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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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 Probability-and-statistics/298904: On a standard measure of hearing ability, the mean is 300 and the standard deviation is 20. Give the Z scores for persons who score (a) 340, (b) 310, and (c) 260. Give the raw scores for persons whose Z scores on this test are (d) 2.4, (e) 1.5, (f) 0, and (g)-4.5 I'm having so much trouble with this course!!!!!!!1 solutions Answer 214932 by stanbon(57410)   on 2010-04-30 20:06:00 (Show Source): You can put this solution on YOUR website!On a standard measure of hearing ability, the mean is 300 and the standard deviation is 20. Give the Z scores for persons who score (a) z(340) = (340-300)/20 = 2 (b) z(310) = (310-300)/20 = 1/2 You can do "c": (c) 260. Give the raw scores for persons whose Z scores on this test are (d) x(2.4) = 2.4*20 + 300 = 348 (e) x(1.5) = 1.5*20 + 300 = 330 (f) x(0) = 0*20 + 300 = 300 You can do "g". (g)-4.5 ------------------------- Cheers, Stan H.
 Percentage-and-ratio-word-problems/298709: If a:b=9:4, and b:c=5:3, then (a-b) : (b-c) is equal to A. 7:12 B. 25:8 C. 4:1 D. 5:2 E. this cannot be determined 1 solutions Answer 214795 by stanbon(57410)   on 2010-04-30 07:48:34 (Show Source): You can put this solution on YOUR website!If a:b=9:4, and b:c=5:3, then (a-b) : (b-c) is equal to ? -------------------------------------------------------------- Let a = 9x, then b = 4x Let b = 5x, then c = 3x ----- Then a-b = 5x and b-c = 2x --- So (a-b):(b-c) = 5x/2x = 5:2 =================================== Cheers, Stan H. =================================== A. 7:12 B. 25:8 C. 4:1 D. 5:2 E. this cannot be determined
 test/298710: I need help solving this equation! Please show me how to solve this step by step!1 solutions Answer 214794 by stanbon(57410)   on 2010-04-30 07:43:57 (Show Source): You can put this solution on YOUR website!I need help solving this equation! 4x^2(x-1)^(1/3) + 6x(x-1)^(4/3) = 0 --- Factor: 2x(x-1)^(1/3)[2x + 3(x-1)] = 0 --- Simplify: 2x(x-1)^(1/3)[5x-3] = 0 x = 0 or (x-1)^(1/3) = 0 or (5x-3) = 0 --- x = 0 or x = 1 or x = 3/5 ================================ Cheers, Stan H.
 Polynomials-and-rational-expressions/298715: A rancher in Dallas decides to build a silo inside his corral. The rectangular corral measures 25 meters by 15 meters and the silos base is circular with a diameter of 2 meters. Find a polynomial for the remaining area of the corral (in square meters) after the silo is built?1 solutions Answer 214793 by stanbon(57410)   on 2010-04-30 07:40:12 (Show Source): You can put this solution on YOUR website!A rancher in Dallas decides to build a silo inside his corral. The rectangular corral measures 25 meters by 15 meters and the silos base is circular with a diameter of 2 meters. Find a polynomial for the remaining area of the corral (in square meters) after the silo is built? --------------- Rectangle area = 25*15 sq. meters --- Silo base area = (pi)(1)^2 = pi sq meters --- Remaining area: 25*15 - pi = (375-pi) sq meters ===================================================== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/298684: Can some help solve this story problem, please and thank you! Tropical Pools sells an aboveground model for p dollars each. The monthly revenue for this model is given by the formula: R (p) -0.08p^2 + 300p (the formula) a) Factor out the price on the right-hand side of the formula. b) Write a formula D (p) for the monthly demand. c) Find D (3000). 1 solutions Answer 214791 by stanbon(57410)   on 2010-04-30 07:36:09 (Show Source): You can put this solution on YOUR website!The monthly revenue for this model is given by the formula: R(p) = 0.08p^2 + 300p (the formula) a) Factor out the price on the right-hand side of the formula. R(p) = p(0.08p + 300) -------------------------------- b) Write a formula D(p) for the monthly demand. D(p) = 0.08p + 300 -------------------------------- c) Find D (3000). D(3000) = 0.08*3000+300 = 540 ==================================== Cheers, Stan H.
 Quadratic_Equations/298661: Working together, Rick and Juanita can complete a job in 6 hours. It would take Rick 9 hours longer than Juanita to do the job alone. How long would it take Juanita alone? Show your work.1 solutions Answer 214767 by stanbon(57410)   on 2010-04-29 23:06:36 (Show Source): You can put this solution on YOUR website!Working together, Rick and Juanita can complete a job in 6 hours. It would take Rick 9 hours longer than Juanita to do the job alone. How long would it take Juanita alone? Show your work. ---- Together DATA: time = 6 hrs/job ; rate = 1/6 job/hr --- Juanita DATA: time = x hrs/job ; rate = 1/x job/hr --- Rick = (x+9) hrs/job ; rate = 1/(x+9) job/hr --------------------------------------------- Equation: rate + rate = together rate: 1/x + 1/(x+9) = 1/6 --- Multiply thru by 6x(x+9) 6(x+9) + 6x = x(x+9) 6x + 54 + 6x = x^2 + 9x x^2 -3x - 54 = 0 Factor: x^2 -9x+6x - 54 = 0 x(x-9) + 6(x-9) = 0 (x-9)(x+6) = 0 Positive solution: x = 9 (time for Juanita to do the job alone) x+9 = 18 (time for Rick to do the job alone) ================================================ Cheers, Stan H.
 Probability-and-statistics/298588: If there are six contestants in a contest, in how many ways can 1st, 2nd and 3rd prize be won? 1 solutions Answer 214765 by stanbon(57410)   on 2010-04-29 22:50:20 (Show Source): You can put this solution on YOUR website!If there are six contestants in a contest, in how many ways can 1st, 2nd and 3rd prize be won? # of ways to win 1st prize: 6 # of ways to win 2nd prize: 5 # of ways to win 3rd prize: 4 --- Total number of ways: 6*5*4 = 120 ====================================== Another way to do it. # of ways to pick 3 people from 6: 6C3 = 20 # of ways to give the prizes to the 3 people selected: 3! = 6 --- Total number of ways: 20*6 = 120 ==================================== Cheers, Stan H.
 Polynomials-and-rational-expressions/298601: What is the x-factor of this problem? 2x^2+17x-301 solutions Answer 214744 by stanbon(57410)   on 2010-04-29 20:58:33 (Show Source): You can put this solution on YOUR website!2x^2+17x-30 Use the AC Method to factor: 2x^2 + 20x - 3x - 30 --- 2x(x+10) - 3(x+10) --- (x+10)(2x-3) =================== Cheers, Stan H.
 Linear-systems/298597: Write a system of two equations in two solutions for each problem. Solve each system by substitution. Jay Lenos's garage. Jay Leno's collection of cars and motorcycles totals 187. When he checks the air in the tires he has 588 tires to check. How many cars and how many motorcycles does he own? Assume that the cars all have four tires and the motorcyles have two.1 solutions Answer 214743 by stanbon(57410)   on 2010-04-29 20:55:53 (Show Source): You can put this solution on YOUR website!Jay Lenos's garage. Jay Leno's collection of cars and motorcycles totals 187. When he checks the air in the tires he has 588 tires to check. How many cars and how many motorcycles does he own? Assume that the cars all have four tires and the motorcyles have two. --------------------------- Cars Equation: c + m = 187 Tires Equation:4c + 2m = 588 --------------------------------- Multiply thru 1st by 4 to get: 4c + 4m = 4*187 --- Subtract the Tires Equation from that and solve for "m": 2m = 160 m = 80 (# of motorcycles) --- Since c+m = 187, c = 107 (# of cars) ======================================= cheers, Stan H. =======================================
 Trigonometry-basics/298598: how to solve: tan^2x - square root 3tanx1 solutions Answer 214742 by stanbon(57410)   on 2010-04-29 20:51:25 (Show Source): You can put this solution on YOUR website!To "solve" you must have an equation. Cheers, Stan H.
 Probability-and-statistics/298402: The state of Florida has a lottery in which 6 numbers out of 53 are drawn at random. What's the probability of a given ticket matching all 6 numbers in any order?1 solutions Answer 214741 by stanbon(57410)   on 2010-04-29 20:50:14 (Show Source): You can put this solution on YOUR website!The state of Florida has a lottery in which 6 numbers out of 53 are drawn at random. What's the probability of a given ticket matching all 6 numbers in any order? ----------- # of groups of 6 numbers = 53C6 = 22,957,480 # of winning groups of 6 numbers = 1 ------------------------------------------ P(having a winning ticket) = 1/22957480 ---- Now, do you feel lucky? Cheers, Stan H.
 Miscellaneous_Word_Problems/298585: two taps can fill a bucket in 2 and 3 minutes respectively. if they are turned on together, how long will theytake to fill the bucket?1 solutions Answer 214740 by stanbon(57410)   on 2010-04-29 20:23:48 (Show Source): You can put this solution on YOUR website!two taps can fill a bucket in 2 and 3 minutes respectively. if they are turned on together, how long will theytake to fill the bucket? ------- Faster Tap DATA: time = 2 minutes/job ; rate = 1/2 job/minutes ------- Slower Tap DATA: time = 3 minutes/job ; rate = 1/3 job/minutes ------- Together DATA: time = x minutes/job ; rate = 1/x job/minutes -------- Equation: rate + rate = together rate 1/2 + 1/3 = 1/x 3x + 2x = 6 5x = 6 x = 6/5 = 1.2 minutes ========================= Cheers, Stan H.
 logarithm/298583: Solve (2x+1 is the exponent) 3^2x+1=271 solutions Answer 214738 by stanbon(57410)   on 2010-04-29 20:22:00 (Show Source): You can put this solution on YOUR website!3^(2x+1) = 27 ----- 3^(2x+1) = 3^3 --- Equate the exponents to get: 2x+1 = 3 2x = 2 x = 1 ============ Cheers, Stan H.
 Equations/298579: im confused and i need help i need to simplify an equation 3x-6/5x-20(10x-40/27x-54) i know its not cross multiply and i did the problem 5 times and i get a different answer so i know im doing it wrong please help1 solutions Answer 214737 by stanbon(57410)   on 2010-04-29 20:19:51 (Show Source): You can put this solution on YOUR website!(3x-6)/(5x-20)*(10x-40)/(27x-54) I'm going to assume you meant the product of two rational fractions. --------------------------------------- Factor where you can: (3(x-2))/(5(x-4))*(10(x-4))/(27(x-2)) ------ Cancel factors common to a numerator and a denominator such as 3,5,(x-4)(x-2) to get: = (1)/(1(1))*(2(1))/(9(1)) ---- = 2/9 ============== Cheers, Stan H.
 logarithm/298576: write log x + log(x^2 - 4) - log 15 - log(x+2) as a single logarithmic expression. 1 solutions Answer 214733 by stanbon(57410)   on 2010-04-29 20:11:04 (Show Source): You can put this solution on YOUR website!write log x + log(x^2 - 4) - log 15 - log(x+2) as a single logarithmic expression. --------------------- = log[x(x^2-4)/(15(x+2)] --- This could be simplified: = log[x(x-2)/15] ======================= Cheers, Stan H.
 Probability-and-statistics/298523: There are 60% heating equipment 25% electrical equipment and 15% plumbing equipment in a store, what is the probability that at least 3 out of 5 of the items bought are heating equipment?1 solutions Answer 214728 by stanbon(57410)   on 2010-04-29 20:08:20 (Show Source): You can put this solution on YOUR website!There are 60% heating equipment 25% electrical equipment and 15% plumbing equipment in a store, what is the probability that at least 3 out of 5 of the items bought are heating equipment? ------------------------ P(heating) = 0.6 n = 5 x = 3<= x <=5 ------------------- P(3<= x <=5) = 1 - binomcdf(5,0.6,2) = 0.6826 ================================================= Cheers, Stan H.
 Travel_Word_Problems/298546: if a person walks three miles per hour and are four miles from their destination who long will it take them to reach the destination 1 solutions Answer 214719 by stanbon(57410)   on 2010-04-29 19:36:43 (Show Source): You can put this solution on YOUR website!if a person walks three miles per hour and are four miles from their destination who long will it take them to reach the destination ---- time = distance/rate time = 4 mi/3 mph time = 4/3 hour time = 1 hr 20 min ========================== Cheers, Stan H.
 Miscellaneous_Word_Problems/298531: There are 720 dishes that need to be rinsed. John can rinse them in 144 minutes by himself. It will take his friend Bob 72 minutes to rinse these dishes. How long will it take them if they rinse these 720 dishes together?1 solutions Answer 214717 by stanbon(57410)   on 2010-04-29 19:34:42 (Show Source): You can put this solution on YOUR website!There are 720 dishes that need to be rinsed. John can rinse them in 144 minutes by himself. It will take his friend Bob 72 minutes to rinse these dishes. How long will it take them if they rinse these 720 dishes together? -------- John rate = 1/144 job/min Bob rate = 1/72 job/min ----- Together rate = 1/x job/min =============================== Equation: rate + rate = together rate 1/144 + 1/72 = 1/x ---- Multiply thru by 144x to get: x + 2x = 144 3x = 144 x = 48 minutes (time for them to do the job together. ======================== Cheers, Stan H.
 Quadratic_Equations/298534: Write a quadratic equation having the given numbers as solutions. 2/3, 9/51 solutions Answer 214715 by stanbon(57410)   on 2010-04-29 19:29:32 (Show Source): You can put this solution on YOUR website!Write a quadratic equation having the given numbers as solutions. 2/3, 9/5 x = 2/3 or x = 9/5 3x-2 = 0 or 5x-9 = 0 --------------------------- Multiply the two equations to get: (3x-2)(5x-9) = 0 ------------------------ Let the expression be an equation that equals zero when x = 2/3 or x = 9/5. Let y = (3x-2)(5x-9) Then y = 15x^2-37x + 18 =============================== Cheers, Stan H. ===============================
 Quadratic_Equations/298537: I seriously need help with quadratic formulas. please help. -55x+30=50x21 solutions Answer 214713 by stanbon(57410)   on 2010-04-29 19:25:09 (Show Source): You can put this solution on YOUR website!-55x+30=50x2 --- Rearrange: 50x^2 + 55x - 30 = 0 --- Divide thru by 5 to get: 10x^2 + 11x - 6 = 0 --- a = 10, b = 11, c = -6 ---- Formula: x = [-b +- sqrt(b^2-4ac)]/(2a) --- x = [-11 +- sqrt(121 - 4*10*-6)]/(20) --- x = [-11 +- sqrt(361)]/(20) --- x = [-11 + 19]/(20) or x = [-11 - 19]/(20) --- x = (8/20) or x = -3/2 --- x = 2/5 or x = -3/2 ============================== Cheers, Stan H.
 Triangles/298539: The square and the equilateral triangle at the right have the same perimeter. Find the length of the sides of the triangle1 solutions Answer 214711 by stanbon(57410)   on 2010-04-29 19:19:27 (Show Source): You can put this solution on YOUR website!Not enough information to solve. Cheers, Stan H.
 Length-and-distance/298529: if the ratio of something is 1 to 1.9 and its 25 sqaure feet whats the length and height of the object1 solutions Answer 214710 by stanbon(57410)   on 2010-04-29 19:18:20 (Show Source): You can put this solution on YOUR website!if the ratio of something is 1 to 1.9 and its 25 sqaure feet whats the length and height of the object ------------------- 1 to 1.9 is the same as 1x to 1.9x --- Assuming you are taking about the ratio of length to width you get: Area = (1x)(1.9x) 1.90x^2 = 25 x = 5/sqrt(1.9) ft ---- Length = 5/sqrt(1.9) is approximately 3.627 ft Width = 1.9[5/sqrt(1.9)] is approximately 6.8920 ft ======================================================== Cheers, Stan H.
 Finance/298487: A man travels from Town X to Town Y at an average rate of 60 mph and returns at an average rate of 50 mph. He takes a 1/2 hour longer than he would take if he made the round trip at an average of 55 mph. What is the distance from Town X to Town Y?1 solutions Answer 214697 by stanbon(57410)   on 2010-04-29 18:25:22 (Show Source): You can put this solution on YOUR website!A man travels from Town X to Town Y at an average rate of 60 mph and returns at an average rate of 50 mph. He takes a 1/2 hour longer than he would take if he made the round trip at an average of 55 mph. What is the distance from Town X to Town Y? --------- To-trip DATA: distance = d miles ; rate = 60 mph ; time = d/60 hrs ---------------------- From-trip DATA: distance = d miles ; rate = 50 mph ; time = d/50 hrs ---------------------- Round-trip DATA: distance = 2d miles ; rate = 55 mph ; time = (2d)/55 hrs ----------------------------------------------------------- Equation: Roundtrip time - other time = -1/2 hr (2d)/55 - [(d/60)+(d/50)] = -1/2 (2d)/55 - [(110d)/(50*60)] = -1/2 --- 600(2d) - 11[110d] = -16500 1200d - 1210d = -16500 -10d = -16500 distance = 1650 miles =========================== Cheers, Stan H. ===========================
 Systems-of-equations/298483: Solve by any method. (x - 10)(x - 4) = -51 solutions Answer 214686 by stanbon(57410)   on 2010-04-29 17:51:02 (Show Source): You can put this solution on YOUR website!Solve by any method. (x - 10)(x - 4) = -5 --- x^2-14x+40 = -5 --- x^2 - 14x + 45 = 0 ---- Factor using the AC Method: x^2-9x-5x+45 = 0 x(x-9)-5(x-9) = 0 (x-9)(x-5) = 0 x = 9 or x = 5 ======================= Cheers, Stan .
 Functions/298476: I'm having trouble with writing the inverse of a the function f(x)=e^(x-2). I've plugged in given plotting points of x= -6, -4, -2, 0, 2, 4, and 6. For the inverse, do I write x=lne^(y-2) and bring my exponent to the front of ln? Thank you in advance for your help. Part 2: is my vertical asymptote 2 for the inverse? -Courtney1 solutions Answer 214684 by stanbon(57410)   on 2010-04-29 17:45:49 (Show Source): You can put this solution on YOUR website!I'm having trouble with writing the inverse of a the function f(x)=e^(x-2). I've plugged in given plotting points of x= -6, -4, -2, 0, 2, 4, and 6. For the inverse, do I write x=lne^(y-2) and bring my exponent to the front of ln? Thank you in advance for your help. -------------- Note: The asymptote for y = e^(x-2) is a horizontal axis; it is y = 0. The (x-2) moves the graph 2 to the right but does not change the horizontal asymptotel --------------- To find the inverse proceed as follows: f(x)=e^(x-2) Interchange x and y to get: x = e^(y-2) Now solve for "y": ln(x) = y-2 y = ln(x)+2 is the inverse --- Part 2: is my vertical asymptote 2 for the inverse? The asymptote is now a vertical asymptote. The 2 raises the curve but that has no effect on a vertical asymptote. Just as the horizontal asymptote on the function was y = 0, the inverse has a vertical asymptote and it is x = 0 ================================================= Cheers, Stan H. ==================================
 Geometry_Word_Problems/298474: If the length and width of a rectangle are each increased by ten percent, then the perimeter of the rectangle is increased by what percent?1 solutions Answer 214680 by stanbon(57410)   on 2010-04-29 17:35:07 (Show Source): You can put this solution on YOUR website!If the length and width of a rectangle are each increased by ten percent, then the perimeter of the rectangle is increased by what percent? ------------- Perimeter = 2(L + W) --- New Perimeter = 2(1.1L + 1.1W) --- New Perimeter = 2(1.1)(L+W) NP = 2.2(L+W) = 2(L+W) + 0.2(L+W) ----- The increase is 0.20 = 20% ============================== Cheers, Stan H. ==============================
 Triangles/298429: A triangle has one 45 degree angle and one 65 degree angle.Which is the measure of the triangles third angle1 solutions Answer 214679 by stanbon(57410)   on 2010-04-29 17:29:55 (Show Source): You can put this solution on YOUR website!A triangle has one 45 degree angle and one 65 degree angle.Which is the measure of the triangles third angle ------------------------------- Fact: The sum of the angles of a triangle = 180 degrees ---- Equation: 45 + 65 + x = 180 110 + x = 180 x = 70 degrees =============== Cheers, Stan H.
 Average/298422: write an algorithm to find the average score on five quiz and determine if the average is less than 601 solutions Answer 214670 by stanbon(57410)   on 2010-04-29 16:40:07 (Show Source): You can put this solution on YOUR website!write an algorithm to find the average score on five quiz and determine if the average is less than 60 ----------- (a+b+c+d+e)/5 < 60 where a,b,c,d,e are the 5 scores =============================== Cheers, Stan H.
 Percentage-and-ratio-word-problems/298355: For a research study, a biologist collected a sample of 203 plants, fish, and insects from a stream. There were 1/4 as many insects as there were fish in the sample. There were 1/5 as many plants as there were fish in the sample. How many fish were collected? A) 14 fish B)63 fish C)77 fish D)140 fish1 solutions Answer 214652 by stanbon(57410)   on 2010-04-29 14:08:56 (Show Source): You can put this solution on YOUR website!For a research study, a biologist collected a sample of 203 plants, fish, and insects from a stream. Equations: p + f + i = 203 -- There were 1/4 as many insects as there were fish in the sample. i = (1/4)f --- There were 1/5 as many plants as there were fish in the sample. p = (1/5)f ----- How many fish were collected? --- Substitute for i and p, then solve for "f". (1/5)f + (1/4)f + f = 203 --- Multiply thru by 20 to get: 4f + 5f + 20f = 4060 29f = 4060 --- # of fish = 140 =================== Cheers, Stan H. A) 14 fish B)63 fish C)77 fish D)140 fish
 Quadratic_Equations/298352: Need Help!!! use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions. s^2-5s-6=01 solutions Answer 214651 by stanbon(57410)   on 2010-04-29 13:56:38 (Show Source): You can put this solution on YOUR website!use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions. s^2-5s-6=0 ---- a = 1 ; b = -5 ; c = -6 -------- b^2-4ac = 25 - 4*1*-6 = 49 --- Since 49 is positive there are two different Real solutions. --- The discriminant does not quarantee the solutions will be rational, only that they will be Real. ================================================ Cheers, Stan H. =================
 Mixture_Word_Problems/298345: how much soil containing 45% sand do you need to add to 1 ft3 of soil containing 15% sand in order to make a soil containing 35%?1 solutions Answer 214649 by stanbon(57410)   on 2010-04-29 13:51:47 (Show Source): You can put this solution on YOUR website!how much soil containing 45% sand do you need to add to 1 ft3 of soil containing 15% sand in order to make a soil containing 35%? ------- Equation: sand + sand = sand 0.45x + 0.15*1 = 0.35(x+1) --- Multiply thru by 100: 45x + 15 = 35x + 35 10x = 10 x = 1 ft^3 (amount of 45% soil needed for the mixture) ================ Cheers, Stan H. ================