99997 ~ 2
 Word_Problems_With_Coins/278273: I need to know the linear equation and answer. There are only nickels and dimes. There are 40% less dimes than nickels. The total of all coins is \$11.00. How many nickels and how many dimes are there? Thanks!1 solutions Answer 202636 by ankor@dixie-net.com(16527)   on 2010-03-08 13:03:41 (Show Source): You can put this solution on YOUR website!There are only nickels and dimes. There are 40% less dimes than nickels. The total of all coins is \$11.00. How many nickels and how many dimes are there? : .05n + .10d = 11.00 : "There are 40% less dimes than nickels." means d = .6n : Substitute .6n for d : .05n + .10(.6n) = 11.00 .05n + .06n = 11 .11n = 11 n = 100 nickels : d = .6(100) d = 60 dimes : Check .05(100) + .10(60) = 5 + 6 = 11
 Linear-systems/278160: How do you solve this three variable equation? d + e - f = 11 f + d + 5 = e 2e - 12 = f1 solutions Answer 202507 by ankor@dixie-net.com(16527)   on 2010-03-07 21:43:39 (Show Source): You can put this solution on YOUR website!: How do you solve this three variable equation? d + e - f = 11 f + d + 5 = e 2e - 12 = f : Arrange all in the same order d + e - f = 11 d - e + f = -5 0 +2e - f = 12 : Multiply the 1st equation by - 1 -d - e + f = -11 d - e + f = -5 0 + 2e - f = 12 --------------------adding eliminates d and e, find f 0 + 0 + f = -4 f = -4 : Find e using the last equation 2e - f = 12 2e - (-4) = 12 2e + 4 = 12 2e = 12 - 4 2e = 8 e = +4 : Find d using the 1st equation d + e - f = 11 d + 4 (-4) = 11 d + 4 + 4 = 11 d = 11 - 8 d = 3 : Check solutions in the 2nd equation d - e + f = -5 3 - 4 - 4 = -5