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 Proportions/156410: how could you solve this question: a rock climber burns 60 calories for every 5 minutes of rock climbing. write a proportion on the lines below to determine how many calories a rock climber would burn in 7 minutes. thanks if you answer this but can you try to get it answered by the morning of september 12,2008 thanks1 solutions Answer 115205 by ankor@dixie-net.com(15661)   on 2008-09-11 16:07:14 (Show Source): You can put this solution on YOUR website!a rock climber burns 60 calories for every 5 minutes of rock climbing. write a proportion on the lines below to determine how many calories a rock climber would burn in 7 minutes. : Write a proportion which says,"5 min is to 7 min, as 60 cal is to x cal = Cross multiply 5x = 7*60 x = x = 84 calories ; We can check the solution using a different method Cal/min = 60/5 = 12 cal, hence 7 * 12 = 84
 Radicals/156266: Find the product and completely simplify the radical: square root sign 6 square root sign 201 solutions Answer 115187 by ankor@dixie-net.com(15661)   on 2008-09-11 14:15:55 (Show Source): You can put this solution on YOUR website!square root sign 6 square root sign 20 : = Factor to reveal the perfect squares inside the radical =
 Polynomials-and-rational-expressions/156270: Simplify: 4/x + 1/2x divided by 1/3x - 3/4x1 solutions Answer 115106 by ankor@dixie-net.com(15661)   on 2008-09-10 21:56:19 (Show Source): You can put this solution on YOUR website!Assume the problem is: : ----------- Place each over a common denominator ----------- : Do the math on the numerators: ----- invert the dividing fraction and multiply: * Cancel 2x into 12x 9 * =
 logarithm/156212: How would you be able to condense the Logarithm 2logx ?1 solutions Answer 115102 by ankor@dixie-net.com(15661)   on 2008-09-10 21:28:21 (Show Source): You can put this solution on YOUR website!How would you be able to condense the Logarithm 2logx ? How about
 Money_Word_Problems/156225: Tim bought 3 times as many .20 stamps as .10 stamps and 6 times as many .10 at .05 stamps. He spent \$63.75 on stamps. How many of each kind did he buy?1 solutions Answer 115101 by ankor@dixie-net.com(15661)   on 2008-09-10 21:24:39 (Show Source): You can put this solution on YOUR website!Tim bought 3 times as many .20 stamps as .10 stamps and 6 times as many .10 at .05 stamps. He spent \$63.75 on stamps. How many of each kind did he buy? : Let x, y, z = .20, .10, & .05 stamps respectively : Write an equation for each phrase; "Tim bought 3 times as many .20 stamps as .10 stamps" x = 3y ; " and 6 times as many .10 at .05 stamps." y = 6z or z = ; try to get everything in terms of y "He spent \$63.75 on stamps." .20x + .10y + .05z = 63.75 : How many of each kind did he buy? Substitute 3y for x and for z in above equation .20(3y) + .10y + .05* = 63.75 : .6y + .1y + = 63.75 Multiply equation by 6 to get rid of the denominator, results: 3.6y + .6y + .05y = 6(63.75) 4.25y = 382.5 y = y = 90 ea 10 cent stamps then z = z = 15 ea 5 cent stamps and x = 3*90 x = 270 ea 20 cent stamps : : Check solution in the \$total equation: .2(270) + .1(90) + .05(15) = 54.00 + 9.00 + .75 = 63.75; confirms our solutions
 Percentage-and-ratio-word-problems/156257: The ratio of the # of Conor's marbles to the # of Lillian's marbles is 3:4. After Conor bought another 60 marbles, he had twice as many marbles as Lillian. How many marbles did Conor have at first? I don't know how to start to figure this out. Do I use x represent Conor's marbles or Lillian's marbles?1 solutions Answer 115089 by ankor@dixie-net.com(15661)   on 2008-09-10 20:25:01 (Show Source): You can put this solution on YOUR website!The ratio of the # of Conor's marbles to the # of Lillian's marbles is 3:4. After Conor bought another 60 marbles, he had twice as many marbles as Lillian. How many marbles did Conor have at first? : Let x = no. marbles Conor had originally Let y = no. marbles Lillian has : Write an equation for the statement: "The ratio of the # of Conor's marbles to the # of Lillian's marbles is 3:4." = Cross multiply and we have: 4x = 3y : "After Conor bought another 60 marbles, he had twice as many marbles as Lillian." x + 60 = 2y x = (2y-60) : Substitute (2y-60) for x in the 1st equation 4(2y-60) = 3y 8y - 240 = 3y 8y - 3y = 240 5y = 240 y = y = 48 marbles for Lillian ; Find x x = 2y - 60 x = 2(48) - 60 x = 96 - 60 x = 36 marbles for Conor originally ; : Check solution =
 Age_Word_Problems/156219: Danny is ten years older than his sister Fiona. Danny is also twice as old as his sister Tori. How old is Danny if the sum of their ages is 50? can someone show me how to solve this problem? i can't seem to get it1 solutions Answer 115085 by ankor@dixie-net.com(15661)   on 2008-09-10 18:55:15 (Show Source): You can put this solution on YOUR website!Danny is ten years older than his sister Fiona. Danny is also twice as old as his sister Tori. How old is Danny if the sum of their ages is 50? : Write an equation for each statement We want to rearrange the equations so each age is in terms D : "Danny is ten years older than his sister Fiona." D = F + 10 or F = D - 10 ; " Danny is also twice as old as his sister Tori." D = 2T or T = .5D : "How old is Danny if the sum of their ages is 50?" D + F + T = 50" : Substitute (D-10) for F, and .5D for T in the total age equation: D + (D-10) + .5D = 50 D + D + .5d = 50 + 10 2.5D = 60 D = D = 24 yrs is Danny's age : Check solution: F = 24-10 F = 14 and T = .5(24) T = 12 : 24 + 14 + 12 = 50; confirms our solution
 Travel_Word_Problems/156130: In his second time at bat, the equation h= -.0015d2+ .5d + 4 can be used to model the path of the ball hit by Cecil Fielder. The ball is hit toward the portion of the left field wall that is 347 ft from home plate. a) The left field wall at Fenway Park is 37 ft high. Did he hit the ball over for a home run? Explain. b) Along the the third base line, the wall is 315 ft from home plate. Assume that the angle between the third base line and the wall is a right angle. Find the angle between the third base line and the path of the ball. 1 solutions Answer 115058 by ankor@dixie-net.com(15661)   on 2008-09-10 15:51:20 (Show Source): You can put this solution on YOUR website!In his second time at bat, the equation h= -.0015d2+ .5d + 4 can be used to model the path of the ball hit by Cecil Fielder. The ball is hit toward the portion of the left field wall that is 347 ft from home plate. a) The left field wall at Fenway Park is 37 ft high. Did he hit the ball over for a home run? Explain. : Using the above equation, assume the ball has to clear the fence, not hit the top of it; 38' when it gets out of park: -.0015d^2 + .5d + 4 = 38 : -.0015d^2 + .5d + 4 - 38 = 0 : -.0015d^2 + .5d - 34 = 0 ; Positive solution is about 238 ft, well within the park : If you graphed this, you have good picture of this: distance on the x axis, ball height on the y axis you can see it would hit the ground just before the base of the wall at 347 ft (The wall is probably too high for a ground rule double possibility) : b) Along the the third base line, the wall is 315 ft from home plate. Assume that the angle between the third base line and the wall is a right angle. Find the angle between the third base line and the path of the ball. : Side opposite = 37, side adjacent = 315; find angle A : Tan(A) = A = 6.7 degrees
 Expressions-with-variables/155980: three times the difference of a number x and 5 = ?1 solutions Answer 115055 by ankor@dixie-net.com(15661)   on 2008-09-10 15:24:55 (Show Source): You can put this solution on YOUR website!three times the difference of a number x and 5 = ? 3(x - 5) = which is 3x - 15 =
 Linear_Equations_And_Systems_Word_Problems/156173: Bobby has a bag containing two sizes of marbles. The big ones weigh 8 g and the small ones weigh 2 g. If there are twice as many small ones as big ones and the bag weighs 324 g, how many big marbles does he have?1 solutions Answer 115054 by ankor@dixie-net.com(15661)   on 2008-09-10 15:19:48 (Show Source): You can put this solution on YOUR website!The big ones weigh 8 g and the small ones weigh 2 g. If there are twice as many small ones as big ones and the bag weighs 324 g, how many big marbles does he have? : Let x = no. of big ones and Let y = no. of small ones ; Write an equation for the total weight 8x + 2y = 324 : Write an equation for the statement: "there are twice as many small ones as big ones" y = 2x ; Substitute 2x for y in the total weight equation, find x: 8x + 2(2x) = 324 : 8x + 4x = 324 : 12x = 324 x = x = 27 big ones then y = 2(27) y = 54 small ones : : Check solution in the total weight equation: 8(27) + 2(54) = 216 + 108 = 324
 Linear_Equations_And_Systems_Word_Problems/156177: I can not figure out how to do algebric word problems. Not one. If 2 is added to five times a number, the result is equal to 5 more than four times the number. find the number.1 solutions Answer 115050 by ankor@dixie-net.com(15661)   on 2008-09-10 15:08:53 (Show Source): You can put this solution on YOUR website!If 2 is added to five times a number, the result is equal to 5 more than four times the number. find the number. : Let x = "a number" : Write an equation for what it says: 5x + 2 = 4x + 5 : 5x - 4x = 5 - 2 : x = 3 : Is that so hard?
 Human-and-algebraic-language/156081: This question is from textbook Diophantus passed one-sixth of his life in childhood, one-twelfth in youth, one-seventh more as a bachelor. Five years after his marriage, a son was born who died four years before his father, at half his father's [final] age. How old was Diophantus when he died.1 solutions Answer 114978 by ankor@dixie-net.com(15661)   on 2008-09-10 10:32:42 (Show Source): You can put this solution on YOUR website!Diophantus passed one-sixth of his life in childhood, one-twelfth in youth, one-seventh more as a bachelor. Five years after his marriage, a son was born who died four years before his father, at half his father's [final] age. How old was Diophantus when he died. : Let x = his final age : a lengthy but simple equation Final age = child + youth + bach + marriage + son's age + 4 x = x + x + x + 5 + x + 4 : Common denominator of 12*7 = 84 x = x + x + x + 5 + x + 4 : x = x + 9 : x - x = 9 : x = 9 : x = 84 is his final age : Check: 14 + 7 + 12 + 5 + 42 + 4 = 84
 Polynomials-and-rational-expressions/156110: CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM: CONSIDER g(x) = (x + 2)^3; what is the new equation for g(x) if it is shifted up 6 units and shifted right 9 units?1 solutions Answer 114967 by ankor@dixie-net.com(15661)   on 2008-09-10 09:44:23 (Show Source): You can put this solution on YOUR website!g(x) = (x + 2)^3; what is the new equation for g(x) if it is shifted up 6 units and shifted right 9 units? : Shift it 6 units up g(x) = (x+2)^3 + 6 : Shift it right 9 units g(x) = (x+2-9)^3 + 6 which is: g(x) = (x-7)^3 + 6 : If you have a graphing calc, put this and the original equation in (y=g(x)). it will illustrate this.
 Surface-area/156035: This question is from textbook College Algebra Planting windscreens: A farmer intends to construct a windscreen by planting trees in a quarter-mile row. His daughter points out that 44 fewer trees will be needed if they are planted 1 foot farther apart. If her dad takes her advice, how many trees will be needed? A row starts and ends with a tree. (Hint: 1 mile = 5,280 feet) I give up...Everything I have tried does not seem to work. 1 solutions Answer 114964 by ankor@dixie-net.com(15661)   on 2008-09-10 09:31:39 (Show Source): You can put this solution on YOUR website!A farmer intends to construct a windscreen by planting trees in a quarter-mile row. His daughter points out that 44 fewer trees will be needed if they are planted 1 foot father apart. If her dad takes her advice, how many trees will be needed. A row starts and ends with a tree. (1 mile = 5,280 feet) : Find ft in 1/4 mile; *5280 = 1320 ft : Not including the extra tree on the end Let x = no of trees suggested Then (x+44) = original no. of trees proposed : Write expressions that calculate distance between the trees:(1320/no. of trees) : Original dist + 1 ft = suggested distance + 1 = ; Multiply equation by common denominator x(x+44); results: 1320x + x(x+44) = 1320(x+44) : 1320x + x^2 + 44x = 1320x + 58080 : Arrange on the left as a quadratic equation: x^2 + 44x + 5280x - 5280x - 58080= 0 ; x^2 + 44x - 58080 = 0 ; This will actually factor, but you can use the quadratic formula if wish: (x-220)(x+264) = 0 The positive solution x = 220 + 1 = 221 trees to save 44 trees ; We added one because there is a tree on each end ; : Check solution by finding the distance between each tree 1320/220 = 6 ft 1320/264 = 5 ft (with 44 more trees)
 Human-and-algebraic-language/155945: A circular table has an area of 1256 sq. in. The table opens in the middle to allow the addition of leaves. Each leaf is 12 " wide and is rectangular in shape. How many leaves must be added to change the area of the table to 2696 sq. in? 1 solutions Answer 114898 by ankor@dixie-net.com(15661)   on 2008-09-09 20:30:29 (Show Source): You can put this solution on YOUR website!A circular table has an area of 1256 sq. in. The table opens in the middle to allow the addition of leaves. Each leaf is 12 " wide and is rectangular in shape. How many leaves must be added to change the area of the table to 2696 sq. in? : I think the previous solution is wrong. He should have used the diameter: 40" then only 3 leaves would be required
 Numeric_Fractions/155886: Hello 17x+9 = 12x² + 14x-6 How would I simplify this to discover X's value Thank you 1 solutions Answer 114877 by ankor@dixie-net.com(15661)   on 2008-09-09 19:24:21 (Show Source): You can put this solution on YOUR website!17x + 9 = 12x² + 14x - 6 ; Group everything on the left 0 = 12x^2 + 14x - 17x - 6 - 9 : A quadratic equation: 12x^2 - 3x - 15 = 0 : Simplify, divide by 3: 4x^2 - x - 5 = 0 Factors to: (4x-5)(x+1) = 0 : 4x = 5 x = 5/4 x = 1.25 and x = -1 : : Check solution in original equation using x = 1.25 17(1.25) + 9 = 12(1.25^2) + 14(1.25) - 6 21.25 + 9 = 18.75 + 17.5 - 6 30.25 = 30.25 : You can check the x=-1 solution in the same way
 Geometry_Word_Problems/155898: A farmer intends to contruct a windscreen by planting trees in a quarter-mile row. His daughter points out that 44 fewer trees will be needed if they are planted 1 foot father apart. If her dad takes her advice, how many trees will be needed. A row starts and ends with a tree. (1 mile= 5,280 feet)1 solutions Answer 114871 by ankor@dixie-net.com(15661)   on 2008-09-09 19:08:52 (Show Source): You can put this solution on YOUR website!A farmer intends to construct a windscreen by planting trees in a quarter-mile row. His daughter points out that 44 fewer trees will be needed if they are planted 1 foot father apart. If her dad takes her advice, how many trees will be needed. A row starts and ends with a tree. (1 mile = 5,280 feet) : Find ft in 1/4 mile; *5280 = 1320 ft : Not including the extra tree on the end Let x = no of trees suggested Then (x+44) = original no. of trees proposed : Write expressions that calculate distance between the trees:(1320/no. of trees) : Original dist + 1 ft = suggested distance + 1 = ; Multiply equation by common denominator x(x+44); results: 1320x + x(x+44) = 1320(x+44) : 1320x + x^2 + 44x = 1320x + 58080 : Arrange on the left as a quadratic equation: x^2 + 44x + 5280x - 5280x - 58080= 0 ; x^2 + 44x - 58080 = 0 ; This will actually factor, but you can use the quadratic formula if wish: (x-220)(x+264) = 0 The positive solution x = 220 + 1 = 221 trees to save 44 trees ; We added one because there is a tree on each end ; : Check solution by finding the distance between each tree 1320/220 = 6 ft 1320/264 = 5 ft (with 44 more trees)
 Percentage-and-ratio-word-problems/155896: Four firefighters were discussing the number of fires they extinguished for the month of February. Rafael extinguished 25% fewer fires than Louis in February. William extinguished 50% more fires than Rafael. Albert extinguished 20% fewer fires than Rafael and William combined. If Louis extinguished 6 fires per week, how many fires did all four men extinguish during the entire month? 1 solutions Answer 114849 by ankor@dixie-net.com(15661)   on 2008-09-09 15:55:11 (Show Source): You can put this solution on YOUR website!Rafael extinguished 25% fewer fires than Louis in February. William extinguished 50% more fires than Rafael. Albert extinguished 20% fewer fires than Rafael and William combined. If Louis extinguished 6 fires per week, how many fires did all four men extinguish : Write an equation for each statement: "Rafael extinguished 25% fewer fires than Louis in February." R = .75L : " William extinguished 50% more fires than Rafael." W = 1.5R : "Albert extinguished 20% fewer fires than Rafael and William combined." A = .80(R+W) : " If Louis extinguished 6 fires per week," L = 4*6 = 24 fires in one month ; how many fires did all four men extinguish during the entire month? : Using the 1st equation, find R R = .75(24) R = 18 fires : Using the 2nd equation: W = 1.5(18) W = 27 fires : Using the 3rd equation; A = .8(18+27) A = .8(45) A = 36 fires : Summing up L + R + W + A 24 + 18 + 27 + 36 = 105 fires
 Square-cubic-other-roots/155883: The distance d in miles that can be seen on the surface of the ocean is given by d=1.3√(h,) where h is the height in feet above the surface. How high (to the nearest foot) would a platform have to see a distance of 13.5 miles?1 solutions Answer 114834 by ankor@dixie-net.com(15661)   on 2008-09-09 14:27:06 (Show Source): You can put this solution on YOUR website!The distance d in miles that can be seen on the surface of the ocean is given by d=1.3√(h,) where h is the height in feet above the surface. How high (to the nearest foot) would a platform have to see a distance of 13.5 miles? : The equation: = d : = 13.5 : = : = 10.3846 Square both sides h = 107.84 ft
 Square-cubic-other-roots/155882: y=√(3y+10)please help solve1 solutions Answer 114832 by ankor@dixie-net.com(15661)   on 2008-09-09 12:49:38 (Show Source): You can put this solution on YOUR website!y = Square both sides: y^2 = 3y + 10 Arrange as a quadratic equation on the left: y^2 - 3y - 10 = 0 Factor (y-5)(y+2) = 0 Two solutions y = +5 y = -2 : Always test solutions in the original equation, especially when dealing with radicals y = 5: 5 = 5 = a good solution : y =-2: -2 = -2 = -2 does not = +2, not a solution
 Linear_Algebra/155761: Hi, I'm having a difficult time with this words problem from chapter 1.5, i would really appreciate it if you can help me sove for it. Thanks. 11. A chess tutor charges a fee for the first lesson that is 1.5 times the fee for the later lessons. You spend \$315 for 10 lessons. How much does the first lessons cost? How much does a later lesson cost?1 solutions Answer 114798 by ankor@dixie-net.com(15661)   on 2008-09-09 08:15:52 (Show Source): You can put this solution on YOUR website!A chess tutor charges a fee for the first lesson that is 1.5 times the fee for the later lessons. You spend \$315 for 10 lessons. How much does the first lessons cost? How much does a later lesson cost? : Let x = cost of the later lessons then 1.5x = cost of the 1st lesson ; A simple equation: 1.5x + 9x = 315 : Do you think you can do this now?
 Polynomials-and-rational-expressions/155721: I need help with this problem: The number of tickets sold each day for an upcoming performance of Handels Messiah is given by N(x)=-0.3^2+7.8x+12, where x is the number of days since the concert was first announced. When will daily ticket sales peak and how many tickets will be sold that day? (I don't know how to go about doing this problem)1 solutions Answer 114756 by ankor@dixie-net.com(15661)   on 2008-09-08 22:04:47 (Show Source): You can put this solution on YOUR website!N(x)= -0.3^2+7.8x+12, where x is the number of days since the concert was first announced. When will daily ticket sales peak and how many tickets will be sold that day? : Notice that this is a quadratic equation, if we find the axis of symmetry we can find the maximum (vertex); : Find the axis of symmetry using the formula x = -b/(2a) In this equation it would be x = x = x = +13 days from the announcement for max ticket sales : Find the max number of tickets by substituting 13 for x in the equation: N(x)= -0.3^13^2 + 7.8(13) + 12 N(x) = -.3(169) + 101.4 + 12 N(x) = -50.7 + 101.4 + 12 N(x) = 62.7 ~ 63 is the maximum tickets sold. : Did this make sense to you now?
 Problems-with-consecutive-odd-even-integers/155748: 1) find 4 consecutive even integers such that the sum of twice the first, five times the second and four times the third divided by three times the fourth equals 3. 2) Find three consecutive odd integers such that 4 less than twice the second has the same value as three times the number that is one more that the third. 1 solutions Answer 114745 by ankor@dixie-net.com(15661)   on 2008-09-08 21:41:57 (Show Source): You can put this solution on YOUR website!1) find 4 consecutive even integers such that the sum of twice the first, five times the second and four times the third divided by three times the fourth equals 3. : 4 consecutive integers: x, x+2, x+4, x+6 : Write an equation for the statement: "the sum of twice the first, five times the second and four times the third divided by three times the fourth equals 3." = 3 : = 3 : = 3 Multiply both sides by (3x+18) 11x + 26 = 3(3x + 18) : 11x + 26 = 9x + 54 : 11x - 9x = 54 - 26 : 2x = 28 x = x = 14 : The four numbers: 14, 16, 18, 20 : Check the solutions in the statement: "the sum of twice the first, five times the second and four times the third divided by three times the fourth equals 3." = 3 = 3 = 3 : : 2) Find three consecutive odd integers such that 4 less than twice the second has the same value as three times the number that is one more that the third. : We have: x, (x+2), (x+4) as the three consecutive odd numbers : 2(x+2)- 4 = 3(x+4+1) 2x + 4 - 4 = 3(x+5) 2x = 3x + 15 2x = 3x = 15 -x = 15 x = -15 ; The numbers: -15, -13, -11 : ; Check: 2(-13) - 4 = 3(-11+1) -26 - 4 = 3(-10)
 Points-lines-and-rays/155739: how do you find the perimeter and area of a square whose side is y-3? 1 solutions Answer 114715 by ankor@dixie-net.com(15661)   on 2008-09-08 18:56:01 (Show Source): You can put this solution on YOUR website!P = 4(y-3) P = 4y - 12 : A = (y-3)^2 FOIL A = y^2 - 6y + 9