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 Average/452131: The Average (arithmetic mean) of a student's scores on 4 tests was 77. If he recieved a score of 69 on each of the first two tests and an 82 on the third, what was his score on the fourth test?1 solutions Answer 310848 by ankor@dixie-net.com(15660)   on 2011-05-20 20:32:21 (Show Source): You can put this solution on YOUR website!The Average (arithmetic mean) of a student's scores on 4 tests was 77. If he recieved a score of 69 on each of the first two tests and an 82 on the third, what was his score on the fourth test? : let x = fourth test score : = 77 : = 77 multiply both sides by 4 220 + x = 4(77) x = 308 - 220 x = 88 on the 4th test : : You can check this =
 test/452169: can someone help me pls i need help by monday? solve the equation. check your answer. 2/b-2-5/b+7=2/b+5b-141 solutions Answer 310845 by ankor@dixie-net.com(15660)   on 2011-05-20 20:24:11 (Show Source): You can put this solution on YOUR website!solve the equation. check your answer. Assume the problem is: : Factor the quadratic denominator : multiply by (b+7)(b-2), results: 2(b+7) - 5(b-2) = 2 : 2b + 14 - 5b + 10 = 2 : 2b - 5b + 24 = 2 : -3b = 2 - 24 : -3b = -22 b = b = +7 : ; I'll let you check this, substitute 7.33 for b in the original problem
 Linear_Algebra/451929: Write the quadratic equation of y = -2 (x + 7)^2 -5 in standard form. Show all work.1 solutions Answer 310838 by ankor@dixie-net.com(15660)   on 2011-05-20 19:26:19 (Show Source): You can put this solution on YOUR website!y = -2 (x + 7)^2 - 5 in standard form : y = -2(x^2 +14x + 49) - 5 : y = -2x^2 - 28x - 98 - 5 : y = -2x^2 - 28x - 103
 Travel_Word_Problems/452071: a boat can travel 18 miles up a river in the same amount of time it takes to travel 42 miles down the same river. if the current is 2 miles per hour, what is the speed in still water?1 solutions Answer 310817 by ankor@dixie-net.com(15660)   on 2011-05-20 16:15:50 (Show Source): You can put this solution on YOUR website!A boat can travel 18 miles up a river in the same amount of time it takes to travel 42 miles down the same river. If the current is 2 miles per hour, what is the speed in still water? : Let s = boat speed in still water then (s+2) = effective speed downstream and (s-2) = effective speed upstream : Write time equation, time = dist/speed : = cross multiply and solve for s
 Linear-equations/452144: Find the slope and the y-intercept of the line. 7x = 5y+40 I'm confused because the other examples don't have the equals sign in this place. So, I'm not sure how to break up the equation. 1 solutions Answer 310815 by ankor@dixie-net.com(15660)   on 2011-05-20 15:41:53 (Show Source): You can put this solution on YOUR website!Find the slope and the y-intercept of the line. 7x = 5y + 40 : Put the equation into the slope/intercept form (y = mx + b) 7x = 5y + 40 : subtract 5y from both sides 7x - 5y = 40 : subtract 7x from both sides -5y = -7x + 40 : y has to be positive, multiply both sides by -1 5y = 7x - 40 : y has to have a coefficient of 1, divide both sides 5 y = x - y = x - 8 we can see the slope (m) is , the y-intercept (b) is -8
 Linear_Equations_And_Systems_Word_Problems/451979: for the first performance of a play in a community theater, 50 reserved-seat tickets and80 general-admission tickets were sold. the total reciepts were \$980. for the second performance, 60 resevered-seat tickets and 90 general-admission tickets were sold. the total receipts were \$1140. find the price of a resered-set ticket and the price of a general-admission ticket.1 solutions Answer 310811 by ankor@dixie-net.com(15660)   on 2011-05-20 15:28:39 (Show Source): You can put this solution on YOUR website!for the first performance of a play in a community theater, 50 reserved-seat tickets and80 general-admission tickets were sold. the total reciepts were \$980. for the second performance, 60 resevered-seat tickets and 90 general-admission tickets were sold. the total receipts were \$1140. find the price of a reserved-set ticket and the price of a general-admission ticket. : Let r = reserved seats price Let g = general seats price : 1st perform 50r + 80g = 980 Simplify, divide by 10 5r + 8g = 98 : 2nd perform 60r + 90g = 1140 Simplify, divide by 10 6r + 9g = 114 : Multiply the 1st eq by 6, multiply the 2nd eq by -5, add the two equations +30r + 48g = 588 -30r - 45g =-570 ---------------------- 0 + 3g = 18 g = g = \$6.00 general admission price : Find r using the 1st simplified equation 5r + 8(6) = 98 5r = 98 - 48 5r = 50 r = r = \$10 reserved ticket price : : Check solution in the 2nd original equation 60r + 90g = 1140 60(10) + 90(6) = 1140 600 + 540 = 1140
 Trigonometry-basics/451819: Two drivers leave home at the same time and travel on straight roads that diverge by 70 degrees. One driver travels at an average speed of 83.0 km/h. The other driver travels at an average speed of 95.0 km/h. How far apart will the two drivers be after 45 min?1 solutions Answer 310809 by ankor@dixie-net.com(15660)   on 2011-05-20 14:56:22 (Show Source): You can put this solution on YOUR website!Two drivers leave home at the same time and travel on straight roads that diverge by 70 degrees. One driver travels at an average speed of 83.0 km/h. The other driver travels at an average speed of 95.0 km/h. How far apart will the two drivers be after 45 min? : Convert 45 min to .75 hrs : Let A = 70 degrees then a = distance between the cars after 45 min b = .75(83) = 62.25 km c = .75(95) = 71.25 km : Use the law of cosines a^2 = b^2 + c^2 - 2bc*cos(A) a^2 = 62.25^2 + 71.25^2 - 2(62.25*71.25)*cos(70) a^2 = 3875.0625 + 5076.5625 - 2(4435.3125)*.34202 a^2 = 8951.625 - 3033.9324 a = a = 76.92 km apart after 45 min
 Evaluation_Word_Problems/451896: The bases in a baseball diamond are 90 ft apart. A player picks up a ground ball 11 ft from third base, along the line from second base to third base. Determine the angle that is formed between first base, the player's present position, and home base. I'm not sure as to where to start with this question. Please clarify by showing all steps.1 solutions Answer 310748 by ankor@dixie-net.com(15660)   on 2011-05-20 09:40:24 (Show Source): You can put this solution on YOUR website!The bases in a baseball diamond are 90 ft apart. A player picks up a ground ball 11 ft from third base, along the line from second base to third base. Determine the angle that is formed between first base, the player's present position, and home base. : We can solve this by using the right triangle formed by lines from: 1st base to the player, a line from the player to 2nd base, (90-11 = 79 ft) the line from 2nd base back to 1st base, (90 ft) : Find the angle at 1st base (A) using the tangent Tan(A) = A = 41.276 degrees : Find the angle formed by home plate, 1st base and the player 90 - 41.276 = 48.724 degrees
 Miscellaneous_Word_Problems/451879: A football team snaps the ball from their 10 yard line. The quaterback throws to a receiver who line up 20 yards to the right of the quaterback and ran straight downfield. If the pass was 25 yards, how far downfield was the receiver when he caught the ball? A)15 yards , B)5 yards, C) 5 square root of 41, d) 10 square root of 21 solutions Answer 310744 by ankor@dixie-net.com(15660)   on 2011-05-20 08:27:57 (Show Source): You can put this solution on YOUR website!A football team snaps the ball from their 10 yard line. The quarterback throws to a receiver who line up 20 yards to the right of the quarterback and ran straight downfield. If the pass was 25 yards, how far downfield was the receiver when he caught the ball? : This forms a right triangle with the pass being the hypotenuse (25 yds), therefore let r = dist run downfield : r^2 + 20^2 = 25^2 which is r = r = 15 yds
 Rectangles/451846: the perimeter of a rectangle is 14 feet and the area is 12 square ft what is the width1 solutions Answer 310698 by ankor@dixie-net.com(15660)   on 2011-05-19 21:32:06 (Show Source): You can put this solution on YOUR website!the perimeter of a rectangle is 14 feet 2L + 2W = 14 Simplify, divide 2 L + W = 7 L = {7-W) : the area is 12 square ft what is the width L*W = 12 replace L with (7-W), find W W(7-W) = 12 -W^2 + 7W = 12 0 = W^2 - 7W + 12 Factors to (W-4)(W-3) = 0 W = 4, then L = 3 or W = 3, then L = 4
 Linear_Algebra/451865: I need help solving equations similar to this one: 36 divided by "p" = 6 36/p=6 I am looking for the step-by-step sequence to solve it so I can explain it to another person. Thank you. Mark1 solutions Answer 310669 by ankor@dixie-net.com(15660)   on 2011-05-19 19:46:15 (Show Source): You can put this solution on YOUR website! = 6 : Multiply both sides by P P* = P*6 P cancels 36 = 6p Divide both sides by 6 6 = p : : Check solution = 6
 Travel_Word_Problems/451534: Debbie leaves the house walking at a rate of 3 miles per hour. After 10 minutes, her mother realizes that Debbie has forgotten her homework and leaves the house riding a bicycle at a rate of 10 miles per hour. How many minutes after Debbie initially left the house will her mother catch up to her?1 solutions Answer 310668 by ankor@dixie-net.com(15660)   on 2011-05-19 19:39:12 (Show Source): You can put this solution on YOUR website!Debbie leaves the house walking at a rate of 3 miles per hour. After 10 minutes, her mother realizes that Debbie has forgotten her homework and leaves the house riding a bicycle at a rate of 10 miles per hour. How many minutes after Debbie initially left the house will her mother catch up to her? : Convert 10 min to hrs : Let t = D's travel time (hrs) when Mom catches her then (t - ) = Mom's travel time : When Mom catches D, they will have traveled the same distance. Write a distance equation; dist = speed*time 10(t-) = 3t 10t - = 3t 10t - 3t = 7t = multiply both sides by6 6*7t = 10 42t = 10 t = t = .2381 * 60 = 14.3 min is D's travel time, when Mom catches her. : :
 Equations/451766: I need help with this one homework problem I don't understand how to set up: If the product of a number and -15 is decreased by 25, the result is 23 greater than the product of the number and 9. Thank you very much for taking the time to help me.1 solutions Answer 310647 by ankor@dixie-net.com(15660)   on 2011-05-19 18:08:36 (Show Source): You can put this solution on YOUR website!let n = "a number" : Write an equation for exactly what it says: ; If the product of a number and -15 is decreased by 25, the result is 23 greater than the product of the number and 9. : -15n - 25 = 9n + 23 -15n - 9n = 23 + 25 -24n = 48 n = n = -2 : : You can confirm this answer in the original equation
 Linear-equations/451340: If the line passing through the points (a, 1) and (2, 3) is parallel to the line passing through the points (3, 10) and (a + 2, 1), what is the value of a?1 solutions Answer 310413 by ankor@dixie-net.com(15660)   on 2011-05-18 20:50:41 (Show Source): You can put this solution on YOUR website!If the line passing through the points (a, 1) and (2, 3) is parallel to the line passing through the points (3, 10) and (a + 2, 1), what is the value of a? : Parallel lines have equal slopes, using slope formula, we have = = cross multiply 2(a-1) = -9(-a+2) 2a - 2 = 9a - 18 2a - 9a = -18 + 2 -7a = - 16 a = a = 2.2857 : : Check this rather disgusting solution by finding the slope of each: : = ~ -7.000 and = ~ -7.000
 Miscellaneous_Word_Problems/451082: Michael mows lawns for his summer job. He only averages three lawns a week for the first eight weeks, but then averages six lawns a week for the last four. What is the average number of lawns he mowed per week during the entire summer?1 solutions Answer 310369 by ankor@dixie-net.com(15660)   on 2011-05-18 19:00:02 (Show Source): You can put this solution on YOUR website!Michael mows lawns for his summer job. He only averages three lawns a week for the first eight weeks, but then averages six lawns a week for the last four. What is the average number of lawns he mowed per week during the entire summer? : A total of 8(3) + 4(6) = 48 lawns A total of 8 + 4 = 12 weeks : Av = Av = 4 lawns/week
 Numbers_Word_Problems/451265: Bo took three positive numbers, subtracted the second from the first, and then subtracted the third from that difference. Jo took the same three numbers in the same order, but subtracted the third from the second, then subtracted this difference from the first number. If jo's result was 12 larger than bo's, what was the third number that they both used? explain how you got this answer?1 solutions Answer 310347 by ankor@dixie-net.com(15660)   on 2011-05-18 16:51:21 (Show Source): You can put this solution on YOUR website!Three positive numbers, a, b, c : Bo took three positive numbers, subtracted the second from the first, and then subtracted the third from that difference. a - b - c : Jo took the same three numbers in the same order, but subtracted the third from the second, then subtracted this difference from the first number. a - (b - c) a - b + c : If jo's result was 12 larger than bo's, what was the third number that they both used? bo's + 12 = jo's a - b - c + 12 = a - b + c combine like terms on the left a - a - b + b - c - c + 12 = 0 -2c + 12 = 0 -2c = -12 2c = 12 c = 12/2 c = +6
 Miscellaneous_Word_Problems/451028: the force exerted by the wind on a plane surface varies directly with the area of the surface and the square of the velocity of the wind. If the force on an area of 20 square feet is 11 pounds when the wind velocity is 22 miles per hour, find the force on a surface area of 47.125 square feet when the wind velocity is 36.5 miles per hour. 1 solutions Answer 310302 by ankor@dixie-net.com(15660)   on 2011-05-18 14:43:39 (Show Source): You can put this solution on YOUR website!the force exerted by the wind on a plane surface varies directly with the area of the surface and the square of the velocity of the wind. If the force on an area of 20 square feet is 11 pounds when the wind velocity is 22 miles per hour, find the force on a surface area of 47.125 square feet when the wind velocity is 36.5 miles per hour. : Find the constant of variation (k): "the force on an area of 20 sq/ft is 11 pounds when the wind velocity is 22 mph" 20*22^2*k = 11 9680k = 11 k = k = .00113636 : find the force (f) on a surface area of 47.125 square feet when the wind velocity is 36.5 miles per hour. f = s.a * wind vel^2 * k f = 47.125 * 36.5^2 * .00113636 f = 47.125 * 1332.25 * .00113636 f = 71.34 lbs
 Geometry_Word_Problems/450763: A crew can row 60 km downstream in 3 hours. The return trip takes 5 hours. Find the rowing rate of the crew in still water and the rate of the current.1 solutions Answer 310230 by ankor@dixie-net.com(15660)   on 2011-05-18 08:46:57 (Show Source): You can put this solution on YOUR website! A crew can row 60 km downstream in 3 hours. The return trip takes 5 hours. Find the rowing rate of the crew in still water and the rate of the current. : Let s = rowing rate in still water Let c = rate of the current : Write a distance equation for each half of the trip : 3(s+c) = 60 5(s-c) = 60 : We can simplify these equations, divide the 1st eq by 3, the 2nd eq by 5; you have: s + c = 20 s - c = 12 --------------adding eliminates c, find s 2s = 32 s = s = 16 km/hr in still water then 16 + c = 20 c = 20 - 16 c = 4 km/hr is the current : Check solution in the original upstream equation 5(16 - 4) = 60
 Polynomials-and-rational-expressions/450893: Help me factor these plz...... 5x^2+16x+3 Help me factor these completely..... plz.... 4x^2+5x+1=0 (4x-8)^2=0 x^2-49=01 solutions Answer 310113 by ankor@dixie-net.com(15660)   on 2011-05-17 21:36:50 (Show Source): You can put this solution on YOUR website!Help me factor these plz...... 5x^2 + 16x + 3 We know the x coefficients have to be 5 and 1, the last term factors 1 and 3 Just decide which goes where (5x + 1)(x + 3), FOIL this to check it : Help me factor these completely..... plz.... 4x^2 + 5x + 1 = 0 It should be apparent that it has to be (4x + 1)(x + 1) = 0, FOIL this to check it : (4x-8)^2 = 0 FOIL(4x-8)(4x-8) 16x^2 - 32x - 32x + 64 = 0 16x^2 - 64x + 64 = 0 Factor out 16 16(x^2 - 4x + 4) = 0 Factor this 16(x-2)(x-2) = 0 : x^2-49 = 0 recognize this as the difference of squares, which is: (x-7)(x+7) = 0; FOIL this to check it
 Miscellaneous_Word_Problems/450738: the cost of electricity in a certain city is 0.08 for each of the first 300k wh a month and 0.13 for eack kilowatt hour over 300k wh a month. find the amount of money a family pays with a monthly use of 425 k wh.1 solutions Answer 310053 by ankor@dixie-net.com(15660)   on 2011-05-17 19:36:54 (Show Source): You can put this solution on YOUR website!the cost of electricity in a certain city is 0.08 for each of the first 300 kwh a month and 0.13 for each kilowatt hour over 300 kwh a month. find the amount of money a family pays with a monthly use of 425 k wh. : Find the no. of kwh over 300 kwh: 425 - 300 = 125 kwh : cost = .08(300) + .13(125) c = 24.00 + 16.25 c = \$40.25 :
 logarithm/450668: Change to exponential form: Logbase2 4=Y1 solutions Answer 310050 by ankor@dixie-net.com(15660)   on 2011-05-17 19:23:39 (Show Source): You can put this solution on YOUR website!Change to exponential form: Logbase2 4=Y y^2 = 4
 Evaluation_Word_Problems/450807: Thanks for answering! WILL LEAVE GREAT COMMENT FOR YOU ! Two years from now, Jim will be twice as old as Joe will then be. Ten years ago, Jim was 5 times as old as Joe was. Find the present age of each person. GOD BLESS!1 solutions Answer 310032 by ankor@dixie-net.com(15660)   on 2011-05-17 18:12:40 (Show Source): You can put this solution on YOUR website!Let x = Jim's present age Let y = Joe's present age : "Two years from now, Jim will be twice as old as Joe will then be." x + 2 = 2(y+2) x + 2 = 2y + 4 x = 2y + 4 - 2 x = 2y + 2 : "Ten years ago, Jim was 5 times as old as Joe was." x - 10 = 5(y - 10) x - 10 = 5y - 50 x = 5y - 50 + 10 x = 5y - 40 : Replace x in the 1st equation with (5y-40) 5y - 40 = 2y + 2 5y - 2y = 2 + 40 3y = 42 y = y = 14 yr Joe's present age : then x = 2(14) + 2 x = 30 yrs is Jim's age : : Check solutions in the statement: "Ten years ago, Jim was 5 times as old as Joe was." 30 - 10 = 5(14 - 10) 20 = 5(4); confirms our solutions : : Looking forward to that comment!
 Travel_Word_Problems/450457: George bicycles at 18mph. Sam roller blades at 22mph. If they both leave the same place at the same time,after how much time will they be 12 miles apart?1 solutions Answer 310028 by ankor@dixie-net.com(15660)   on 2011-05-17 17:55:06 (Show Source): You can put this solution on YOUR website!George bicycles at 18mph. Sam roller blades at 22mph. If they both leave the same place at the same time, after how much time will they be 12 miles apart? : let t = travel times (hrs) for them to be 12 mi apart : 18t + 22t = 12 40t = 12 t = t = .3 hrs which is .3(60) = 18 min
 percentage/450428: To reduce 16 ounces of a 25% solution of antiseptic to a 10% solution, how much distilled water should a nurse add? 1 solutions Answer 310018 by ankor@dixie-net.com(15660)   on 2011-05-17 16:14:35 (Show Source): You can put this solution on YOUR website!To reduce 16 ounces of a 25% solution of antiseptic to a 10% solution, how much distilled water should a nurse add? : Let x = amt of distilled water : A simple equation .25(16) = .10(x+16) 4 = .10x + 1.6 4 - 1.6 = .1x 2.4 = .1x x = x = 24 oz of distilled water : : Prove this by seeing the amt of antiseptic is the same (only the % changes) .25(16) = .10(24+16) 4 = .1(40)
 Quadratic_Equations/450742: Find all numbers for which the rational expression is undefined: m^3 - 4m -------- m^2 - 81 I do not have any work on this, but I know that the first step is to make the denominator = to 0. then to solve for m.1 solutions Answer 310015 by ankor@dixie-net.com(15660)   on 2011-05-17 16:08:20 (Show Source): You can put this solution on YOUR website!Find all numbers for which the rational expression is undefined: m^3 - 4m -------- m^2 - 81 : Yes, just do that m^2 - 81 = 0 m^2 = 81 m = +/- m = 9 and m = -9 : undefined when m = 9 and m = -9
 Percentage-and-ratio-word-problems/450614: I made up this problem but I have no idea if it even makes sense. I plan on being a substance abuse counselor, which is pretty far from mathematician, and I have to make up a problem that relates to my future profession. This is what I came up with. Can this be put into some algebraic sense or is it futile? If an alcoholic drinks 36oz. of beer containing 0.05% alcohol within 45 minutes, while another drinks 2, 10oz glasses of cheap wine containing 14% alcohol in 30 minutes. Which alcoholic has consumed the largest percentage of alcohol? Was there any time when the 2 drinkers had the same amount of alcohol at the same amount of time? 1 solutions Answer 310013 by ankor@dixie-net.com(15660)   on 2011-05-17 15:59:24 (Show Source): You can put this solution on YOUR website!If an alcoholic drinks 36oz. of beer containing 0.05% alcohol within 45 minutes, while another drinks 2, 10oz glasses of cheap wine containing 14% alcohol in 30 minutes. Which alcoholic has consumed the largest percentage of alcohol? : I think you mean 5% alcohol for beer, .05% is not even considered as an alcoholic drink Use the decimal equiv of percent : beer guy: .05*36 = 1.8 oz of alcohol the wino: .14*20 = 2.8 oz : Was there any time when the 2 drinkers had the same amount of alcohol at the same amount of time? : Only when they start
 Travel_Word_Problems/450441: A rowing team practices rowing 2 miles upstream and 2 miles downstream. The team can row downstream 25% faster than they can row upstream. Let r represent their rate upstream. Write and simplify an expression for the amount of time they spend rowing. 1 solutions Answer 310011 by ankor@dixie-net.com(15660)   on 2011-05-17 15:26:22 (Show Source): You can put this solution on YOUR website!A rowing team practices rowing 2 miles upstream and 2 miles downstream. The team can row downstream 25% faster than they can row upstream. Let r represent their rate upstream. Write and simplify an expression for the amount of time they spend rowing. : Let r = rowing speed upstream then 1.25r = rowing speed downstream : Write a time equation; time = dist/speed rowing time = + simplify r.t = = = cancel r r.t. = , simplified expression for time spent rowing
 Age_Word_Problems/450432: The two Taylor girls were born in a consecutive, even years. If the product of their ages is 224, how old is each girl. 1 solutions Answer 310004 by ankor@dixie-net.com(15660)   on 2011-05-17 14:40:07 (Show Source): You can put this solution on YOUR website!The two Taylor girls were born in a consecutive, even years. If the product of their ages is 224, how old is each girl. Let x = younger girl then (x+2) = older girl : x(x+2) = 224 : x^2 + 2x - 224 = 0 Factors to (x+14)(x-12) = 0 positive solution x = 12 yrs is the younger girl then, obviously: 14 yrs is the older
 Exponential-and-logarithmic-functions/450671: (4)cubed root of(m-1)=7 i dont know how to write cubed root1 solutions Answer 309995 by ankor@dixie-net.com(15660)   on 2011-05-17 14:29:57 (Show Source): You can put this solution on YOUR website! cube both sides 64(m-1) = 343 : Divide both sides by 64 m - 1 = m - 1 = 5.359375 m = 6.359375 : : Check solution on a calc, enter 4(6.359375-1)^(1/3). results: 7