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 Equations/490590: how do I subtract: (3x^2-2x+5)-(2x^2-5x1) Thanks:)1 solutions Answer 334230 by ankor@dixie-net.com(15649)   on 2011-09-03 17:10:38 (Show Source): You can put this solution on YOUR website!subtract: (3x^2-2x+5)-(2x^2-5x1) perhaps you mean subtract: (3x^2-2x+5)-(2x^2-5x+1) : Remember the rule, when you remove brackets, a minus outside the brackets changes the signs inside the bracket ; 3x^2 - 2x + 5 - 2x^2 + 5x - 1 group the like terms 3x^2 - 2x^2 - 2x + 5x + 5 - 1 do the math x^2 + 3x + 4
 Numbers_Word_Problems/490489: how would you write ten times the difference of 6 and a number yields 1901 solutions Answer 334228 by ankor@dixie-net.com(15649)   on 2011-09-03 17:04:08 (Show Source): You can put this solution on YOUR website!write ten times the difference of 6 and a number yields 190 A simple equation 10(n - 6) = 190 10n - 60 = 190 10n = 190 + 60 10n = 250 n = 25 : : Check: 10(25-6) = 190
 Geometry_Word_Problems/490575: A rectangular garden bounded on one side by a river is to be fenced on the other three sides. Fencing material for the side parallel to the river costs \$30 per foot, and material for the other two sides costs \$10 per foot. What are the dimensions of the garden of largest possible area if \$1200 is to be spent for fencing material?1 solutions Answer 334224 by ankor@dixie-net.com(15649)   on 2011-09-03 16:55:05 (Show Source): You can put this solution on YOUR website!A rectangular garden bounded on one side by a river is to be fenced on the other three sides. Fencing material for the side parallel to the river costs \$30 per foot, and material for the other two sides costs \$10 per foot. What are the dimensions of the garden of largest possible area if \$1200 is to be spent for fencing material? : the total cost for three fenced sides 30L + 10(2W) = 1200 30L + 20W = 1200 simplify divide by 10 3L + 2W = 120 2W = 120 - 3L W = W = (60-1.5L) : A = L * W replace W A = L(60-1.5L) A = -1.5L^2 + 60L to find max area, find the axis of symmetry; x = -b/(2a) L = L = L = + 20 ft is the length Find the width W = 60 - 1.5(20) W = 30 ft the width then max area for \$1200, 20 by 30 ft : : Check this finding the cost for the perimeter with these dimensions 30(20) + 10*2(30) = 600 + 600 = 1200
 Circles/490553: A landscape architect used the entire length of an 80-foot rope to lay out a flower bed in the shape of a square. in another area, he used the entire length of the same rope to lay out a second flower bed in the shape of a circle. The perimeter of the square is 80 feet. The circumference of the circle is 80 feet. How many square feet greater is the area of one flower bed than the other? ( use 3.14 for pie) * if possible could you please explain how you got your answer , i couldnt solve this problem for hours!1 solutions Answer 334201 by ankor@dixie-net.com(15649)   on 2011-09-03 15:29:15 (Show Source): You can put this solution on YOUR website!A landscape architect used the entire length of an 80-foot rope to lay out a flower bed in the shape of a square. in another area, he used the entire length of the same rope to lay out a second flower bed in the shape of a circle. The perimeter of the square is 80 feet. The circumference of the circle is 80 feet. How many square feet greater is the area of one flower bed than the other? ( use 3.14 for pie) : A square with a perimeter of 80 ft, one side: 80/4 = 20 ft Area = 20^2 A = 400 sq/ft : A circle with a circumference of 80 ft, find r C = 2*3.14*r = 80 6.28r = 80 r = r ~ 12.74 ft is the radius Find the area A = A = 3.14*12.74^2 A = 509.55 sq/ft : Difference 509.55 400.00 ------ 109.55 sq/ft difference
 Miscellaneous_Word_Problems/490664: Hi, can someone help please? The area of a rectangular athletic field is represented by the expression 13z^6+5z^3+12z square meters. Write an algebraic expression to represent one possible set of dimensions (in the sense “length times width”) of the athletic field. Include correct units with your solution. 1 solutions Answer 334199 by ankor@dixie-net.com(15649)   on 2011-09-03 15:14:54 (Show Source): You can put this solution on YOUR website!The area of a rectangular athletic field is represented by the expression 13z^6+5z^3+12z square meters. Write an algebraic expression to represent one possible set of dimensions (in the sense “length times width”) of the athletic field. : 13z^6 + 5z^3 + 12z Factor out z A = z(13z^5 + 5z^2 + 12) then 13z^5 + 5z^2 + 12 = Length in meter and z = width in meters
 Volume/490573: Consider a rectangular box with a volume of 300 cubic centimeters. Suppose that the base is a rectangle with sides x centimeters and 3x centimeters. Let h(x) give the height of the box in centimeters and let A(x)be the total area of the six sides of the box. Find h(x) and A(x).1 solutions Answer 334197 by ankor@dixie-net.com(15649)   on 2011-09-03 15:07:09 (Show Source): You can put this solution on YOUR website!Consider a rectangular box with a volume of 300 cubic centimeters. Suppose that the base is a rectangle with sides x centimeters and 3x centimeters. Let h(x) give the height of the box in centimeters and let A(x)be the total area of the six sides of the box. Find h(x) and A(x). : Using the given volume, find the h in terms of x L * W * h = 300 3x * x * h = 300 3x^2h = 300 divide both sides by 3 x^2h = 100 divide both sides by x^2 h(x) = : Area of the sides A = 2(L*W) + 2(L*h) + 2(W*h) L=3x; W=x A = 2(3x*x) + 2(3x*h) + 2(x*h) A = 6x^2 + 6xh + 2xh A = 6x^2 + 8xh Replace h with A = 6x^2 + 8x* A(x) = 6x^2 +
 Equations/490504: Find the value of C such that the graph of 3x+c=5y has an intercept of (-4,0). 1 solutions Answer 334188 by ankor@dixie-net.com(15649)   on 2011-09-03 13:29:53 (Show Source): You can put this solution on YOUR website!Find the value of C such that the graph of 3x+c=5y has an intercept of (-4,0). : 3x + c = 5y substitute for x and y, -4 and 0 3(-4) + c = 5(0) -12 + c = 0 c = +12
 Exponents/490262: I don't even understand this let alone know how to answer it, could someone please explain? it would be really appreciated. The following is an exponential relationship between unemployment rate, U, and inflation rate, I depicted by the function I = 24e^(-0.3U) a. Sketch a graph of this function, for domain 0 ≤ U ≤ 10 b. Rearrange the formula for the above function to make U the subject. 1 solutions Answer 334187 by ankor@dixie-net.com(15649)   on 2011-09-03 13:20:54 (Show Source): You can put this solution on YOUR website!The following is an exponential relationship between unemployment rate, U, and inflation rate, I depicted by the function I = 24e^(-0.3U) a. Sketch a graph of this function, for domain 0 ≤ U ≤ 10 Rewrite the given equation using x & y, more understandable for graphing it y = 24e^(-.3x) They want us to plots this for x=0 to x=10, using a calc, substitute values for x and find y using the given equations, round to the nearest 10th : x | y ------- 0| 24;;; y = 24*e^(-.3*0)" 1| 17.8; y = 24*e^(-.3*1) 2| 13.2; y = 24*e^(-.3*2) 4| 7.2;; y = 24*e^(-.3*4) 6| 4.0;; y = 24*e^(-.3*6) 8| 2.2;; y = 24*e^(-.3*8) 10| 1.2;; y = 24*3^(-.3*10) : Plot these x/y points, it should look like this: : : b. Rearrange the formula for the above function to make U the subject. I = 24*e^(-.3u) divide both sides by 24, and write it: = Find the natural log of both sides = using the log equiv of exponents = the ln of e is 1, so we can write it; -.3u = divide both sides by -.3 u = * or using decimals we can write it u =
 Rate-of-work-word-problems/490214: A can do a work in 36 days, B can do the work in 72 days and C can do the work in 78 days. The three take turns in working, i.e. A works on the first day, B works on the second day, C on the third day and so on. Which day will they finish the work?1 solutions Answer 334075 by ankor@dixie-net.com(15649)   on 2011-09-02 21:05:07 (Show Source): You can put this solution on YOUR website!A can do a work in 36 days, B can do the work in 72 days and C can do the work in 78 days. The three take turns in working, i.e. A works on the first day, B works on the second day, C on the third day and so on. Which day will they finish the work? : Let d = the no. of days for the three men to do the work Let the completed job = 1 : + + = 1 Multiply by 2808 to clear the denominators 78(d) + 39(d) + 36(d) = 2808 26d + 13d + 12d = 2808 51d = 2808 d = d = 55.06, therefore completion will occur on the 56th day
 Miscellaneous_Word_Problems/490203: A man can make 15 boxes in 10 minutes. How many boxes can 5 men make in 2 minutes? 1 solutions Answer 334001 by ankor@dixie-net.com(15649)   on 2011-09-02 15:49:59 (Show Source): You can put this solution on YOUR website!A man can make 15 boxes in 10 minutes. How many boxes can 5 men make in 2 minutes? : Find how many minutes for one man to make 1 box = .6667 min/per box : = 15 boxes also
 logarithm/489711: 1+(4/3)log(base x-3) 4 = 11/3 base= x-3 this is soo confusing, i spent so long but i just don't get it =(. please help !1 solutions Answer 333773 by ankor@dixie-net.com(15649)   on 2011-09-01 14:10:54 (Show Source): You can put this solution on YOUR website!1+log(basex-3)(4) = Simplify by just using basic algebra subtract 1 from both sides log(basex-3)(4) = : log(basex-3)(4) = : multiply both sides by 3 4log(base x-3)(4) = 8 : divide both sides by 4 log(base x-3)(4) = 2 : Write the exponent equiv of logs (x-3)^2 = 4 : FOIL(x-3)(x-3) x^2 - 6x + 9 = 4 : Subtract 4 from both sides x^2 - 6x + 5 = 0 : Factors to (x-1)(x-5) = 0 : Two solutions x = 1, not a solution, can't have a base of a neg number x = 5, this is the valid solution : : see if it works in the original problem 1+log(base5-3)(4) = 1+log(base2)(4) = simplify using the same rules we did above. log(base2)(4) = log(base2)(4) = 4log(base2)(4) = 8 log(base2)(4^4) = 8 log(base2)(256) = 8 exponent equiv 2^8 = 256, equality reigns
 Rate-of-work-word-problems/489531: The fill pipe for a tank can fill the tank in 4 hours, and the drain pipe can drain it in 2 hours. If both pipes are accidentally opened, how long will it take to empty a half-filled tank?1 solutions Answer 333764 by ankor@dixie-net.com(15649)   on 2011-09-01 13:37:00 (Show Source): You can put this solution on YOUR website!The fill pipe for a tank can fill the tank in 4 hours, and the drain pipe can drain it in 2 hours. If both pipes are accidentally opened, how long will it take to empty a half-filled tank? : Let t = time to empty the tank with both valves open Let an empty tank = 1 then a half empty tank = .5 : - = .5 multiply 4, results: 2t - t = 4(.5) t = 2 hrs to empty the tank
 Rate-of-work-word-problems/489529: It takes my father 3 hours to plow our cornfield with his new tractor. Using the old tractor it takes me 5 hours. If we both plow for 1 hour before I go to school, how long will it take Dad to finish the plowing?1 solutions Answer 333735 by ankor@dixie-net.com(15649)   on 2011-09-01 10:38:34 (Show Source): You can put this solution on YOUR website!It takes my father 3 hours to plow our cornfield with his new tractor. Using the old tractor it takes me 5 hours. If we both plow for 1 hour before I go to school, how long will it take Dad to finish the plowing? : let t = time it takes Dad to finish plowing let the completed job = 1 (a plowed field) : + = 1 Multiply by 15 to clear the denominators results: 3 + 5(5+1) = 15 3 + 5t + 5 = 15 5t = 15 - 8 5t = 7 t = t = 1.4 hrs for Dad to finish : : Check solution (Dad plowed for a total of 2.4 hrs) 1/5 + 2.4/3 = .2 + .8 = 1; confirms our solution
 Rate-of-work-word-problems/489288: Vanessa can do a job in 12 days. After she has worked for 4 days, she is joined by Susan, and they finish the job together in 2 more days. How long would it have taken Susan to do the whole job herself?1 solutions Answer 333668 by ankor@dixie-net.com(15649)   on 2011-08-31 21:53:57 (Show Source): You can put this solution on YOUR website!Vanessa can do a job in 12 days. After she has worked for 4 days, she is joined by Susan, and they finish the job together in 2 more days. How long would it have taken Susan to do the whole job herself? : Let s = time required by Susan completing the job by herself let the completed job = 1 : From the given information we can see that V worked a total of 6 days, S worked 2 days : + = 1 multiply by 12s, results: 6s + 12(2) = 12s 24 = 12s - 6s 24 = 6s s = 24/6 s = 4 days for Susan to do the job alone.
 Rate-of-work-word-problems/489266: Can you please help me set up a formula for figuring out how long it would take two people to do one task together. Example: it takes you 30 minutes to rake the yard and it takes your brother 45 minutes, how long would it take for you both to rake the yard together?1 solutions Answer 333640 by ankor@dixie-net.com(15649)   on 2011-08-31 20:35:23 (Show Source): You can put this solution on YOUR website!it takes you 30 minutes to rake the yard and it takes your brother 45 minutes, how long would it take for you both to rake the yard together? : Here's pretty easy method, : let x = time required, when raking together (in minutes) let the completed job = 1 (a raked yard) : Each man will do a fraction of the job, the two fractions add up to 1 : + = 1 multiply by by 90 to clear the denominators, results 3x + 2x = 90 5x = 90 x = 90/5 x = 18 minutes working together : :
 Travel_Word_Problems/489028: A car and a van leave from the same point, at the same time, on the same path. The van travels 48mph, car travels 40mph. The van stops after driving 35 miles. How long till the car catches up to the van?1 solutions Answer 333586 by ankor@dixie-net.com(15649)   on 2011-08-31 16:51:18 (Show Source): You can put this solution on YOUR website!A car and a van leave from the same point, at the same time, on the same path. The van travels 48mph, car travels 40mph. The van stops after driving 35 miles. How long till the car catches up to the van? : Let w = time the van waits : write a time equation, time = dist/speed : w = - Multiply by a common denominator of 240, results 240w = 6(35) - 5(35) 240w = 210 - 175 240w = 35 w = 35/240 * 60 (to get time in minutes) w = 8.75 minutes