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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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 Graphs/348269: solve the compound inequality. graph the solution set and give the solution in interval notation x≤3 or x≥51 solutions Answer 248983 by stanbon(57961)   on 2010-09-26 14:51:20 (Show Source): You can put this solution on YOUR website! solve the compound inequality. graph the solution set and give the solution in interval notation x≤3 or x≥5 (-oo,3]U[5,+oo) ===================== Cheers, Stan H.
 test/348268: Find three consecutive integers such that the sum of twice the smallest and three times the largest is 126. Please explain how to do it thanks:)1 solutions Answer 248981 by stanbon(57961)   on 2010-09-26 14:48:31 (Show Source): You can put this solution on YOUR website!Find three consecutive integers such that the sum of twice the smallest and three times the largest is 126. Please explain how to do it --------------- 1st: x 2nd: x+1 3rd: x+2 ---- Equation: 2x+3(x+2) = 126 --- 2x+3x+6 = 126 5x = 120 x = 24 x+1 = 25 x+2 = 26 ==================== Cheers, Stan H.
 Travel_Word_Problems/348262: A car goes at v mph for a hours then goes in the opposite direction at u mph for b hours. How far is the car from where it started at the end?1 solutions Answer 248980 by stanbon(57961)   on 2010-09-26 14:44:52 (Show Source): You can put this solution on YOUR website!A car goes at v mph for a hours then goes in the opposite direction at u mph for b hours. How far is the car from where it started at the end? -------------------------------- 1st leg DATA: rate = v mph ; time = a hrs ; distance = va miles ---------------- 2nd leg DATA: rate = u mph ; time = b hrs ; distance = ub miles ----------------- End how far from start: va-ub miles ============================================ Cheers, Stan H.
 Mixture_Word_Problems/348257: How much water must be added to 20.0ml of a 60.0% saline solution in order to make a 45.0% saline solution?1 solutions Answer 248978 by stanbon(57961)   on 2010-09-26 14:39:00 (Show Source): You can put this solution on YOUR website!How much water must be added to 20.0 ml of a 60.0% saline solution in order to make a 45.0% saline solution? --------------------------------------- Equation: salt + salt = salt 0*x + 0.60*20 = 0.45(x+20) Multiply thru by 100 to get: 60*20 = 45x + 45*20 45x = 15*20 x = (1/3)20 x = 6 2/3 ml (amount of water needed for the mixture) ========================= Cheers, Stan H.
 Linear_Algebra/348243: how do you graph this linear inequality? x less than equal to 01 solutions Answer 248976 by stanbon(57961)   on 2010-09-26 14:32:17 (Show Source): You can put this solution on YOUR website!how do you graph this linear inequality? x less than equal to 0 ---------------------- Note: You never graph an inequality directly. You graph the boundary, which is always an equality. =============== Graph x = 0 as a dashed line. --- Ssince you want x LESS than 0, shade the half-plane to the left of the boundary. That is the graph of the inequality. ----------------------- Cheers, Stan H.
 Angles/348247: Find the measure of an angle if its measure is 5 degree less than four times the measure of its complement. A) 37 degrees B) 19 degrees C) 71 degrees D) 143 degrees1 solutions Answer 248975 by stanbon(57961)   on 2010-09-26 14:23:58 (Show Source): You can put this solution on YOUR website!duplicate
 Angles/348240: Find the measure of an angle if its measure is 5 degrees less than four times the measure of its complement. 1 solutions Answer 248974 by stanbon(57961)   on 2010-09-26 14:22:31 (Show Source): You can put this solution on YOUR website!Find the measure of an angle if its measure is 5 degrees less than four times the measure of its complement. ---- angle : x complement : 90-x ------------------------ Equation: x = 4(90-x)-5 x = 360-4x-5 5x = 355 x = 71 degrees ================= Cheers, Stan H. =================
 Miscellaneous_Word_Problems/348176: A random sample of 600 high school boys showed that 40 had taken diet pills during the past 30 days to lose weight The researcher wants to test the hypotheses below for p = the proportion of all high school boys who take diet pills to lose weight. H0: p = 0.10 Ha: p ≠ 0.10 1.State the null hypothesis (H0) and the alternative hypothesis (Ha) in words. 2.Verify necessary data conditions for a z-statistic and calculate the z-statistic. 3.Assuming the null hypothesis is true, find the p-value. 4.Are the results statistically significant at a significance level of α = 0.05? 5.Report the conclusion in the context of the situation1 solutions Answer 248960 by stanbon(57961)   on 2010-09-26 12:45:14 (Show Source): You can put this solution on YOUR website! A random sample of 600 high school boys showed that 40 had taken diet pills during the past 30 days to lose weight The researcher wants to test the hypotheses below for p = the proportion of all high school boys who take diet pills to lose weight. H0: p = 0.10 Ha: p ≠ 0.10 1.State the null hypothesis (H0) and the alternative hypothesis (Ha) in words. Ho: 10% of high school boys take diet pills Ha: The % of high school boys who take diet pills is not 10%. ------------------------------------------------- 2.Verify necessary data conditions for a z-statistic and calculate the z-statistic. I'll leave that to you. Check your textbook. ------------------------------------------------- 3.Assuming the null hypothesis is true, find the p-value. p-hat = 40/600 = 0.4 z(0.4) = (0.4-0.1)/sqrt(0.4*0.6/600) = 15 --- p-value = 2*P(z > 15) = 2*3.85x10^-51 = 7.70x10^-71 ================ 4.Are the results statistically significant at a significance level of α = 0.05? Since the p-value is less than 5%, reject Ho. ------ 5.Report the conclusion in the context of the situation The test does not support the claim that the \$ of high school boys taking diet pills is 10% ================================= cheers, Stan H.
 Quadratic_Equations/348179: Solving a quadratic equation with the Indian method: Solve x^2+3x-10=0 x^2+3x=10 Next step is to multiply each term by four times the original coefficient of the x^2 term 4x^2+12x=40 Next square the original coefficient of x and add it to both sides of the equation: 4x^2+12x+9=40+9 4x^2+12x+9=49 Next is to take the square root of both sides, this is where I'm confused by my textbook: I know that the square root of 4x^2 = 2x but the square root of 12x is not going to be a 'clean' number and the square root of 9 and 49 are 3 and 7... the textbook says that 4x^2+12x+9=49 taken to the square root is 2x + 3= +-7 Where did the 12x go?1 solutions Answer 248958 by stanbon(57961)   on 2010-09-26 12:27:19 (Show Source): You can put this solution on YOUR website!Solve x^2+3x-10=0 x^2+3x=10 Next step is to multiply each term by four times the original coefficient of the x^2 term 4x^2+12x=40 Next square the original coefficient of x and add it to both sides of the equation: 4x^2+12x+9=40+9 4x^2+12x+9=49 Next is to take the square root of both sides ------------------- The left side factors as (2x+3)^2 ---- (2x+3)^2 = 49 Taking the square root of both sides you get: 2x+3 = 7 or 2x+3 = -7 2x = 4 or 2x = -10 x = 2 or x = -5 ==================== Cheers, Stan H. ====================
 Rational-functions/348136: Problem 1: (√x+4) +2 = (√x + 20) I know the answer is 5, but do not understand how to work the problem. Problem 2: (5√x-2) -3 = (√19x-29) How do you get 27 as the answer?1 solutions Answer 248945 by stanbon(57961)   on 2010-09-26 10:18:18 (Show Source): You can put this solution on YOUR website!Problem 1: (√x+4) +2 = (√(x + 20)) I know the answer is 5, but do not understand how to work the problem. --- Square both sides to get: (x+4) + 4(sqrt(x+4)) + 4 = x + 20 ------ 4sqrt(x+4) = 12 sqrt(x+4) = 3 ---- Square both sides to get: x+4 = 9 x = 5 =============== Problem 2: (5√x-2) -3 = (√19x-29) Square both sides to get: 25(x-2) - 6*5sqrt(x-2) + 9 = 19x-29 ---- 25x-50 - 30sqrt(x-2) = 19x-38 -30sqrt(x-2) = 12-6x ------------------------ (5√x-2) -3 = (√19x-29) --- x cannot be 2 ---- Final Answer: x = 27 ========================== Cheers, Stan H. -5sqrt(x-2) = 2-x ---- Square both sides: 25(x-2) = 4 - 4x + x^2 25x-50 = 4 - 4x + x^2 x^2 -29x+54 = 0 (x-27)(x-2) = 0 --- x = 27 or x = 2 ------------------------ Checking in original equation: How do you get 27 as the answer?
 logarithm/348140: ln(y+4)=ln(y+1)+ln5; I tried working each side out individually on my calculator but the answers do not agree with my any of my 4 choices. I came up with 2.639 for left side and 4.007 for right side1 solutions Answer 248944 by stanbon(57961)   on 2010-09-26 10:02:14 (Show Source): You can put this solution on YOUR website!ln(y+4) = ln(y+1)+ln5 ---- ln(y+4) = ln[5(y+1)] ---- y+4 = 5(y+1) y+4 = 5y+5 4y = -1 y = -1/4 ==================== Cheers, Stan H.
 logarithm/348143: Assume that x,y, and z are positive numbers. Us the properties of logarithms to write expression in terms of the logarithms of x, y, and z. log(base b)x^1/2y^31 solutions Answer 248943 by stanbon(57961)   on 2010-09-26 09:59:19 (Show Source): You can put this solution on YOUR website!Assume that x,y, and z are positive numbers. Use the properties of logarithms to write expression in terms of the logarithms of x, y, and z. log(base b)x^1/2y^3 ------ = logb[x^(1/2)] - logb[y^3] ------ = (1/2)logb(x) - 3logb(y) ============================== Cheers, Stan H.
 Quadratic_Equations/348144: What are the dimensions of a rectangular box that has w=x h=x and length=x+1? I have given up! I came up with answers that did not match, and then tried to put answers into the quadratic formula, and still nothing. Your help would be much appreciated. Thank you.1 solutions Answer 248941 by stanbon(57961)   on 2010-09-26 09:55:39 (Show Source): You can put this solution on YOUR website!What are the dimensions of a rectangular box that has w=x h=x and length=x+1? total Surface Area of the box = 130cm^2. ------------------ Equation: SA = 2(lw)+2(lh)+2(wh) = 2(lw+lh+wh) --- 130 = 2[(x+1)x + (x+1)x + x^2] 65 = x^2+x+x^2+x + x^2 3x^2 + 2x-65 = 0 ---- Use the quadratic formula to get: x = 4.333 ----- width = 4.333 height = 4.333 length = 5.333 ===================== Cheers, Stan H. =================
 Angles/348142: hey how are you? i really need help on this qs... The sum of the measures of the angle of any triangle is 180.In traingle ABC, angles A and B have the same measure, while the measure of angle C is 135 larger than each of A and B. what are the measures of the three angles? the choices are A.) A and B:25; C:130 B)A and B:15 ; C:150 C). A and C:130, B:25 D)A and B: 150, C:15 i think the answer is A but imnot suree?? 1 solutions Answer 248940 by stanbon(57961)   on 2010-09-26 09:53:14 (Show Source): You can put this solution on YOUR website!The sum of the measures of the angle of any triangle is 180.In traingle ABC, angles A and B have the same measure, while the measure of angle C is 135 larger than each of A and B. what are the measures of the three angles? ----- Equations: a + b + c = 180 a = b c = a + 135 ----------------------- Substitute for b and c and solve for "a": a + a + a+135 = 180 --- 3a = 45 a = 15 degrees b = 15 degrees c = 150 degrees ------------------ Cheers, Stan H. ========== the choices are A.) A and B:25; C:130 B)A and B:15 ; C:150 C). A and C:130, B:25 D)A and B: 150, C:15
 Probability-and-statistics/348132: An office employs seven women and five men. One employee will be randomly selected to receive a free lunch with the boss. What is the probability that the selected employee will be a woman?1 solutions Answer 248938 by stanbon(57961)   on 2010-09-26 09:44:17 (Show Source): You can put this solution on YOUR website!An office employs seven women and five men. One employee will be randomly selected to receive a free lunch with the boss. What is the probability that the selected employee will be a woman? ------------- P(woman) = 7/12 ====================== Cheers, Stan H.
 Expressions-with-variables/348096: Tracy, Stacy and Fred assembled a very large puzzle together in 40 hours. If Stacy worked twice as fast as Fred and Tracy worked just as fast as Stacy, how long would it have taken Fred to assemble the puzzle alone?1 solutions Answer 248924 by stanbon(57961)   on 2010-09-26 08:18:38 (Show Source): You can put this solution on YOUR website!Tracy, Stacy and Fred assembled a very large puzzle together in 40 hours. If Stacy worked twice as fast as Fred and Tracy worked just as fast as Stacy, how long would it have taken Fred to assemble the puzzle alone? -------------- Together rate: 1/40 job/hr --- Fred rate = 1/2x job/hr --- Stacy rate = 1/x job/hr --- Tracy rate = 1/x job/hr --------------------------- Equation: 1/x + 1/x + 1/2x = 1/40 --- 40 + 40 + 20 = x x = 100 hrs --- Fred's time alone = 2x = 200 hrs. ==================================== Cheers, Stan H.
 Expressions-with-variables/348105: 1 solutions Answer 248921 by stanbon(57961)   on 2010-09-26 08:13:16 (Show Source): You can put this solution on YOUR website!5/(y-3) = (y+7)/(2y-6) + 1 ---- Multiply thru by 2y-6 to get: 10 = y+7 + 2y-6 --- 3y+1 = 10 3y = 9 y = 3 ====================== But 3 cannot be a solution because y-3 is a denominator. ======================= Ans: No solution ====================== Cheers, Stan H.
 Expressions-with-variables/348108: It takes a computer 8 days to print all of personalized letters for a national sweepstakes. A new computer is purchased that can do the same job in 5 days. How long would it take to do the job with both computers working on it?1 solutions Answer 248918 by stanbon(57961)   on 2010-09-26 08:09:43 (Show Source): You can put this solution on YOUR website!It takes a computer 8 days to print all of personalized letters for a national sweepstakes. A new computer is purchased that can do the same job in 5 days. How long would it take to do the job with both computers working on it? ---- Older computer rate = 1/8 job/day --- new computer rate = 1/5 job/day ----- Let together rate = 1/x =============================== Equation: rate + rate = together rate 1/8 + 1/5 = 1/x 5x + 8x = 40 13x = 40 x = 40/13 = 3.08 days (time working together) ===================================================== Cheers, Stan H.
 Quadratic_Equations/348121: A plasma TV company determines that its total profit on the production and sale of x TVs is given by: P (x) = -sqrt 2 +812 - 96001 solutions Answer 248912 by stanbon(57961)   on 2010-09-26 08:00:39 (Show Source): You can put this solution on YOUR website!A plasma TV company determines that its total profit on the production and sale of x TVs is given by: P (x) = -sqrt 2 +812 - 9600 -------------- What is the question? Cheers, stan H.
 test/348122: An admission to a museum costs \$11 for children and seniors and \$14 for adults. If \$24726 was collected from the sale admission tickets, how many adult tickets were sold?1 solutions Answer 248910 by stanbon(57961)   on 2010-09-26 07:59:23 (Show Source): You can put this solution on YOUR website!An admission to a museum costs \$11 for children and seniors and \$14 for adults. If \$24726 was collected from the sale admission tickets, how many adult tickets were sold? ------------------------- You have to know the total number of tickets sold. Ceers, Stan H.
 Evaluation_Word_Problems/348115: as x approaches 1 find the limit of e^(x-x^2)1 solutions Answer 248908 by stanbon(57961)   on 2010-09-26 07:57:32 (Show Source): You can put this solution on YOUR website!as x approaches 1 find the limit of e^(x-x^2) lim[e^(x-x^2)] as x approaches 1 = e^(1-1) = e^0 = 1 ====================== Cheers, Stan H.
 Evaluation_Word_Problems/348116: as x approaches infinity find the limit of e^ (x- x^2)1 solutions Answer 248907 by stanbon(57961)   on 2010-09-26 07:51:36 (Show Source): You can put this solution on YOUR website!as x approaches infinity find the limit of e^ (x- x^2) ---- e^(x-x^2) = e^x/e^x^2 = 1/e^x -- lim as x approaches oo = 1/oo = 0 ======================================== Cheers, stan H.
 Evaluation_Word_Problems/348114: as x approaches 4^+ find the limit of (4-v)/ | 4-v |1 solutions Answer 248906 by stanbon(57961)   on 2010-09-26 07:43:17 (Show Source): You can put this solution on YOUR website!as x approaches 4^+ find the limit of (4-v)/ | 4-v | ---------------- As v approaches 4 from the right |4-v| approaches (4-x) --- Ans: 1 ============= Cheers, Stan H.
 Permutations/348117: How many arrangements of the letters in the word COUNTING are possible? 1 solutions Answer 248905 by stanbon(57961)   on 2010-09-26 07:40:12 (Show Source): You can put this solution on YOUR website!How many arrangements of the letters in the word COUNTING are possible? --- The 2 N's are indistinguishable, so # of arrangements = 8!/2! = 20160 ====================================== Cheers, Stan H.
 Quadratic_Equations/348118: A little girl throws a Frisbee. It is 3 feet above the ground at the time she lets go. The Frisbee follows a parabolic path and after 5 seconds it is 6 feet above the ground. After 10 seconds it is again six feet above the ground. a. Write the particular equation of the quadratic b. How high is the frisbee after 3 seconds? c. How high is the frisbee after 12 seconds? 1 solutions Answer 248904 by stanbon(57961)   on 2010-09-26 07:37:38 (Show Source): You can put this solution on YOUR website!A little girl throws a Frisbee. It is 3 feet above the ground at the time she lets go. The Frisbee follows a parabolic path and after 5 seconds it is 6 feet above the ground. After 10 seconds it is again six feet above the ground. ---- You have three points: (0,3),(5,6),(10,6) --------------- a. Write the particular equation of the quadratic Substitute each point-pair into the following form to get three equations with variables a,b,c. ============ Form ax^2 + bx + c = y 0 + 0 + c = 3 25a + 5b + c = 6 100a+10b + c = 6 ------------------- Solve by any method you know to get: f(x) = -0.06x^2 + 0.9x + 3 --------------------------- b. How high is the frisbee after 3 seconds? f(3) = 5.16 ft. ------ c. How high is the frisbee after 12 seconds? f(12) = 5.16 ft. ======================= Cheers, stan H.
 Probability-and-statistics/348063: In a shipment of 78 vials, only 18 do not have airline cracks. If you randomly select 3 vials from the shipment, what is the probability that none of the 3 vials have airlines? what is the probability that all 3 selected have airlines?1 solutions Answer 248903 by stanbon(57961)   on 2010-09-26 07:23:31 (Show Source): You can put this solution on YOUR website!In a shipment of 78 vials, only 18 do not have hairline cracks. If you randomly select 3 vials from the shipment, P(have crack) = 18/78 P(no crack) = 60/78 -------------------------------------- what is the probability that none of the 3 vials have hairlines? Ans: (60/78)^3 = 0.4552 ------------------------------------ what is the probability that all 3 selected have hairlines? Ans: (18/78)^3 = 0.0123 ================================ Cheers, Stan H.
 Radicals/347958: p(-6,-5), q(6,10)points.....the d=(p,q) and the midpoint thanks for ur time and help!1 solutions Answer 248766 by stanbon(57961)   on 2010-09-25 15:33:05 (Show Source): You can put this solution on YOUR website!p(-6,-5), q(6,10)points.....the d=(p,q) and the midpoint thanks for ur time and help! ----- Are you saying (p,q) is the midpoint? --- If so, p = (-6+6)/2 = 0 And q = (10-5)/2 = 2.5 ---- (p,q) = (0,2.5) ======================== Cheers, Stan H.
 Expressions-with-variables/347960: how do you find the value of x in this problem 2x+3/4(4x+16)=7 ?1 solutions Answer 248762 by stanbon(57961)   on 2010-09-25 15:28:09 (Show Source): You can put this solution on YOUR website!2x+3/4(4x+16)=7 --- cross-multiply to get: 2x+3 = 28(4x+16) 2x + 3 = 112x + 448 10x = -445 x = -44.5 ========================= Cheers, Stan H. ================
 Probability-and-statistics/347921: In a blood testing procedure, blood samples from 6 people are combined into one mixture. The mixture will only test negative if all the individual samples are negative. If the probability that an individual sample tests positive is 0.11, what is the probability that the mixture will test positive1 solutions Answer 248759 by stanbon(57961)   on 2010-09-25 15:23:12 (Show Source): You can put this solution on YOUR website!In a blood testing procedure, blood samples from 6 people are combined into one mixture. The mixture will only test negative if all the individual samples are negative. If the probability that an individual sample tests positive is 0.11, what is the probability that the mixture will test positive ---- Tests positive if one or more is positive. ---- P(tests negative) = 0.89^6 = 0.4950 --- P(tests positive) = 1-0.4950 = 0.5030 ================================== Cheers, Stan H.
 Probability-and-statistics/347933: In a large vase, there are 8 roses, 5 daisies, 12 lilies, and 9 orchids. If 4 flowers are selected at random, find the probability that at least 1 of the flowers is a rose.1 solutions Answer 248758 by stanbon(57961)   on 2010-09-25 15:13:07 (Show Source): You can put this solution on YOUR website!In a large vase, there are 8 roses, 5 daisies, 12 lilies, and 9 orchids. If 4 flowers are selected at random, find the probability that at least 1 of the flowers is a rose. ------------- P(at least one rose in picking 4) = 1 - P(no rose in picking 4) = 1 - [26C4/34C4] --- = 1 - 0.3224 --- = 0.6776 ============== Cheers, Stan H.
 test/347897: Can you please help me subtract and simplify by collecting like radical terms, if possible? a 3sqrt 7 - 2 3sqrt 7 = Thanks 1 solutions Answer 248746 by stanbon(57961)   on 2010-09-25 11:21:48 (Show Source): You can put this solution on YOUR website!(3sqrt(7)) - 2*(3sqrt(7)) ----- Factor: (3sqrt(7)(1-2) =(3sqrt(7))(-1) --- = -3sqrt(7) ================== Cheers, Stan H. ==================