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 Square-cubic-other-roots/167014: At a height of h meters you can see V kilometere to the hozizon These number are related by the equation V = 3.5 sqrt(h) A person can see 392 km to the horizon from an airplane window. How high is the airplane?1 solutions Answer 123027 by ankor@dixie-net.com(15660)   on 2008-11-11 15:38:52 (Show Source): You can put this solution on YOUR website!At a height of h meters you can see V kilometers to the horizon. These numbers are related by the equation V = 3.5 sqrt(h) A person can see 392 km to the horizon from an airplane window. How high is the airplane? : Substitute 392 for V in the given equation and find h 3.5* = 392 : Divide both sides by 3.5: = : = 112 : Square both sides: h = 112^2 : h = 12,544 meters : : Check solution on a calc: enter 3.5* = 392
 Numbers_Word_Problems/167005: The sum of the digits of a three-digit number is 11. If the digits are reversed, the new number is 46 more that five the old number. If the hundreds digit plus twice the tens digit is equal to the units digit, then what is the number,1 solutions Answer 123026 by ankor@dixie-net.com(15660)   on 2008-11-11 15:21:34 (Show Source): You can put this solution on YOUR website!I am going to re-write the problem to what I think you meant: : The sum of the digits of a three-digit number is 11. If the digits are reversed, the new number is 46 more than five times the old number. If the hundreds digit plus twice the tens digit is equal to the units digit, then what is the number, : Let the number be: 100x + 10y + z : Let's try solving this using only the 1st and last statements: "The sum of the digits of a three-digit number is 11." x + y + z = 11 : "the hundreds digit plus twice the tens digit is equal to the units digit," x + 2y = z x + 2y - z = 0 : Add to the 1st equation to eliminate z x + y + z = 11 x +2y - z = 0 -------------- 2x + 3y = 11 : 2x = 11 - 3y x = Only two values for y will give a positive integer value for x, namely 1 and 3: From the 2nd statement we know that x is a low value, therefore 3 seems likely: x = x = x = x = 1 when y = 3 Find z 1 + 3 + z = 11 z = 11-4 z = 7 ; Our number is 137 : See if that makes the 2nd statement true. "If the digits are reversed, the new number is 46 more than five times the old number" 731 = 5(137) + 46 731 = 685 + 46
 Age_Word_Problems/167013: The sum of the ages of four daughters, Abigail, Bonnie, Cena, and Daphne, is 40. The difference between the ages of the youngest, Daphne, and the oldest, Abigail, is 6. The second born, Bonnie, is 2 years younger than the oldest, Abigail, and the third born, Cena, is the average of the ages of the youngest, Daphne, and the second born, Bonnie. How old is the father, who is 30 years older than the youngest daughter?1 solutions Answer 123024 by ankor@dixie-net.com(15660)   on 2008-11-11 13:52:29 (Show Source): You can put this solution on YOUR website!Write an equation for each statement, we will try to get everything in terms of a : The sum of the ages of four daughters, Abigail, Bonnie, Cena, and Daphne, is 40. a + b + c + d = 40 : The difference between the ages of the youngest, Daphne, and the oldest, Abigail, is 6. a - d = 6 -d = 6 - a d = a - 6; multiplied equation by -1 : The second born, Bonnie, is 2 years younger than the oldest, Abigail, a - b = 2 -b = 2 - a b = a - 2 : third born, Cena, is the average of the ages of the youngest, Daphne, and the second born, Bonnie. c = Substitute (a-2) for b and (a-6) for d c = = Cancel out the denominator and we have: c = a - 4 : Substitute for b, c, d in the first equation, find a: a + (a-2) + (a-4) + (a-6) = 40 4a - 12 = 40 4a = 40 + 12 4a = 52 a = a = 13 yrs is Abigail's age Then b = 13 - 2 b = 11 yrs is Bonnie and c = 13 - 4 c = 9 yrs is Cena and d = 13 - 6 d = 7 yrs is Daphne : How old is the father, who is 30 years older than the youngest daughter? Father = 7 + 30 = 37 yrs old : : Check solution, find the total 13 + 11 + 9 + 7 = 40 : A lot of steps but not that hard, right?
 Graphs/166915: This question is from textbook Algebra 1 After visiting relatives who live 200 miles away, your family drives home at an average speed of 50 miles per hour. Your distance d (in miles) from home is given by d = 200 - 50t where t is the time (in hours) spent driving. Graph the function and identify its domain and range. What is your distance from home after driving for 1.5 hours?1 solutions Answer 123021 by ankor@dixie-net.com(15660)   on 2008-11-11 12:36:16 (Show Source): You can put this solution on YOUR website!After visiting relatives who live 200 miles away, your family drives home at an average speed of 50 miles per hour. Your distance d (in miles) from home is given by d = 200 - 50t where t is the time (in hours) spent driving. Graph the function and identify its domain and range. What is your distance from home after driving for 1.5 hours? : A graph of this: : You can see from the graph: Domain; 0 to +4 Range: 0 to +200 : What is your distance from home after driving for 1.5 hours? : You can estimate this from the graph, however find the exact solution: Substitute 1.5 for t in the equation: d = 200 - 50(1.5) d = 200 - 75 d = 125 mi in 1.5 hrs :
 Rate-of-work-word-problems/166983: this in rational equations in word problems. Jay can clean the house in 6 hours. After Jay and Jim have both been cleaning for an hour, they are joined by Jen and they completed the cleaning in 2 more hours. If it takes Jim 10 hours to clean the house alone, how long would it take Jen to do the job alone?1 solutions Answer 123013 by ankor@dixie-net.com(15660)   on 2008-11-11 09:45:22 (Show Source): You can put this solution on YOUR website!Jay can clean the house in 6 hours. After Jay and Jim have both been cleaning for an hour, they are joined by Jen and they completed the cleaning in 2 more hours. If it takes Jim 10 hours to clean the house alone, how long would it take Jen to do the job alone? : From above information we know: Jay & Jim have been working a total of 3 hrs, Jen worked 2 hrs : Let t = time required by Jen working alone : Let the completed job = 1 : + + = 1 : Multiply equation by 30t to get rid of the denominators; 30t* + 30t* + 30t* = 30t(1) : Cancel out the denominators and you have; 5t(3) + 3t(3) + 30(2) = 30t : 15t + 9t + 60 = 30t : 24t + 60 = 30t : 60 = 30t - 24t : 60t = 6t t = t = 10 hrs Jen working alone : : Check solution in original equation + + = 1
 Surface-area/166932: This problem is from a problem solving worksheet known as "Math Olympiads" It is labeled "Problems-Division E Olympiads" The title at the top of the page is "Set 3 Olympiad 1" A circle and a triangle overlap as shown. The area of the circle is three times the area of the triangle. If the common region is removed, then the area of the rest of the circle would be 14 square centimeters more that the area of the reast of the triangle. What is the area of the complete triangle, in sq cm? Please help us! This is our 5th grade son's homework. We are both college educated and my husband even has a math minor. This is not our finest moment. Thank You!!1 solutions Answer 122971 by ankor@dixie-net.com(15660)   on 2008-11-10 21:40:18 (Show Source): You can put this solution on YOUR website!A circle and a triangle overlap as shown. The area of the circle is three times the area of the triangle. If the common region is removed, then the area of the rest of the circle would be 14 square centimeters more that the area of the rest of the triangle. What is the area of the complete triangle, in sq cm? : Let A = triangle area then 3A = circle area and let x = the common area that is removed : from the statement we can write an equation: 3A - x = A - x + 14 Add x to both sides and find A 3A - A = 14 2A = 14 A = 7 sq/cm is the area of the triangle
 Miscellaneous_Word_Problems/166738: a pedestrian is three eights of the way across the a train bridge when he hears a train coming! If he runs as fast as possible back toward the train, he will get off just in in time to aviod a collision. Also, if he runs as fast as possible away from the train, he will get off the bridge (on the other side) just in time to aviod a collision. If the train is traveling at 60 miles per hour. How fast does the person run? 1 solutions Answer 122969 by ankor@dixie-net.com(15660)   on 2008-11-10 20:00:30 (Show Source): You can put this solution on YOUR website!a pedestrian is three eights of the way across the a train bridge when he hears a train coming! If he runs as fast as possible back toward the train, he will get off just in in time to avoid a collision. Also, if he runs as fast as possible away from the train, he will get off the bridge (on the other side) just in time to avoid a collision. If the train is traveling at 60 miles per hour. How fast does the person run? : : Train----------d------------Br.....3x......P..........5x.........Br : Let d = dist train is from the bridge Let 8x = length of the bridge Pedestrian is 3x from one end and 5x from the other end of the bridge : Let s = running speed of p (mph) : Toward the train time equation (arrive at end of the bridge at the same time) = : Away from the train time equation (arrive at other end at the same time) = : After much manipulation of these equations (too much, to record here) I came up with: d = 7.2 8x = 4.8 mi P = 1.8 mi from one end and 3 mi from the other end : s = 15 mph running speed : : Check this using the "away from the train" situation: = = = .2 hrs : Check using the "toward the train" situation = = .12 hrs
 Polynomials-and-rational-expressions/166805: This question is from textbook Intermediate Algebra How do you factor this polynomial? 27a^3-64b^3+15a-20b 1 solutions Answer 122940 by ankor@dixie-net.com(15660)   on 2008-11-10 16:22:26 (Show Source): You can put this solution on YOUR website!27a^3 - 64b^3 + 15a - 20b ; Regroup 27a^3 + 15a - 64b^3 - 20b : factor out 3a and 4b 3a(9a^2 + 5) - 4b(16b^2 + 5); note the sign change when you factor out -4b
 logarithm/166858: rewrite the following Expression using one or more Logarithms and evaluate without a calculator. Log ( 1/10^-3) + log 10^4 = 1 solutions Answer 122939 by ankor@dixie-net.com(15660)   on 2008-11-10 16:14:32 (Show Source): You can put this solution on YOUR website!Log ( 1/10^-3) + log 10^4 = Same as: Reciprocal gets rid of the negative exponent we know the log of 10^7 = 7; 10^7 = 10,000,000
 logarithm/166859: Rewrite the following Expression using one or more Logarithms and evaluate without a calculator. Log5 125 + log5 5= 1 solutions Answer 122935 by ankor@dixie-net.com(15660)   on 2008-11-10 15:50:24 (Show Source): You can put this solution on YOUR website!Log5 125 + log5 5 = Log5(125*5) = Log5(625) Log5(625) = y : Evaluate using the exponent equivalent of logs 5^y = 625 5^4 = 625 : we could say: Log5 125 + log5 5 = 4
 Radicals/166804: Can someone help the hypotenuse of a right triangle is 2.5 units long. The longer leg is 1.3 units longer then the shorter leg. Find the lengths of the sides of the triangle.1 solutions Answer 122934 by ankor@dixie-net.com(15660)   on 2008-11-10 15:35:10 (Show Source): You can put this solution on YOUR website!the hypotenuse of a right triangle is 2.5 units long. The longer leg is 1.3 units longer then the shorter leg. Find the lengths of the sides. : Remember our old friend; a^2 + b^2 = c^2 : Let x = the shorter leg then (x+1.3) = the longer leg: : Replace a & b with these expressions, replace c with 2.5 : x^2 + (x+1.3)^2 = 2.5^2 : x^2 + (x^2 + 2.6x + 1.69) = 6.25 : x^2 + x^2 + 3.6x + 1.69 - 6.25 = 0; arrange to form a quadratic equation : 2x^2 + 3.6x - 4.56 = 0 : Using the quadratic equation, a=2; b=3.6; c=-4.56 x ~ .9938 ~ 1; the shorter leg and 1 + 1.3 = 2.3; the longer leg : Check solution with calc; enter = 2.508 ~ 2.5
 Systems-of-equations/166691: Please help with the following equation: A medical supply company has 1150 worker-hours for production, maintenance, and inspection. Using this and other factors, the number of hours used for each operation, P, M, and I, respectively, is found by solving the following system of equations. Find P, M and I. P + M + I = 1150 P = 4I - 100 P = 6M + 50 1 solutions Answer 122845 by ankor@dixie-net.com(15660)   on 2008-11-09 16:57:19 (Show Source): You can put this solution on YOUR website!A medical supply company has 1150 worker-hours for production, maintenance, and inspection. Using this and other factors, the number of hours used for each operation, P, M, and I, respectively, is found by solving the following system of equations. Find P, M and I. P + M + I = 1150 P = 4I - 100 P = 6M + 50 : Using the 1st two equations, rearrange the 2nd to have: P + M + I = 1150 P + 0 -4I = -100 -------------------subtraction eliminates P M + 5I = 1250 : Using the 1st and 3rd equation, rearrange the 3rd to have: P + M + I = 1150 P -6M + 0 = 50 -------------------Subtraction eliminate P +7M + I = 1100 : Multiply the above equation by 5, subtract M + 5I = 1250 from it: 35M + 5I = 5500 M + 5I = 1250 ---------------------Subtraction eliminates I, find M 34M = 4250 M = M = 125 hrs of maint : Using M + 5I = 1250, Find I 125 + 5I = 1250 5I = 1250 - 125 I = : I = 225 hrs of inspection : Use P = 6M + 50 to find P P = 6(125) + 50 P = 750 + 50 P = 800 hrs production : Confirm solutions in the 1st equation 800 + 125 + 225 = 1150
 expressions/166657: eleven is subtracted form a number and then the difference is multiplied by 5 the result is 30 1 solutions Answer 122844 by ankor@dixie-net.com(15660)   on 2008-11-09 16:19:31 (Show Source): You can put this solution on YOUR website!Just write an equation for what it says: x = "a number" : eleven is subtracted form a number and then the difference is multiplied by 5 the result is 30 5(x - 11) = 30 5x - 55 = 30 5x = 30 + 55 5x = 85 x = x = 17 : You can check it in the original equation
 Miscellaneous_Word_Problems/166678: When the digits of a two-digit number are reversed, the new nwmber is 9 more than the original number, and the sum of the digits of the original number is 11.What is the original number?1 solutions Answer 122843 by ankor@dixie-net.com(15660)   on 2008-11-09 16:13:48 (Show Source): You can put this solution on YOUR website!When the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 11. What is the original number? : Write the two digit number as: (10x + y); where x=10's digit and y=units digit : "When the digits of a two-digit number are reversed, the new number is 9 more than the original number," (10y+x) = (10x+y) + 9 10y - y = 10x - x + 9 9y = 9x + 9 Simplify, divide equation by 9 y = x + 1 : and the sum of the digits of the original number is 11. x + y = 11 : What is the original number? : Substitute (x+1) for y in the above equation x + (x+1) = 11 2x = 11 - 1 2x = 10 x = 5, then obviously y = 6 ; The number is: 56 : : Check solution in the statement: "When the digits of a two-digit number are reversed, the new number is 9 more than the original number," 65 = 56 + 9
 Polynomials-and-rational-expressions/166548: Can someone help me with this question please? Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x). P(x)= x^4+2x^3-2x+4 d(x)= x-2 Thanks1 solutions Answer 122823 by ankor@dixie-net.com(15660)   on 2008-11-09 14:29:24 (Show Source): You can put this solution on YOUR website!Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x). P(x)= x^4+2x^3-2x+4 d(x)= x-2 : You need to set it up like this, note the 0x^2: :......____________________________ (x-2) | x^4 + 2x^3 + 0x^2 - 2x + 4 : Follow the rules of long division and you will have: : ..........................x^3 + 4x^2 + 8x + 14; remainder 32/(x-2) :...........----------------------------- (x-2) | x^4 + 2x^3 + 0x^2 - 2x + 4
 Quadratic_Equations/166632: An NFL kicker attempts a 41-yard field goal. The path of the football toward the uprights can be represented by the graph of the quadratic function f(x)= -.0625x²+2.7x, where x is the horizontal distance the football travels in yards and the f(x) is the vertical distance the football travels. The bottom of the uprights is 3.5 yards above the ground. 1. Assuming the kick is in between the uprights, did the kicker make the field goal? Why or Why not? 2. Would the kicker have made a 42-yard field goal with the same kick? Why or Why not?1 solutions Answer 122812 by ankor@dixie-net.com(15660)   on 2008-11-09 13:29:29 (Show Source): You can put this solution on YOUR website!An NFL kicker attempts a 41-yard field goal. The path of the football toward the uprights can be represented by the graph of the quadratic function f(x)= -.0625x²+2.7x, where x is the horizontal distance the football travels in yards and f(x) is the vertical distance the football travels. The bottom of the upright is 3.5 yards above the ground. Assuming the kick is in between the uprights, did the kicker make the field goal? Why or Why not? : Find value of (x) (dist) when f(x) = 3.5 (height) -.0625x² + 2.7x = 3.5 : -.0625x² + 2.7x - 3.5 = 0 : Use the quadratic formula: In this problem a=-.0625; b=+2.7; c=-3.5 : : : x = 1.33; not the solution we want here and x = 41.86 yds; clears the upright nicely : The ball had traveled almost 42 yds when it had descended to 3.5 meters : : 2. Would the kicker have made a 42-yard field goal with the same kick? Why or Why not?. Find the height at 42 yds h = -.0625x² + 2.7x Substitute 42 for x h = -.0625(42^2) + 2.7(42) h = -.0625(1764) + 113.4 h = -110.25 + 113.4 h = 3.15 yds, So No; just under the bar at 3.5 yds high
 Linear_Algebra/166513: For x²(a-b)+a²(b-x)+b²(x-a) show that (x-a) is a linear factor. PLEASE HELP ME!!!!!!1 solutions Answer 122803 by ankor@dixie-net.com(15660)   on 2008-11-09 12:20:56 (Show Source): You can put this solution on YOUR website!For x²(a-b)+ a²(b-x)+ b²(x-a) show that (x-a) is a linear factor. : Multiply to eliminate the brackets, we can leave the last term alone x^2a - x^2b + a^2b - xa^2 + b^2(x-a) : Regroup: x^2a - xa^2 + a^2b - x^2b + b^2(x-a) : Factor out xa and b xa(x-a) + b(a^2 - x^2) + b^2(x-a) : Change the sign of b to -, to change signs inside the brackets xa(x-a) - b(x^2 - b^2) + b^2(x-a) : Note that x^2 - b^2 is the "difference of squares and can be factored xa(x-a) - b(x-a)(x+a) + b^2(x-a) : Note that each term contains the factor (x-a) now
 Travel_Word_Problems/166415: Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking? 1 solutions Answer 122766 by ankor@dixie-net.com(15660)   on 2008-11-08 21:44:28 (Show Source): You can put this solution on YOUR website!Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking? : Let t = travel time of the 2nd cyclist (10 mph) then (t+3) = travel time of the 1st cyclist (6 mph) : When the 2nd cyclist catches up with the 1st they will have traveled the same distance : Write a distance equation using this fact: (Dist = speed * time) : 10s = 6(s+3) : 10s = 6s + 18 : 10s - 6s = 18 : 4s = 18 s = s = 4.5 hrs travel time of the 2nd cyclist : ; Check solution by confirming they traveled the same distance 7.5 * 6 = 45 mi 4.5 * 10 = 45 mi
 Systems-of-equations/166466: A local electronics store will sell 7 AC adaptors and 3 rechargeable flashlights for \$84. what is the price of a single AC adaptor and a single reachargeable flashlight?1 solutions Answer 122762 by ankor@dixie-net.com(15660)   on 2008-11-08 20:58:49 (Show Source): You can put this solution on YOUR website! A local electronics store will sell 7 AC adapters and 3 rechargeable flashlights for \$84. what is the price of a single AC adapter and a single rechargeable flashlight? : We know that the cost of 7 Adapters is a multiple of 7 and the cost of 3 flashlights is a multiple of 3, and together they add up to 84 Multiples of 7: 21, 28, 35, 42, 49, 56, 63 Multiples of 3: 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54 : Find the the multiple of each which add up to 84 : A little research reveals \$21 for 3 flashlights, and \$63 for 7 Chargers : \$9 for a charger and \$7 for flashlight
 test/166509: a picture is 1 inch longer than it is wide. it is put into a frame one half inch wider on every side. find the area of the picture if the frame area is eight inches squared.1 solutions Answer 122717 by ankor@dixie-net.com(15660)   on 2008-11-08 13:55:00 (Show Source): You can put this solution on YOUR website!a picture is 1 inch longer than it is wide. it is put into a frame one half inch wider on every side. find the area of the picture if the frame area is eight inches squared. : Let x = width of the picture then (x+1) = length of the picture : Frame 1/2 inch wider all around, therefore x + 2(.5)= (x+1) = width of the frame and (x+1) + 2(.5) = x + 1 + 1 = (x+2) = length of the the frame : Frame area given as 8 sq/in, therefore (x+1)*(x+2) = 8 FOIL x^2 + 3x + 2 = 8 x^2 + 3x + 2 - 8 = 0 : a quadratic equation x^2 + 3x - 6 = 0 Use the quadratic formula to find x: a=1; b=3; c=-6 : You should get a positive solution about x = 1.37 inches is the width of the pic then, 2.37 = length : A = 1.37 * 2.37 A = 3.25 sq/in is the picture : : Check solution: Frame dimensions 2.37 by 3.37 Frame area = 2.37 * 3.37 = 7.77 ~ 8 sq/in as given
 Equations/166459: 7x-2 divided by 10 = 9x divided by 4 + 6 I understand that I must get rid of the fractions first but cannot determine how to do this with the fractions on both sides. If I multipy by 10 on the right side and left side do I then multipy by 4 on both sides.1 solutions Answer 122710 by ankor@dixie-net.com(15660)   on 2008-11-08 12:39:50 (Show Source): You can put this solution on YOUR website!7x-2 divided by 10 = 9x divided by 4 + 6 : = + 6 : Multiply equation by common denominator, a value which is a multiple of 10 and 4 20 would do this for us 20* = 20* + 20(6) : Cancel out the denominators and you have: 2(7x - 2) = 5(9x) + 120 : 14x - 4 = 45x + 120 : 14x - 45x = 120 + 4 : -31x = 124 x x = -4 : : Check solution in original equation: = + 6 = + 6 = + 6 -3 = -9 + 6; confirms our solution
 Travel_Word_Problems/166236: Lerry drove 329 miles in 2 hours more then it took Terrell to drive 260 miles. Terrell drove at and average reate of 5 miles per hour faster then Larry. How fast did Larry travel?1 solutions Answer 122559 by ankor@dixie-net.com(15660)   on 2008-11-06 21:18:36 (Show Source): You can put this solution on YOUR website!Lerry drove 329 miles in 2 hours more then it took Terrell to drive 260 miles. Terrell drove at an average rate of 5 miles per hour faster then Larry. How fast did Larry travel? : Let s = Larry's speed then (s+5) = Terry's speed : Write a time equation: Time = dist/speed : L's time - 2 hr = T's time - 2 = : Multiply equation by s(s+5) s(s+5)* - 2s(s+5) = s(s+5)* : This eliminates the denominators and you have: 329(s+5) -2s^2 - 10s = 260s : 329s + 1645 - 2s^2 - 10s - 260s = 0; arrange as a quadratic on the left : -2s^2 + 329s - 260s - 10s + 1645 = 0 : -2s^2 + 59s + 1645 = 0 : Easier to factor if change the signs, mult by -1 2s^2 - 59s - 1654 Factors to: (2s + 35)(s - 47) = 0; use the quadratic formula if you need to: Positive solution s = 47 mph is L's speed then 47 + 5 = 52 mph is T's speed : : Check solution by finding the travel time of each 329/47 = 7 hr 260/52 = 5 hr ------------- differ = 2 hrs as given
 Human-and-algebraic-language/166271: Three lighthouses on three nearby islands flash their lights every evening beginning at 8:35pm. On one island, the ligh flashes every 45 seconds. The lighthouse on the second island has a light that flashes every 2 minutes. The third lighthouse flashes a light every 1 1/4 minutes. At what time will all three lights flash together again? This is a problem of the week just given to my child on a single piece of paper. 1 solutions Answer 122552 by ankor@dixie-net.com(15660)   on 2008-11-06 20:46:58 (Show Source): You can put this solution on YOUR website!Three lighthouses on three nearby islands flash their lights every evening beginning at 8:35pm. On one island, the ligh flashes every 45 seconds. The lighthouse on the second island has a light that flashes every 2 minutes. The third lighthouse flashes a light every 1 1/4 minutes. At what time will all three lights flash together again? : Convert 2 min to seconds and 1.25 min to seconds. : So we have: : Lt1 = 45; Lt2 = 120; Lt3 = 75 : Prime factor each: 45: 3,3,5, 120: 2,2,2,3,5 75: 3,5,5 : Lcm of all three: 2,2,2,3,3,5,5 Multiply this: 1800 secs they will all Flash : 1800/60 = 30 min: At 9:05Pm this should occur
 Inverses/166215: Hi there please help I am parent trying to help my eldest on Equation in year 9, this the question, This is where I am stuck because I don't if my equation is correct or not? thanks Nick.1 solutions Answer 122489 by ankor@dixie-net.com(15660)   on 2008-11-06 14:27:47 (Show Source): You can put this solution on YOUR website!In two years time Geoff will be three times as old as he was ten years ago. a)Using y for his present age, write down an equation connecting his present age with his age ten years ago? : Two things to note in this: : Age in two years: (y+2) Age 10 yrs ago: (y-10) : In two yrs = 3 times age 10 yrs ago y + 2 = 3(y - 10) : b)Solve the equation. : y + 2 = 3y - 30; multiplied what's inside the bracket : y + 2 + 30 = 3y; add 30 to both sides : 32 = 3y - y; subtract y from both sides : y = : y = 16 yrs; his age now : : Try this in the original statement, see if works "In two years time Geoff will be three times as old as he was ten years ago." 16 + 2 = 3(16 - 10) 18 = 3(6) : You don't need brackets around the problem
 Travel_Word_Problems/165965: an airplane made a flight of 1600 miles in 5 hours. during the first 3 hours of the trip it had good weather. it then ran into bad weather, which decreased its rate by 75 mph for the rest of the flight. find the rate on each part of the flight. 1 solutions Answer 122487 by ankor@dixie-net.com(15660)   on 2008-11-06 14:17:36 (Show Source): You can put this solution on YOUR website!an airplane made a flight of 1600 miles in 5 hours. during the first 3 hours of the trip it had good weather. it then ran into bad weather, which decreased its rate by 75 mph for the rest of the flight. find the rate on each part of the flight. : Let s = speed the 1st 3 hrs (good weather) Then (s-75) = speed the last two hours : Write a distance equation: Dist = time * speed : 3s + 2(s-75) = 1600 : 3s + 2s - 150 = 1600 : 5s = 1600 + 150 : 5s = 1750 s = s = 350 mph in good weather and 350 - 75 = 275 mph in bad weather : : Check solution find the distance 3(350) = 1050 mi 2(275) = 550 mi ---------------- total = 1600 mi, confirms our sollutions ; : That wasn't so hard, was it?
 Polynomials-and-rational-expressions/166018: This question is from textbook Physics: How many meters does light travel 8 hours? The speed of light is 3x10(8th power)m/s?1 solutions Answer 122483 by ankor@dixie-net.com(15660)   on 2008-11-06 13:39:04 (Show Source): You can put this solution on YOUR website!How many meters does light travel 8 hours? : The speed of light is: m/s? : Find the number of seconds in 8 hrs: 8 *60 * 60 = 28,800 sec or 2.88(10^4) sec : * = = meters in 8 hrs
 Complex_Numbers/166032: can someone help me with this problem: Solve the problem. If the average cost per unit C(x) to produce x units of plywood is given by: C(x) = 900 / x+30 What do 600 units cost? Round your answer to the nearest cent. a. \$857.14 b. \$899.95 c. \$180.00 d. \$18,000.001 solutions Answer 122477 by ankor@dixie-net.com(15660)   on 2008-11-06 12:52:39 (Show Source): You can put this solution on YOUR website!If the average cost per unit C(x) to produce x units of plywood is given by: C(x) = : What do 600 units cost? Round your answer to the nearest cent. ; You are looking for the total cost which is no. of units sold (x) times cost/unit, which is the given equation : C(x) = x* : Substitute 600 for x in the given equation: C(x) = 600* : C(x) = 600* : C(x) = 600 * 1.42857 : C(x) = \$857.14
 test/166179: 36.) If a manufacturer charges q dollars each for footballs, then he can sell 3000 - 150q footballs per week. Find a polynomial R(q) that represents the revenue for one week. Find the weekly revenue if the price is \$8 for each football. This is the answer that it is showing r(q)= -150q^2 + 3000q, 14,400 Can you show me how they got this answer please. 1 solutions Answer 122473 by ankor@dixie-net.com(15660)   on 2008-11-06 12:34:32 (Show Source): You can put this solution on YOUR website!This football problem has been kicking around for few days. : If a manufacturer charges q dollars each for footballs, then he can sell 3000 - 150q footballs per week. Find a polynomial R(q) that represents the revenue for one week. : Revenue = price times number sold (q=price), (number sold = 3000-150q) R(q) = q(3000-150q) ; Multiply what's inside the brackets R(q) = 3000q - 150q^2 or R(q) = -150q^2 + 3000q : : Find the weekly revenue if the price is \$8 for each football. : Take the above equation, substitute 8 for q and find R(q) R(q) = -150(8^2) + 3000(8) : R(q) = -150(64) + 24000 : R(q) = -9600 + 24000 : R(q) = \$14,400 : : Did this explain it to you?
 test/166033: 36.) If a manufacturer charges q dollars each for footballs, then he can sell 3000 - 150q footballs per week. Find a polynomial R(q) that represents the revenue for one week. Find the weekly revenue if the price is \$8 for each football. This is the answer that it is showing r(q)= -150q^2 + 3000q, 14,400 Can you show me how they got this answer please. 1 solutions Answer 122472 by ankor@dixie-net.com(15660)   on 2008-11-06 12:31:38 (Show Source): You can put this solution on YOUR website!This football problem has been kicking around for few days. : If a manufacturer charges q dollars each for footballs, then he can sell 3000 - 150q footballs per week. Find a polynomial R(q) that represents the revenue for one week. : Revenue = price times number sold (q=price), (number sold = 3000-150q) R(q) = q(3000-150q) ; Multiply what's inside the brackets R(q) = 3000q - 150q^2 or R(q) = -150q^2 + 3000q : : Find the weekly revenue if the price is \$8 for each football. : Take the above equation, substitute 8 for q and find R(q) R(q) = -150(8^2) + 3000(8) : R(q) = -150(64) + 24000 : R(q) = -9600 + 24000 : R(q) = \$14,400 : : Did this explain it to you?
 Polynomials-and-rational-expressions/166017: This question is from textbook Physics: The mass of an electron is 9.109x10(-31power)kg. The mass of a proton is 1.673x10(-27power)kg. Hwo many times heavier is a proton than a electron.1 solutions Answer 122466 by ankor@dixie-net.com(15660)   on 2008-11-06 11:28:59 (Show Source): You can put this solution on YOUR website!The mass of an electron is 9.109x10(-31power)kg. The mass of a proton is 1.673x10(-27power)kg. How many times heavier is a proton than a electron. : = = = : We can say that the proton is 1837 times heavier than the electron