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 Equations/141402: it it take 15 people 8 hours to make 100 items how long would it take 6 people working the same rate to make half as many items? i tried working this out by dividing 6 and 15 to get 0.4 then i took 8 and divided it by 0.4 and got 20. so i ended up with 6 people, 20 hours and 100 items. sinse the question asks for half the items i devided 20 hours and 100 items by 2. and ended up getting 10 hours for 50 items (half the items) but when i showed it to my teach she wanted and actual equation for the problem. but i cant find one for it. 1 solutions Answer 103020 by ankor@dixie-net.com(15660)   on 2008-05-13 18:49:32 (Show Source): You can put this solution on YOUR website!it it take 15 people 8 hours to make 100 items how long would it take 6 people working the same rate to make half as many items? : I think you are right; Here's one way to do it: : Find out how many man-hrs per item man-hrs = = = 1.2 man-hrs per item : Let x = hrs for 6 people to make 50 items 6x = 1.2(50) : 6x = 60 x = x = 10 hrs for 6 people to make 50 items : Put this all in one equation x = *
 Polynomials-and-rational-expressions/141378: Tutor how do I do this problem:* Use synthetic division to find the quotient and the remainder (x^5+32)divided by (x+2)1 solutions Answer 103016 by ankor@dixie-net.com(15660)   on 2008-05-13 16:16:40 (Show Source): You can put this solution on YOUR website!Use synthetic division to find the quotient and the remainder (x^5+32)divided by (x+2) : : Write it like this and proceed ....._____________________ -2|1 + 0 + 0 + 0 + 0 + 32 : I got x^4 - 2x^3 + 4x^2 - 8x + 16, and remainder 0
 Miscellaneous_Word_Problems/141373: This question is from textbook Introductory Algebra I was hoping you could provide me some direction as to how to solve this polynomial word problem. A polynomial in x has degree 3. The coefficient of x(with an exponent of 2) is 3 less than the coefficient of x(with an exponent of 3). The coefficient of x is three times the coefficient of x(with an exponent of 2). The remaining coefficient is 2 more than the coefficient of x(with an exponent of 3). The sum of the coefficients is -4. Find the polynomial.1 solutions Answer 103014 by ankor@dixie-net.com(15660)   on 2008-05-13 15:57:20 (Show Source): You can put this solution on YOUR website!A polynomial in x has degree 3. The coefficient of x(with an exponent of 2) is 3 less than the coefficient of x(with an exponent of 3). The coefficient of x is three times the coefficient of x(with an exponent of 2). The remaining coefficient is 2 more than the coefficient of x(with an exponent of 3). The sum of the coefficients is -4. Find the polynomial. : Let a = coefficient of x^3 : Write an expression for each statement: ; "The coefficient of x^2 is 3 less than the coefficient of x^3" (a-3) : "The coefficient of x is three times the coefficient of x^2." 3(a-3) : "The remaining coefficient is 2 more than the coefficient of x^3". (a+2) : "The sum of the coefficients is -4." a + (a-3) + 3(a-3) + (a+2) = -4 a + a - 3 + 3a - 9 + a + 2 = -4 6a - 10 = -4 6a = -4 + 10 6a = +6 a = +1 : Using a = 1 we can write it: (1)x^3 + (1-3)x^2 + 3(-2)x + (1+2) : y = x^3 - 2x^2 - 6x + 3; is the polynomial : Did this help?
 Linear-systems/141363: This question is from textbook Prentice hall algebra 1 How do I solve by using a system of two equations in two variables? The units digit of a two-digit number is 1 less than 3 times the tens digit. If the digits are reversed, the new number is 45 more than the original number. Find the number.1 solutions Answer 103009 by ankor@dixie-net.com(15660)   on 2008-05-13 15:05:52 (Show Source): You can put this solution on YOUR website!Let x = 10's digit Let y = units digit : The original 2 digit number: (10x + y) : Write an equation for each statement: "The units digit of a two-digit number is 1 less than 3 times the tens digit." y = 3x - 1 : "If the digits are reversed, the new number is 45 more than the original number." 10y + x = 45 + 10x + y : Find the number. 10y - y = 10x - x + 45 9y = 9x + 45 Simplify divide equation by 9 y = x + 5 ; Using the equation from the 1st statement, substitute (3x-1) for y; find x 3x - 1 = x + 5 3x - x = 5 + 1 2x = 6 x = x = 3 : Find y using y = x + 5 y = 3 + 5 y = 8 : Our original number = 38 : : Check solution in statement: "If the digits are reversed, the new number is 45 more than the original number." 83 = 45 + 38; confirms our solutions
 Linear-systems/141359: This question is from textbook Prentice hall algebra 1 How do I solve using a system of two linear equations in two variables? Barry is 8 years older than his sister. In 3 years, he will be twice as old as she will be then. How old is each now?1 solutions Answer 103002 by ankor@dixie-net.com(15660)   on 2008-05-13 14:34:34 (Show Source): You can put this solution on YOUR website!How do I solve using a system of two linear equations in two variables? Barry is 8 years older than his sister. In 3 years, he will be twice as old as she will be then. How old is each now? : Let x = B's age now Let y = S's age now : Write an equation for the statement,"Barry is 8 years older than his sister." x = y + 8 or x - y = 8 : The same for this statement," In 3 years, he will be twice as old as she will be then. (x+3) = 2(y+3) x + 3 = 2y + 6 x = 2y + 6 - 3 x = 2y + 3 x - 2y = 3 : The system, two equations two variables x - y = 8 x - 2y = 3 ------------ subtracting eliminates x 0 + y = 5 yrs is sister's age now : I'll let you find Barry's age
 Miscellaneous_Word_Problems/141348: Phil and Phyllis are siblings. Phyllis has twice as many brothers as she has sisters. Phil has the same number of brothers as sisters. How many girls and how many boys are in the family?1 solutions Answer 103000 by ankor@dixie-net.com(15660)   on 2008-05-13 14:21:14 (Show Source): You can put this solution on YOUR website!Phil and Phyllis are siblings. Phyllis has twice as many brothers as she has sisters. Phil has the same number of brothers as sisters. How many girls and how many boys are in the family? : x = no. boys y = no. girls : Phil: (x-1) bro, y sis same number bro than sis: (x-1) = y x - y = 1 : Phyl: x bro, (y-1) sis Twice as many bro as sis: x = 2(y-1) x = 2y - 2 x - 2y = -2 ; Using these two equation for elimination x - 2y = -2 x - y = 1 -------------subtracting eliminates x 0 - y = -3 y = 3 girls : We know x = 2y -2: x = 2(3) - 2 x = 4 boys : Therefore: Phil has 3 brothers, 3 sisters Phyl has 4 brothers, 2 sisters
 Miscellaneous_Word_Problems/141347: A plane is flying the 3,458 mile trip from New York City to London has a 50 MPH tailwind. The flight's Point of No Return is the point at which the flight time required to return to New York is the same a the time required to continue to London. If the speed on the plane in still air is 360 MPH, how far is New York from the point of no return?1 solutions Answer 102990 by ankor@dixie-net.com(15660)   on 2008-05-13 13:45:20 (Show Source): You can put this solution on YOUR website!A plane is flying the 3,458 mile trip from New York City to London has a 50 MPH tailwind. The flight's Point of No Return is the point at which the flight time required to return to New York is the same a the time required to continue to London. If the speed on the plane in still air is 360 MPH, how far is New York from the point of no return? : From the given information we can say: 360 + 50 = 410 mph speed (relative to the earth) with the wind 360 - 50 - 310 mph speed against the wind : Let d = dist to New York from point of no return Then (3458-d) = dist to London from point of no return : Write a time equation: Time = dist/speed : Return to N.Y time = Continue to London time = Cross multiply: 410d = 310(3458-d) : 410d = 1071980 - 310d : 410d + 310d = 1071980 : 720d = 1071980 d = d = 1488.86 mi from N.Y. : : Check solution by finding the distance to London and calculating the time to both: 3458 - 1488.86 = 1969.14 mi to London : Time to N.Y.: 1488.86/310 = 4.8 hrs Time to Lond: 1969.14/410 = 4.8 hrs
 Surface-area/141243: A rectangular lot measures 66m by 107m A sidewalk surrounds the lot The sidewalk is 2m wide what would the area of the sidewalk be 1 solutions Answer 102915 by ankor@dixie-net.com(15660)   on 2008-05-12 19:55:37 (Show Source): You can put this solution on YOUR website!A rectangular lot measures 66m by 107m A sidewalk surrounds the lot The sidewalk is 2m wide what would the area of the sidewalk be : The overall dimensions including the surrounding sidewalk: 70 by 111 (add 4 m) : Overall area - lot area = sidewalk area (70*111) - (66*107) = 7770 - 7072 = 708 sq/m is the sidewalk area
 Polynomials-and-rational-expressions/141130: suppose the record shown played for 16.5 minutes on one side and the average of the radii of the grooves on the record was 3 and 3/4 inches. there are 33 1/3 revolutions per minute. Write an expression involving units that represents how manby inches the needle passed through the grooves while the record was being played. then evaluate the expression.1 solutions Answer 102908 by ankor@dixie-net.com(15660)   on 2008-05-12 19:10:59 (Show Source): You can put this solution on YOUR website!Suppose the record shown played for 16.5 minutes on one side and the average of the radii of the grooves on the record was 3 and 3/4 inches. there are 33 1/3 revolutions per minute. Write an expression involving units that represents how many inches the needle passed through the grooves while the record was being played. then evaluate the expression. : This involves finding the average circumference, from the average radius (3.75") Multiply this by the no. of minutes played at 33 1/3 rpm : D = 2*pi*r * time * record speed (rpm) : D = 2*pi*3.75 * 16.5 * 33.33 : D = 25.562 * 16.5 * 33.33 : D = 12,958 inches
 Money_Word_Problems/141224: Mr. Graham invested some of his \$18,000 in bonds and made a 5% profit and the rest in bonds that made a 12% profit. If the profit on the 12% bonds was \$885 more than the profit on the 5% bonds, how much did Mr. Graham invest in the 5% bonds?1 solutions Answer 102903 by ankor@dixie-net.com(15660)   on 2008-05-12 18:53:08 (Show Source): You can put this solution on YOUR website!Mr. Graham invested some of his \$18,000 in bonds and made a 5% profit and the rest in bonds that made a 12% profit. If the profit on the 12% bonds was \$885 more than the profit on the 5% bonds, how much did Mr. Graham invest in the 5% bonds? : Let x = amt invested at 5% : It said the total invested was 18000, therefore: (18000-x) = amt invested at 12% : 5% profit + 885 = 12% profit .05x + 885 = .12(18000-x) : .05x + 885 = 2160 - .12x : .05x + .12x = 2160 - 885 : .17x = 1275 x = x = \$7500 invested at 5% ; : Check solution find the profit on each; 18000-7500 = 10500 invested at 12% .12*10500 = 1260 .05*7500 = 375 ---------------- difference = 885; confirms our solution
 Expressions-with-variables/141146: Solve x - 3/4 - x/7 = 51 solutions Answer 102893 by ankor@dixie-net.com(15660)   on 2008-05-12 18:13:48 (Show Source): You can put this solution on YOUR website!Solve x - = 5 Multiply equation by the common denominator, that would be 4*7 = 28 28(x) - 28* - 28* = 28(5) Cancel the denominators: 28x - 7(3) - 4x = 140 : 28x - 4x - 21 = 140 : 24x = 140 + 21 : 24x = 161 x = : : Check solution using decimals in calc; 161/24 ~ 6.71 6.71 - .75 - (6.71/7) = 5.00
 Expressions-with-variables/141228: Solve for the indicated variable r+s/t=u.....solve for t1 solutions Answer 102890 by ankor@dixie-net.com(15660)   on 2008-05-12 17:58:01 (Show Source): You can put this solution on YOUR website!Solve for the indicated variable r+s/t=u.....solve for t : Assume you mean: = u Multiply both sides by t: t* = t(u) Cancel the t's on the left: r + s = tu : Divide both sides by u and you have: = t : : If you meant the problem to be: r + = u, let me know, and I will edit this solution.
 Travel_Word_Problems/141168: Each day a man meets his wife at the commuter train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home, the man notices that they arrived 20 minutes earlier than usual. How much time did the man spend walking?1 solutions Answer 102885 by ankor@dixie-net.com(15660)   on 2008-05-12 17:42:11 (Show Source): You can put this solution on YOUR website!Each day a man meets his wife at the commuter train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home, the man notices that they arrived 20 minutes earlier than usual. How much time did the man spend walking? : Here's what I think. Let me know if I am wrong. If she met him at the earlier time, he would be home 1 hr early. Since he is only 20 min early, he was walking for 40 min, before she picked him up
 Expressions-with-variables/141142: Factor completely: -2x to 3rd power + 16x to 2nd power - 24x1 solutions Answer 102866 by ankor@dixie-net.com(15660)   on 2008-05-12 15:41:47 (Show Source): You can put this solution on YOUR website!Factor completely: -2x to 3rd power + 16x to 2nd power - 24x : -2x^3 + 16x^2 - 24x : Factor out -2x and you have: -2x(x^2 - 8x + 12) Factors to -2x(x - 6)(x - 2)
 Expressions-with-variables/141093: Find 2 numbers such that their sum, their difference, and their product have the ratio 3:2:5.1 solutions Answer 102777 by ankor@dixie-net.com(15660)   on 2008-05-11 21:54:57 (Show Source): You can put this solution on YOUR website!ratio 3:2:5. ind 2 numbers such that their sum, their difference, and their product have the ratio 3:2:5. : Let the two numbers be x & y: = Cross multiply: 2(x+y) = 3(x-y) 2x + 2y = 3x - 3y 3y + 2y = 3x - 2x 5y = x : and = Cross multiply: 5(x-y) = 2xy 5x - 5y = 2xy 5x - 2xy = 5y x(5-2y) = 5y x = Substitute 5y for x 5y = Just looking at this we can assume (5-2y) = 1 -2y = 1 - 5 -2y = -4 y = +2 : Therefore: x = 5(2) x = 10 : Testing the solution: x=10, y=2 = and =
 Quadratic_Equations/141057: The sum of the base and height of a triangle is 25 cm. What is the maximum area of the triangle? 1 solutions Answer 102753 by ankor@dixie-net.com(15660)   on 2008-05-11 19:29:42 (Show Source): You can put this solution on YOUR website!he sum of the base and height of a triangle is 25 cm. What is the maximum area of the triangle? : Let x = length of the base Then (25-x) = length of the height : Area = .5*L*B Substituting of L and B A = .5x(25-x) A = 12.5x - .5x^2 As a quadratic equation find the axis of symmetry x = ; a=-.5 b= 12.5 x = x = x = + 12.5 is base for max area then 25 - 12.5 = 12.5 is the length for max area : A = .5 * 12.5 * 12.5 A = 78.25 sq cm is max area :
 Linear-systems/141077: This question is from textbook Prentice hall Algebra 1 How do I solve using a system of two equations in two variables? With the wind, a plane flew 1400 km in 4 hours. On the return trip, the pilot was forced to land after 1 h 30 min, having traveled only 450 km. Find the rate of the plane in still air and the rate of the wind.1 solutions Answer 102746 by ankor@dixie-net.com(15660)   on 2008-05-11 19:10:01 (Show Source): You can put this solution on YOUR website!With the wind, a plane flew 1400 km in 4 hours. On the return trip, the pilot was forced to land after 1 h 30 min, having traveled only 450 km. Find the rate of the plane in still air and the rate of the wind. : Let x = speed of the plane in still air Let y = speed of the wind then (x-y) = speed against the wind (x+y) = speed with the wind : Write two distance equations; dist = time * speed: ; 4(x+y) = 1400 1.5(x-y) = 450 : Simplify the 1st equation divide by 4 Simplify the 2nd equation divide by 1.5 : x + y = 350 x - y = 300 -------------adding eliminates y 2x = 650 x = x = 325 mph plane speed in still air : Use x + y = 350 to find y 325 + y = 325 y = 350 - 325 y = 25 mph wind speed. : : Check solution in original 1st equation 4(325 + 25) = 4 * 350 = 1400, confirms our solutions
 Mixture_Word_Problems/141043: This question is from textbook The rectangular part of the field below is 140 yards long, and the diameter of each semicircle is 40 yards. Find the cost of reseeding the field at .70 per square yard.1 solutions Answer 102701 by ankor@dixie-net.com(15660)   on 2008-05-11 14:35:25 (Show Source): You can put this solution on YOUR website!he rectangular part of the field below is 140 yards long, and the diameter of each semicircle is 40 yards. Find the cost of reseeding the field at .70 per square yard. : Find the area of the two half circles, radius = 20 A = A = 1256.637 : Find the area of the rectangular portion: A = 140 * 40 A = 5600 : Total: 1256.637 + 5600 = 6856.637 sq yds : Cost: .7 * 6856.637 = \$4799.65
 Linear-systems/140983: This question is from textbook Prentice Hall Algebra 1 How do I solve this system of equations by using multiplication with the addition method? 1/5(x+2y)=-2 x/4-3y/2=15/21 solutions Answer 102687 by ankor@dixie-net.com(15660)   on 2008-05-11 11:34:19 (Show Source): You can put this solution on YOUR website!How do I solve this system of equations by using multiplication with the addition method? : 1/5(x+2y) = -2 Multiply by 5 to get rid of the denominator x + 2y = 5(-2) x + 2y = -10 : - = Multiply equation by 4 to get rid of the denominator, resulting: x - 2(3y) = 2(15) x - 6y = 30 : Multiply the 1st equation by -1 and add to the above equation -x - 2y = +10 +x - 6y = +30 ----------------- 0x - 8y = +40 y = y = -5 : Find x using x - 6y = 30: x - 6(-5) = 30 x + 30 = 30 x = 0 ; : Check solution using the 1st original equation: 1/5(x + 2y) = -2 1/5(0 + 2(-5) = 1/5 * -10 = -2
 Rational-functions/141033: seven times the reciprocal of a number plus 2/3 is 3. Find the number1 solutions Answer 102679 by ankor@dixie-net.com(15660)   on 2008-05-11 11:18:47 (Show Source): You can put this solution on YOUR website!seven times the reciprocal of a number plus 2/3 is 3. Find the number : Let the number = x : + = 3 : multiply equation by 3x to get rid of the denominators 3(7) + 2x = 3(3x) 21 + 2x = 9x 21 = 9x - 2x 21 = 7x x = x = 3 : : check solution: + = 3
 Linear-equations/140997: The director of a summer day cmp estimates that 100 children will join if the camp fee is 250.00, but for each 20.00 decrease in the fee, ten more children will enroll. Determine the linear equation tha will represent the number of children who will enroll a a given fee. Graph the linear equatin that rpresens the number of children who will enroll at a given fee. How many students will enroll if the camp fee is 180.00? How many studens will enroll if the camp is free?1 solutions Answer 102665 by ankor@dixie-net.com(15660)   on 2008-05-11 10:28:48 (Show Source): You can put this solution on YOUR website!The director of a summer day camp estimates that 100 children will join if the camp fee is 250.00, but for each 20.00 decrease in the fee, ten more children will enroll. Determine the linear equation that will represent the number of children who will enroll a a given fee. : Let x = cost per child Let y = no. of children enrolled : From the information given, derive two set of x/y coordinates 100 kid at \$250: x1=250, y1=100 and 110 kids at \$230: x2=230, y2=110 : Find the slope using the slope equation: m = m = = m = : Use the point/slope equation: y -y1 = m(x-x1) : y - 100 = (x - 250) y - 100 = x + 125 y = x + 125 + 100 y = x + 225; is the linear equation : : Graph the linear equation that represents the number of children who will enroll at a given fee. : Graph y = x + 225, To graph this, use an x scale of 0 to +450, and y scale from 0 to 300 (we are not interested in any neg values here) You only need two pair of coordinates to plot a linear (straight line) graph However here are three sets: we will find y for x = 100, x = 200, x = 250 : Substitute 100 for x, in the equation y = -.5x + 225 and find y y = -.5(100) + 225 y = -50 + 225 y = +175 : If we were making a table for x/y values, it would be: x | y ------- 100|175 : Substitute 200 for x and find y: y = -.5(200) + 225 y = -100 + 225 y = +125 now our table is: x | y ------- 100|175 200|125 : Substitute 250 for x, find y y = -.5(250) + 225 y = -125 + 225 y = +100 we have: x | y ------- 100|175 200|125 250|100 0 |225, note this is the y intercept (the camp is free, 225 kids) : Plot these 4 points, join them with straight lines : it should look like this: : : How many students will enroll if the camp fee is 180.00? : substitute 180 for x in our equation and find y y = (180) + 225 6 = -90 + 225 y = +135 will enroll ; : How many students will enroll if the camp is free? : In this case x = 0 y = (0) + 225 y = 225 enrolled if it is free, you can see on the graph, that's the y intercept : : did this make sense to you, any questions?
 Quadratic_Equations/140682: need help with these 2 problems.Thanks for all your help. write the equation of each root 1. 6, -2/3 2. -3/4, -81 solutions Answer 102634 by ankor@dixie-net.com(15660)   on 2008-05-10 21:41:47 (Show Source): You can put this solution on YOUR website!need help with these 2 problems.Thanks for all your help. write the equation of each root : 1. 6, -2/3 Two factors (x-6) = 0 and (3x+2) = 0 FOIL 3x^2 - 18x + 2x - 12 = (3x^2 - 16x - 12) is the equation : 2. -3/4, -8 Two factors: (4x+3) = 0 and (x+8) = 0 FOIL 4x^2 + 32x + 3x + 24 = (4x^2 + 35x +24) is the equation
 Distributive-associative-commutative-properties/140939: Which do you think pays more: 4.25% simple interest for 3 years or 4% interest compounded semi-annually for the same amount of time? Explain. Please help with this question because this is so confusing!!!!!!!!!!!!1 solutions Answer 102632 by ankor@dixie-net.com(15660)   on 2008-05-10 21:27:09 (Show Source): You can put this solution on YOUR website!Which do you think pays more: 4.25% simple interest for 3 years or 4% interest compounded semi-annually for the same amount of time? Explain. : Here is the compound interest formula: A = P* where P = principal amt A = resulting amt r = interest rate (decimal) t = time in years n = no. of periods per year : We only need to use the multiplier which is: : For 4.25 % simple interest (compounded once a yr) for 3 yrs = = 1.139955 : For 4% compounded twice a year, for 3 yrs = = 1.126162 : The one with the highest multiplier pays more. (4.25%) : Did this help you understand this?