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# Recent problems solved by 'stanbon'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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 Equations/166786: on a business trip,dana traveled to her destination at an average speed of 55 miles per hour.coming home,her average speed was 45mph and the trip took two hours longer.how many hours did she travel alltogether?1 solutions Answer 122887 by stanbon(57940)   on 2008-11-09 22:02:25 (Show Source): You can put this solution on YOUR website!on a business trip,dana traveled to her destination at an average speed of 55 miles per hour.coming home,her average speed was 45mph and the trip took two hours longer.how many hours did she travel alltogether? ------------------- Going DATA: rate = 55 mph ; time = x hrs ; distance = rt = 55x miles --------------------------- Coming DATA: rate = 45 mph ; time = x+2 hrs ; distance = rt = 45(x+2) ---------------------------- go distance = come distance 55x = 45(x+2) 55x = 45x + 90 10x = 90 x= 9 hours ---------------- Total distance = 55x + 45x + 90 = 100x + 90 = 990 miles ================================== Cheers, Stan H.
 Mixture_Word_Problems/166784: How much water should be added to 30 gallon of a solution that is 70% antifreeze to bring the antifreeze percentage down to 60%.1 solutions Answer 122886 by stanbon(57940)   on 2008-11-09 21:54:53 (Show Source): You can put this solution on YOUR website! How much water should be added to 30 gallon of a solution that is 70% antifreeze to bring the antifreeze percentage down to 60%. ------------------------------------ antifreeze + antifreeze = antifreeze 0.70*30 + 0*x = 0.60(30+x) Multiply thru by 100 to get: 70*30 + 0 = 60(30+x) 2100 = 1800 + 60x 60x = 300 x = 5 gallons (amount of pure water hat should be added to the mixture ) ===================== Cheers, Stan
 logarithm/166783: (4^x+2) (2^x) = 321 solutions Answer 122885 by stanbon(57940)   on 2008-11-09 21:46:00 (Show Source): You can put this solution on YOUR website!(4^(x+2)) (2^x) = 32 ---------- [2^(2x+4)][2^x] = 2^5 ----------- 2^(3x+4) = 2^5 3x+4 = 5 3x + 1 x = 1/3 ============ Cheers, Stan H.
 logarithm/166778: A population grows from 11000 to 15000 in five years. Assuming the growth is exponential, find the: (a) Annual growth rate (b) Continuous growth rate Round your answers to 3 decimal places. (a) The annual growth rate is %. (b) The continuous growth rate is %.1 solutions Answer 122884 by stanbon(57940)   on 2008-11-09 21:34:13 (Show Source): You can put this solution on YOUR website!A population grows from 11000 to 15000 in five years. Assuming the growth is exponential, find the: --------------- Exponential Form: y = ab^x 15000 = 11000b^5 b^5 = 15/11 b = 1.064 ----------------- EQUATION: y = 11000*1.064^t ---------------------------------- (a) Annual growth rate: 0.064 or 6.4% (b) Continuous growth rate: not sure what you mean by this. ============================================================= Cheers, Stan H.
 Polynomials-and-rational-expressions/166621: Please help me with this problem: Determine the horizontal asymptotes of: f(x)=2x^2+3/4x^2+5 g(x)=x+4/x^4+2x^4 h(x)=x^5+2/x^3-21 solutions Answer 122807 by stanbon(57940)   on 2008-11-09 12:40:31 (Show Source): You can put this solution on YOUR website!Determine the horizontal asymptotes of: ----------- Procedure: 1st: Find the coefficient of the highest power term whether in the numerator or in the denominator. 2nd: Form the fraction of the coefficients of that highest power term as they appear in the numerator and in the denominator. 3rd: The horizontal asumptote is y = that ratio, if it exists. ================================== f(x)=2x^2+3/4x^2+5 Highest power: x^2 HA: y = 2/4 = 1/2 ------------------------ g(x)=x+4/x^4+2x^4 Highest power: x^4 HA: y = 0/1 = 0 ----------------------- h(x)=x^5+2/x^3-2 Highest power: x^5 HA: y = 1/0 So, no Horizontal asymptote, There is a slant asymptote. ================================== Cheers, Stan H.
 Money_Word_Problems/166625: Alfred wants to invest \$4,000 at 6% simple interest rate for 5 years. How much interest will he receive?1 solutions Answer 122806 by stanbon(57940)   on 2008-11-09 12:28:14 (Show Source): You can put this solution on YOUR website!Alfred wants to invest \$4,000 at 6% simple interest rate for 5 years. How much interest will he receive? ------------------------------------- I = Prt I = 4000*0.06*5 = \$1200 ========================== Cheers, Stan H.
 Rational-functions/166626: Can someone help me with the question: Use the rational zeros theorem to list all possible rational zeros of P(x)=3x^3-5x^2+4x-2. Thank you.1 solutions Answer 122805 by stanbon(57940)   on 2008-11-09 12:24:57 (Show Source): You can put this solution on YOUR website!Use the rational zeros theorem to list all possible rational zeros of P(x)=3x^3-5x^2+4x-2. ------------------ Since the coefficients add to zero, x=1 is a root. ------- Use synthetic division to find the other roots: 1)....3....-5,,,,4....-2 ........3....-2...2...|..0 ================================= Quotient: 3x^2-2x+2 Remainder: 0 ================================= Find the zeroes of the Remainder, 3x^2 -2x + 2: x = [2 +- sqrt(4 - 4*3*2)]/(2*3) x = [2 +- sqrt(4 - 24)]/6 x = [2 +- sqrt(-20)]/6 These are not rational zeroes. The only rational zero is x=1 ================================== Cheers, Stan H.
 Trigonometry-basics/166629: 2 csc2x + 4 = 1 2 csc2x + 3 = 0 ??1 solutions Answer 122802 by stanbon(57940)   on 2008-11-09 12:15:31 (Show Source): You can put this solution on YOUR website!2 csc2x + 4 = 1 2 csc(2x) = -3 csc(2x) = -3/2 2x = arccsc(-3/2) = -41.81 degrees x = -20.09 degrees or x = 339.09 degrees ============================ 2 csc2x + 3 = 0 2csc(2x) = -3 csc(2x) = -3/2 Same answer as abvove ============================ Cheers, Stan H.
 Quadratic_Equations/166604: Write the equation of a quadratic that has zeros of 5 and 1 with F(0)=1. I understand you need to multiply (x-5)(x-1) to get the polynomial, but f(0) wouldnt equal 1. PLEASE HELP ME OUT!!!1 solutions Answer 122789 by stanbon(57940)   on 2008-11-09 08:46:58 (Show Source): You can put this solution on YOUR website!Write the equation of a quadratic that has zeros of 5 and 1 with F(0)=1. I understand you need to multiply (x-5)(x-1) to get the polynomial, but f(0) wouldnt equal 1. ------------------------ Right. That is why you need a variable factor,like "k" below. --------- f(x) = k(x-5)(x-1) --- Now you get f(0) = k(-5)(-1) = 1 5k = 1 k = 1/5 ------------ EQUATION: y = (1/5)(x-5)(x-1) ========================== Cheers, Stan H.
 Linear-systems/166603: A credit manager rates each applicant for a car loan on a scale of 1 through 5 and then determines the interest rate from the accompanying table FIND THE EQUATION of the linear in slope-intercept form that goes through these points: (1,24)(2,20)(3,16)(4,12)(5,8)1 solutions Answer 122787 by stanbon(57940)   on 2008-11-09 08:42:21 (Show Source): You can put this solution on YOUR website!A credit manager rates each applicant for a car loan on a scale of 1 through 5 and then determines the interest rate from the accompanying table FIND THE EQUATION of the linear in slope-intercept form that goes through these points: (1,24)(2,20)(3,16)(4,12)(5,8) ---------------------------------- slope = (20-24)/(2-1) = -4 ------------ intercept: 24 = (-4)(1) = b b = 28 ------------ EQUATION: y = -4x + 28 =================== Cheers, Stan H.
 Matrices-and-determiminant/166576: can someone please help me with this problem: Find the order of the matrix product AB and the product BA, whenever the products exist. A is 2 x 1, B is 1 x 1 a. AB is 2 x 1, BA is nonexistent. b. AB is nonexistent, BA is 1 x 2 c. AB is 1 x 2, BA is 1 x 1 d. AB is 2 x 2, BA is 1 x 11 solutions Answer 122785 by stanbon(57940)   on 2008-11-09 08:35:56 (Show Source): You can put this solution on YOUR website!Find the order of the matrix product AB and the product BA, whenever the products exist. --------------------- Rule: The number of columns on the left must be the same as the number of rows on the right. The product of an [x by y matrix] and a [w by z matrix] will be x by z] To have a product, y must bethe same as w. -------------------------- A is 2 x 1, B is 1 x 1 AB ? Can be multiplied because 1=1 Product will be 2 x 1 --------------------------- BA ? Cannot be multiplied because 1 is not equal to 2 ---------------------------- Answer: a ============== Cheers, Stan H. ============== a. AB is 2 x 1, BA is nonexistent. b. AB is nonexistent, BA is 1 x 2 c. AB is 1 x 2, BA is 1 x 1 d. AB is 2 x 2, BA is 1 x 1
 Mixture_Word_Problems/166588: You need 880 mL of a 75% alcohol solution. On hand, you have a 20% alcohol mixture. How much of the 20% alcohol mixture and pure alcohol will you need to obtain the desired solution? You will need mL of the 20% solution and mL of pure alcohol.1 solutions Answer 122778 by stanbon(57940)   on 2008-11-09 06:51:23 (Show Source): You can put this solution on YOUR website!You need 880 mL of a 75% alcohol solution. On hand, you have a 20% alcohol mixture. How much of the 20% alcohol mixture and pure alcohol will you need to obtain the desired solution? -------------------------------------- alcohol + alcohol = alcohol 0.20x + 1(880-x) = 0.75*880 Multiply thru by 100 to get: 20x + 100*880 -100x = 75*880 -80x = - -20*880 x = 220 mml ( amt. of pure alcohol needed for the mixture) 880-220 = 660mml ( amt. of 20% solution you need for the mixture) =========== Cheers, Stan H.
 Money_Word_Problems/166594: This question is from textbook The total value of the nickels, dimes, and quarters in a coin bank is \$4. If the nickels were dimes and the dimes were nickels, the total value of the coins would be \$3.75. If the quarters were dimes and the dimes were quarters, the total value would be \$6.25. Find the number of nickels, dimes, and quarters in the bank. 1 solutions Answer 122777 by stanbon(57940)   on 2008-11-09 06:44:21 (Show Source): You can put this solution on YOUR website!The total value of the nickels, dimes, and quarters in a coin bank is \$4. If the nickels were dimes and the dimes were nickels, the total value of the coins would be \$3.75. If the quarters were dimes and the dimes were quarters, the total value would be \$6.25. Find the number of nickels, dimes, and quarters in the bank. -------------- EQUATIONS: 5n + 10d + 25q = 400 10n+ 5d + 25q = 375 5n + 25d + 10q = 625 ------------------------ Solve by any method to get: n=15 d=20 q=5 ========== Cheers, Stan H.
 Graphs/166598: How do I graph the following using slope? 1. 4x + y = 6 2. 2y -2 = 6x 3. 3y - 6 = 6x 4. 2x + 6y = 121 solutions Answer 122776 by stanbon(57940)   on 2008-11-09 06:37:47 (Show Source): You can put this solution on YOUR website!How do I graph the following using slope? ---------------------- In each case you start with the y-intercept, then you apply the slope. ---------------- 1. 4x + y = 6 y =-4x + 6 1st: Mark the intercept at (0,6) 2nd: The slope is -4/1 Procedure: move your pencil 1 to the right and then down 4 to the point (1,2). Draw a line thru the two points. ---------------------- 2. 2y -2 = 6x y = 3x + 1 1st: Mark (0,1) 2nd: The slope is 3/1 Move your pencil 1 to the right and up 3 to the point (1,4) Draw a line thru the two points. ------------------------ 3. 3y - 6 = 6x y = 2x + 2 1st: mark (0,2) 2nd: the slope is 2/1 move your pencil 1 to the right and then up 2 to the point (1,4) Draw the line.--------------------------- 4. 2x + 6y = 12 y = (-1/3)x + 2 slope is (-1/3) which can be written as (-1/3)/1 intercept = (0,2) mark (0,2) move your pencil 1 to the right and down (1/3) to the point (1,1 2/3) or (1,5/3) Draw the line ===================== Cheers, Stan H.
 Quadratic_Equations/166597: if the perimeter of a rectangle is expressed by the formula p=2l+2w the side w can be found by the formula ?1 solutions Answer 122775 by stanbon(57940)   on 2008-11-09 06:24:50 (Show Source): You can put this solution on YOUR website!if the perimeter of a rectangle is expressed by the formula p=2l+2w the side w can be found by the formula ? ------------------ Solve the forula for "w": P = 2l + 2w 2w = P -2l w = (P- 2l)/2 ================== Cheers, Stan H.
 Signed-numbers/166547: this is an order of operation problem: 3x2÷6+2x3÷6 ??????? = 3²+2²+1² can you please help me on this problem i tried really hard but i cant seem to get it right.1 solutions Answer 122745 by stanbon(57940)   on 2008-11-08 18:30:19 (Show Source): You can put this solution on YOUR website!this is an order of operation problem: 3x2÷6+2x3÷6 ??????? = 3²+2²+1² ------------------ QUestion: What are the instructions you have with this problem? It is not clear what you are asked to do. Cheers, Stan H.
 Equations/166546: Hello, I'm stuck on this homework problem. My professor gave us a worksheet and I'm stumped on this one. Instruction: Write an equation for each line. Express it in the standard form Ax + By = C Through (4,2) and (-2,5) Thank you so much, Joan1 solutions Answer 122743 by stanbon(57940)   on 2008-11-08 18:27:46 (Show Source): You can put this solution on YOUR website!Write an equation for each line. Express it in the standard form Ax + By = C Through (4,2) and (-2,5) ----------------------------- slope : (5-2)/(-2-4) = -1/6 ----------------------------- intercept: 2 = (-1/2)*4 + b 2 = -2 + b b = 4 ------------- EQUATIONs; y = (-1/2)x + 4 -------------- Putting it into standard form: 2y = -x + 8 x + 2y = 8 ================= Cheers, Stan H.
 Systems-of-equations/166543: can someone please show me how to do this problem: Use the Gauss-Jordan method to solve the system of equations. x+y+z=7 x-y+2z=7 2x+3z=14 a. 3z+14/2; z/2; z b. -3z-14/2; z/2; z c. -3z+ 14/2; z/2; z d. -3z+14/2; 2z; z1 solutions Answer 122742 by stanbon(57940)   on 2008-11-08 18:22:55 (Show Source): You can put this solution on YOUR website!x+y+z=7 x-y+2z=7 2x+3z=14 --------------- Subtract the 1st row from the 2nd Subtract 2 times the 1st from from the 3rd ----------------------------- x + y + z = 7 0 - 2y + z = 0 0 - 2y + z = 0 - -------------- Subtract the 2nd row from the 3rd row to get: x + y + z = 7 0 - 2y + z = 0 0 +- 0 + 0 = 0 - -------------- Conclusion: z = 2y --------- x + (1/2)z + z = 7 x = (-3/2)z + 7 ---------------------- Solution: x = (-3/2)z+7 y = (1/2)z z = z =========== Cheers, Stan H. ============= Ans: "c" ============= a. 3z+14/2; z/2; z b. -3z-14/2; z/2; z c. -3z+ 14/2; z/2; z d. -3z+14/2; 2z; z
 Polynomials-and-rational-expressions/166545: 4x (2 power)-5x+1 ----------------- x Is this a polynomial and if it is What is the degree what is the leading coeficeint what is constant term1 solutions Answer 122740 by stanbon(57940)   on 2008-11-08 17:40:40 (Show Source): You can put this solution on YOUR website!It is not a polynomial. --------------- Cheers, Stan H.
 Matrices-and-determiminant/166537: can someone show me how to do this problem: Barnes and Able sell life, health, and auto insurance. Sales for May and June are given in the matrices. M = [20,000; 15,000; 8000] [30,000; 0; 17,000] J = [70,000; 0; 30,000] [20,000; 25,000; 32,000] Find the matrix that would give total sales for the months of May and June. a. [90,000; 15,000; 38,000] [50,000; 25,000; 49,000] b. [90,000; 15,000; 38,000] [50,000; 25,000; 32,000] c. [90,000; 0; 38,000] [50,000; 0; 49,000] d. [140,000; 40,000; 87,000]1 solutions Answer 122739 by stanbon(57940)   on 2008-11-08 17:38:32 (Show Source): You can put this solution on YOUR website!Answer: "a" ============== Cheers, Stan H.
 Matrices-and-determiminant/166540: can somoene please show me how to do this problem: Solve the matrix equation for X. A = [2; 2; 0] [-4; -3; 2] [0; -3; -5] B = [-10] [2] [-9] AX = B a. [-113] [108] [-63] b. [-113] [108] [-65] c. [-118] [109] [-63] d. [-113] [107] [-62] 1 solutions Answer 122738 by stanbon(57940)   on 2008-11-08 17:34:28 (Show Source): You can put this solution on YOUR website!Answer is "a". ================= Cheers, Stan H.
 Linear_Algebra/166538: What is the sum of the roots of the equation ax^2+bx+c=01 solutions Answer 122735 by stanbon(57940)   on 2008-11-08 17:30:10 (Show Source): You can put this solution on YOUR website!What is the sum of the roots of the equation ax^2+bx+c=0 Roots: x = [-b + sqrt(b^2-4ac)]2a or x = [-b -sqrt(b^2-4ac)]/2a --------------- Adding you get [-b/2a] + [-b/2a] = 2[-b/2a] = -b/a =============== Cheers, Stan H.
 Money_Word_Problems/166532: Andrea's savings account has a balance of \$504. After 4 years, what will the amount of interest be at 5% compounded quarterly?1 solutions Answer 122730 by stanbon(57940)   on 2008-11-08 16:58:00 (Show Source): You can put this solution on YOUR website!Andrea's savings account has a balance of \$504. After 4 years, what will the amount of interest be at 5% compounded quarterly? ----------------- A(t) = P(1+(r/n))^(nt) 504 = P(1+(0.05/4))^(4*4) 504 = P(1.2199) 504 = P + P(0.2199) ------------- Interest = 0.2199 or 21.99% ============================== Cheers, Stan H.
 Pythagorean-theorem/166528: Use the pythagorean theorem then find the exact length of the hypotenuse in the following right triangle 5 and 71 solutions Answer 122729 by stanbon(57940)   on 2008-11-08 16:51:33 (Show Source): You can put this solution on YOUR website!Use the pythagorean theorem then find the exact length of the hypotenuse in the following right triangle 5 and 7 ----------------------- hypoteuse^2 = 5^2 + 7^2 h^2 = 25+49 h^2 = 74 hypotenuse = sqrt(74) =========================== Cheers, Stan H.
 Exponential-and-logarithmic-functions/166530: Solve using completing the square, 3x^2-6x=271 solutions Answer 122728 by stanbon(57940)   on 2008-11-08 16:48:37 (Show Source): You can put this solution on YOUR website!Solve using completing the square, 3x^2-6x=27 ----------- 1st: Simplify: x^2 - 2x = 9 x^2-2x+1 = 10 (x-1)^2 = 10 x-1 = sqrt(10) or (x-1) = -sqrt(10) x = 1+sqrt(10) or x = 1-sqrt(10) =================================== Cheers, Stan H.
 Linear_Algebra/166495: State the number of positive real zeros, negative real zeros, and imaginary zeros for g(x)=9x^3-7x^2+10x-4. I must show my work. This is from a worksheet and I'm not sure how to do it. Thanks1 solutions Answer 122721 by stanbon(57940)   on 2008-11-08 14:44:31 (Show Source): You can put this solution on YOUR website!State the number of positive real zeros, negative real zeros, and imaginary zeros for g(x)=9x^3-7x^2+10x-4. g(-x) = -9x^2 - 7x^2 - 10x -4 ------------------------------------- Using DesCartes Rule of Signs: # of changes of sign in g(x) = 3; so 1 or 3 positive Real roots ------------------------------ # of changes of sign in g(-x) = 0; so 0 negative Real Roots ------------------------------ # of imaginary zeroes is 0 or two because g(x) is a cubic ================================ Comment: graphing g(x) is find it has one positive Real Root. So it must have 2 imaginary roots. ================================= Cheers, Stan H.
 Rate-of-work-word-problems/166515: Barry can do a certain job in 3 hours, whereas Sanchez 5 hours to do the same job. How long would it take them to do the job working together?1 solutions Answer 122720 by stanbon(57940)   on 2008-11-08 14:03:15 (Show Source): You can put this solution on YOUR website!Barry can do a certain job in 3 hours, whereas Sanchez 5 hours to do the same job. How long would it take them to do the job working together? -------------------------- Barry DATA: time = 3 hrs/job ; rate = 1/3 job/hr. --------------------------- Sanchez DATA: time = 5 hr/job ; rate= 1/5 job/hr --------------------------- Together DATA: time = x hr/job ; rate = 1/x job/hr. --------------- EQUATION: rate + rate = together rate 1/3 + 1/5 = 1/x 5x + 3x = 15 8x = 15 x = 15/8 hrs. (time to do the job together) Comment: 15/8 hrs. = 1 hr. and 52 minutes and 50 seconds ============================================= Cheers, Stan H. =====================
 Percentage-and-ratio-word-problems/166516: A sum of \$2730 is to be divided between two people in the ratio 7 to 6. How much does each person receive?1 solutions Answer 122716 by stanbon(57940)   on 2008-11-08 13:52:51 (Show Source): You can put this solution on YOUR website!A sum of \$2730 is to be divided between two people in the ratio 7 to 6. How much does each person receive? --------------------- 7 to 6 is the same as 7x to 6x. --------------------- EQUATION: 7x + 6x = 2730 13x = 2730 x = 210 -------- 6x = 1260 7x = 1470 ================ Cheers, Stan H.
 Complex_Numbers/166517: Complex Fraction (2/14x)/(4/7xy) 1 solutions Answer 122714 by stanbon(57940)   on 2008-11-08 13:48:28 (Show Source): You can put this solution on YOUR website!(2/14x)/(4/7xy) ------------------ Invert the denominator and change to multiplication to get: = [1/7x] * [7xy/4] Cancel factors common to a numerator and a denominator to get: = [1/1] * [y/4[ = y/4 ============== Cheers, Stan H.
 test/166491: please help me solve 1) 6x^2+24x=2x^2-36 2) 3x^2-17x+20=0 for this one i got (x-6)(3x-5) is this correct 3) x^2-36=01 solutions Answer 122698 by stanbon(57940)   on 2008-11-08 11:21:33 (Show Source): You can put this solution on YOUR website!1) 6x^2+24x=2x^2-36 4x^2 +24x + 36 = 0 x^2 + 6x + 9 = 0 (x+3)^2 = 0 x = -3 with multiplicity 2 =================================== 2) 3x^2-17x+20=0 3x^2 - 12x - -5x + 20 = 0 3x(x-4)-5(x-4) = 0 (x-4)(3x-5) = 0 x = 4 or x = 5/3 ===================== 3) x^2-36=0 (x-6)(x+6) = 0 x = 6 or x = -6 ====================== Cheers, Stan H.
 Linear-equations/166494: x is greater than or equal to -1 can you please help me solve this equation? 1 solutions Answer 122695 by stanbon(57940)   on 2008-11-08 11:12:59 (Show Source): You can put this solution on YOUR website!x is greater than or equal to -1 can you please help me solve this equation? -------------------- That is the solution: x >= -1 ==================================== Cheers, Stan H.