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Recent problems solved by 'stanbon'

stanbon answered: 57911 problems
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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logarithm/173812: i need an example of an exponential function converted into a logarithmic function and graphed. 1 solutions Answer 128676 by stanbon(57984)   on 2008-12-17 08:13:27 (Show Source): You can put this solution on YOUR website! y = e^x y = ln(x) ============ Cheers, Stan H.

Exponential-and-logarithmic-functions/173796: I am having trouble getting these two. Can someone please help me...please..Thank you..Evaluate the functions for the values of x given as 1, 2, 4, 8, and 16. Describe the differences in the rate at which each function changes with increasing values of x. 3.f(x) = 2x3 + 7x2 - x - 1 5.f(x) = ln x 1 solutions Answer 128675 by stanbon(57984)   on 2008-12-17 08:09:58 (Show Source): You can put this solution on YOUR website! I am having trouble getting these two. Can someone please help me...please..Thank you..Evaluate the functions for the values of x given as 1, 2, 4, 8, and 16. Describe the differences in the rate at which each function changes with increasing values of x. 3.f(x) = 2x^3 + 7x^2 - x - 1 ------------------------------- f(1) = 2+7-1-1 = 7 f(2) = 2*8+7*4-2-1 = 16+28-2-1 =41 f(4) = 2*64 + 7*16 - 4 -1 = 235 etc. The function is increasing in the interval x=1 to x = 16 ============================================================== 5.f(x) = ln x f(1) = ln (1) = 0 f(2) = ln (2) = 0.653.. f(4) = 1.386... f(8) = 2.079... f(16) = 2.773... ------------------- The functions is slowly increasing over the interval x = 1 to x = 16 ========================================== Cheers, stan H.

Linear-equations/173782: Please help me solve this equation: Find the slope of the line passing through these pair of points M(-41) and N(6,3) 1 solutions Answer 128652 by stanbon(57984)   on 2008-12-16 23:34:27 (Show Source): You can put this solution on YOUR website! Find the slope of the line passing through these pair of points M(-4,1) and N(6,3) -------- slope = change in y/change in x slope = (3-1)/(-4-6) = 2/-10 = -1/5 =========================================== Cheers, Stan H.

Evaluation_Word_Problems/173781: Jimmy the Rat invested part of $20,000 at 12% annually and the rest at 14%. The total income from these investments is $2560. How much did Jim invest at each rate? 1 solutions Answer 128651 by stanbon(57984)   on 2008-12-16 23:30:24 (Show Source): You can put this solution on YOUR website! Jimmy the Rat invested part of $20,000 at 12% annually and the rest at 14%. The total income from these investments is $2560. How much did Jim invest at each rate? --------- Equation: interext + interest = 2560 0.12x + 0.14(20,000-x) = 2560 12x + 14*20000 - 14x = 256000 -2x = 256000-14*20000 -2x = -24000 x = $12,000 (amt invested at 12%) 20,000-x = $8,000 (amt invested at 14%) ======================================== Cheers, Stan H.

Functions/173780: Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 100mph and train B is traveling at 120mph. Train A passes a station at 8:15A.M. If train B passes the same station at 8:30A.M., what time will train B catch up to train A? I don't even know if I am asking this question in the right section or not, but it has me baffled. 1 solutions Answer 128650 by stanbon(57984)   on 2008-12-16 23:25:19 (Show Source): You can put this solution on YOUR website! Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 100mph and train B is traveling at 120mph. Train A passes a station at 8:15A.M. If train B passes the same station at 8:30A.M., what time will train B catch up to train A? ---------------------- Train A DATA: rate = 100 mph ; distance = x miles ; time = d/r = x/100 hrs ------------------- Train B DATA: rate = 120 mph ; distance = x miles ; time = d/r = x/120 hrs ------------------- EQUATION: time A - time B = (1/4) hr x/100 - x/120 = 1/4 Multiply thru by 4 to get: x/25 - x/30 = 1 30x - 25x = 25*30 5x = 25*30 x = 5*30 = 150 miles ------------------------- Train A time = x/100 = 150/100 = 3/2 hr 8:15 + (3/2) hr = 9:45 A.M.

Equations/173779: Combine. Be sure to simplify your answer whenever possible 5/3 + 5/6 1 solutions Answer 128648 by stanbon(57984)   on 2008-12-16 23:16:02 (Show Source): You can put this solution on YOUR website! 5/3 + 5/6 lcd = 6 = 10/6 + 5/6 = (10+5)/6 = 15/6 = 5/2 ============ Cheers, Stan H.

Functions/173778: The function H described by H(x)=2.75(x)+71.48 can be used to predict the height, in centimeters, of a woman whose humerus is x cm long. Predict the height of a woman whose humerus is 37cm long. I started this problem but I don't know if I am doing it right, what I did was this: H(x)=2.75(x)+71.48 I plugged 37 in for x. H(37)=2.75(37)+71.48 And I got H(37)=173.23 I just want to know if I have done this correctly. I feel very confused. 1 solutions Answer 128646 by stanbon(57984)   on 2008-12-16 23:10:12 (Show Source): You can put this solution on YOUR website! Your answer is correct. Congratulations. Cheers, Stan H.

Inequalities/173777: what is the answer using the elimination/addition method to: 2w+3z=17 3w+4z=24 1 solutions Answer 128645 by stanbon(57984)   on 2008-12-16 23:07:52 (Show Source): You can put this solution on YOUR website! answer using the elimination/addition method to: 2w+3z=17 3w+4z=24 ---------- Multiply 1t by 3 and 2nd by 2 to get: 6w + 9z = 51 6w + 8z = 48 --------------- Subtract 2nd from 1st and solve for "z": z = 3 --------- Substitute into 2w + 3z = 17 and solve for "w" 2w + 3*3 = 17 2w = 8 w = 4 --------- Ans: w = 4; z = 3 ========================= Cheers, stan H.

Linear-equations/173775: Plot the graph of the following functions: f(x)=7^x f(x)=4^x-3 f(x)=(1/5)^x f(x)=log3x Please respond I don't know how to show the work I have tried; but I have tried relentlessy and am getting no where. 1 solutions Answer 128644 by stanbon(57984)   on 2008-12-16 23:04:10 (Show Source): You can put this solution on YOUR website! Plot the graph of the following functions: Plot points, then connect the points with a smooth curve: f(x)=7^x Points: (-1,1/7), (0,1), (1,7), (2,49) etc ---------------------------------------------- f(x)=4^x-3 Points: (-1,-11/4), (0,-2), (1,1), (2,13) etc ---------------------------------------------- f(x)=(1/5)^x Points: (-1,5), (0,1), (1,1/5), (2,1/25),etc ----------------------------------------------- f(x)=log(3x) Points: (1,0.4771), (2,0.7782), (3,0.9542) etc =========================================== Cheers, Stan H.

Inequalities/173776: Is this equation true for all real numbers x: 1 solutions Answer 128642 by stanbon(57984)   on 2008-12-16 22:43:17 (Show Source): You can put this solution on YOUR website! Is this equation true for all real numbers x: x^2 >= x --------- Ans: No If x = 1/2, but x^2 = (1/2)^2 = 1/4 and 1/4 is NOT >- 1/2 =========================== Cheers, Stan H.

Numbers_Word_Problems/172331: the sum of three numbers is 123. the second number is 9 less than two times the first numbner. the third number is 6 more than three times the first numbner. what are the three numbers? 1 solutions Answer 128641 by stanbon(57984)   on 2008-12-16 22:39:10 (Show Source): You can put this solution on YOUR website! the sum of three numbers is 123. the second number is 9 less than two times the first number. the third number is 6 more than three times the first numner. what are the three numbers? -------------------------------- Equations: x + y + z = 123 y = 2x-9 z = 3x+6 ---------------------------- x + y + z = 123 2x - y + 0 = 9 3x + 0 - z = -6 ---------------------------- Solve by any method you know to get: x = 21 y = 33 z = 69 ========================== Cheers, Stan H.

Numbers_Word_Problems/173769: an integers increased by 5 is the same as 5 times the integer. find integer 1 solutions Answer 128637 by stanbon(57984)   on 2008-12-16 22:23:13 (Show Source): You can put this solution on YOUR website! an integer increased by 5 is the same as 5 times the integer. find integer --------- EQUATION: x + 5 = 5x 4x = 5 x = 5/4 ----------- Notice: The answer to your posted problem is not an integer. =================== Cheers, Stan H.

test/173748: hey, could you please solve the following problem for me, thank you, A rate coin is bought at an antique auction in 1998 for $500. Each year, its value appreciates by 6% of its purchase price. Determine the coin's value in 2010. remember we are using Geometric Sequences formula, i will be waiting for the solution, thank you agian 1 solutions Answer 128636 by stanbon(57984)   on 2008-12-16 22:19:22 (Show Source): You can put this solution on YOUR website! A rate coin is bought at an antique auction in 1998 for $500. Each year, its value appreciates by 6% of its purchase price. Determine the coin's value in 2010. -------- Year 0: 500 Year 1: 500 + 0.06*500 = (1.06)500 Year 2: [500 + 0.06*500][1.06] = 500(1.06)^2 ... Year 12: 500(1.06)^12 = $1006.10 ===================================== Cheers, Stan H.

Equations/173766: Evaluate (3/5)^3 1 solutions Answer 128633 by stanbon(57984)   on 2008-12-16 22:12:52 (Show Source): You can put this solution on YOUR website! Evaluate (3/5)^3 ----- = 27/125 ================== Cheers, Stan H.

Linear-equations/173759: Write equations of the horizontal and the vertical lines that pass through the given point. (8,3) 1 solutions Answer 128632 by stanbon(57984)   on 2008-12-16 22:11:14 (Show Source): You can put this solution on YOUR website! Write equations of the horizontal and the vertical lines that pass through the given point. (8,3) ================ Horizontal: y = 3 Vertical: x = 8 ======================== Cheers, Stan H.

logarithm/173762: what is the real value of x in the equation log2 24-log 2 3 = log5 x? 1 solutions Answer 128630 by stanbon(57984)   on 2008-12-16 22:08:21 (Show Source): You can put this solution on YOUR website! what is the real value of x in the equation log2 24-log 2 3 = log5 x log2 (24/3) = log5 (x) log(8)/log(2) = log(x)/log(5) log(x) = [log(5)][3] log(x) = log(5^3) x = 5^3 = 125 ==================== Cheers, Stan H.

Expressions-with-variables/173763: Write an equation of the line passing through the given points (2,-17) and (-5,39) 1 solutions Answer 128628 by stanbon(57984)   on 2008-12-16 22:03:48 (Show Source): You can put this solution on YOUR website! Write an equation of the line passing through the given points (2,-17) and (-5,39) ------------------------- slope = (39--17)/(-5-2) = 56/-7 = -8 -------------------------- intercept: Form y = mx + b -17 = -8*2 + b -17 = -16 + b b = -1 ------------------------- Equation: y = -8x -1 ================= Cheers, Stan H.

Evaluation_Word_Problems/173765: the sum of two numbers is 52. twice the first number is 17 more than the second. find the numbers. 1 solutions Answer 128627 by stanbon(57984)   on 2008-12-16 21:59:51 (Show Source): You can put this solution on YOUR website! the sum of two numbers is 52. twice the first number is 17 more than the second. find the numbers. ------------------- Let one of the numbers be "x"; the other is "52-x". EQUATION: 2x= 52-x+17 3x = 69 x = 23 ========== Cheers, Stan H.

Polynomials-and-rational-expressions/173725: (1-r^3) ------- (1-r)^3 you just have to factor & simplify i guess.. g(x)= x^3+2x over x^2-4 you need to know the domain, and the numbers to get zero , like on the numerator? h(y)=(y^3-8)(y+2)^-3 g(s)=4s^2+15s-4 over (2s-1)^2 x^2+y^2-z^2-2xy over x^2-y2+z^2-2xz 1 solutions Answer 128610 by stanbon(57984)   on 2008-12-16 20:38:54 (Show Source): You can put this solution on YOUR website! (1-r^3) / (1-r)^3 [(1-r)(1+r+r^2)]/[1-r]^3 = (1+r+r^2) / (1-r)^2 =================================== g(x)= (x^3+2x) / (x^2-4) = [x(x^2+2)] / [(x-2)(x+2)] --- Domain: All Real Numbers except x = 2 or x = -2 Zeroes: x = 0 ===================================== you need to know the domain, and the numbers to get zero , like on the numerator? h(y)=(y^3-8)(y+2)^-3 = (y^3-8)/(y+2)^3 = [(y-2)(y^2 + 2y + 4)] / [(y+2)]^3 Domain: All Real Numbers except x = -2 Zeroes: y = 2 =============================== g(s)=4s^2+15s-4 over (2s-1)^2 = [4s^2 +16s - s - 4]/[2s-1]^2 = [(4s-1)(s+4)]/[2s-1]^2 ---- Domain: All Real Numbers except s = 1/2 Zeroes: s = 1/4 and s = -4 -------------------------------------- x^2+y^2-z^2-2xy over x^2-y2+z^2-2xz I'll leave this one to you. ============================= Cheers, Stan H.

Inequalities/173735: Please help me solve this: Graph the following system of inequalities on the graph, find the corner points, and label on the graph. x+y>=14 2x+y>=20 x+3y>=24 x>=0 y>=0 I'm having trouble graphing on this site.my answer was: (0,8) (10,0) Thanks freedom45 1 solutions Answer 128608 by stanbon(57984)   on 2008-12-16 20:21:39 (Show Source): You can put this solution on YOUR website! Graph the following system of inequalities on the graph, find the corner points, and label on the graph. x+y>=14 2x+y>=20 x+3y>=24 x>=0 y>=0 I'm having trouble graphing on this site.my answer was: (0,8) (10,0) ------------------ Graph the boundary lines: x = 0 Shade the half-plane to the right. --------------- y = 0 Shade the half-plane above. ------------------------ y = (-1/3)x + 8 Shade the half-plane above the line. --------------------- y = -2x + 20 Shade the half-plane above the line. y = -x+ 14 Shade the half-plane above the line. ----------------------------- ------------------------------ Find the vertices of the intersection of the half-planes. ============================================================ Cheers, Stan H.

Age_Word_Problems/173693: This question is from textbook Algebra Structure and Method Book 1 I would appreciate your help on the following problem: The two digits in the numerator of a fraction whose value is 4/7 are reversed in its demoninator. The reciprocal of the fraction is the value obtained when 16 is added to the original numerator and 5 is subtracted from the original demonimator. Find the original fraction. I have 10t+u/10u+t=4/7; 10u+t/10t+u=10t+u+16/10u+t-5. 7(10t+u)=4(10u+t), 70t+7u=40u+4t, 66t=33u, t=3/6u. I'm not sure where to go from there. Thank you so much for any help you can give me. I appreciate it so much! 1 solutions Answer 128574 by stanbon(57984)   on 2008-12-16 18:41:24 (Show Source): You can put this solution on YOUR website! I would appreciate your help on the following problem: The two digits in the numerator of a fraction whose value is 4/7 are reversed in its denominator. I have 10t+u/10u+t=4/7 Rearrange: 7(10t+u) = 4(10u+t) 70t + 7u = 40u+4t 66t - 33u = 0 t = (1/2)u ----------------------------- The reciprocal of the fraction is the value obtained when 16 is added to the original numerator and 5 is subtracted from the original denominator. (10u+t)/(10t+u) = [10t+u+16]/[10u+t-5] Rearrange: (10u+t)(10u+t-5) = (10t+u)(10t+u+16) [(10u+t)^2 - 5(10u+t)] = [(10t+u)^2 + 16(10t+u)] [100u^2 + 20tu + t^2 -50u - 5t] = [100t^2 + 20tu + u^2 + 160t + 16u] [99u^2 - 99t^2 -66u - 165t] = 0 ---------------------------------------------- Substitute t = (1/2)u into the last equation to solve for "u": Comment: This is a messy problem. I'll leave the substitution to you. I get u = 2 so t = 1 Number: 12 =================== Cheers, Stan H.

Linear-equations/173697: is (3,21) a solution to y = 2x-4 1 solutions Answer 128560 by stanbon(57984)   on 2008-12-16 17:36:56 (Show Source): You can put this solution on YOUR website! What is the question. Cheers, Stan H.

Square-cubic-other-roots/173695: How would you solve 4x√(9x^2y^4)? in other words: 4x in front of the square root of 9x to the second power and y to the fourth power? 1 solutions Answer 128559 by stanbon(57984)   on 2008-12-16 17:34:11 (Show Source): You can put this solution on YOUR website! solve 4x√(9x^2y^4) = (4x)*3xy^2 = 12x^2y^2 ================== Chers, Stan H.

Coordinate-system/173653: I need help with all these equations, Please! Plot the graph of 3x + 15 = x + 25 Plot the graph of 4x – 3y = 10 Plot the graph of y4 + 3y2 -4 = 0 Plot the graph of 3x2 + 5 + 7x 1 solutions Answer 128507 by stanbon(57984)   on 2008-12-16 12:05:53 (Show Source): You can put this solution on YOUR website! Plot the graph of 3x + 15 = x + 25 2x = 10 x = 5 Draw a vertical line thru all the points where x = 5 ======================================================== Plot the graph of 4x – 3y = 10 Solve for y: y = (4/3)x - (10/3) You need two points: Let x = 0 then y = -(10/3) giving point (0,-10/3) Let x = 3 then y = 4-10/3 = 2/3 giving point (3,2/3) Plot the two points and draw a line thru them. ========================================================= Plot the graph of y^4 + 3y^2 -4 = 0 Factor: (y^2+4)(y^2-1) = 0 True if y = 1 or -1 ---------------------------------------- Plot the graph of 3x2 + 5 + 7x Is this supposed to be y = 3x^2+7x+5 ? If it is, the graph is a parabola that opens up (instead of down). The bottom point (vertex) is at (-7/6,0.91) ======================================== Cheers, stan H.

Probability-and-statistics/173645: 1. Find the probability of 7 tomatos getting accepting in 6 stores when the mean is 5.5 2.Random sample of 120 customers’s spent an average of 9.2 hours on their professional job with a sample standard deviation of 5.1 hours. Calculate the specification hours with confidence of 95%. 3.In a set of 10 samples of bike, the mileage were listed as follows 41, 42, 45, 42, 47, 59, 55, 60, 40, 35 What percent of samples are getting more than 40 mileages? 1 solutions Answer 128504 by stanbon(57984)   on 2008-12-16 11:51:38 (Show Source): You can put this solution on YOUR website! 1. Find the probability of 7 tomatos getting accepting in 6 stores when the mean is 5.5 --- Mean of what? Do you have a standard deviation? -------------------- 2.Random sample of 120 customers’s spent an average of 9.2 hours on their professional job with a sample standard deviation of 5.1 hours. Calculate the specification hours with confidence of 95%. --------------- x-bar = 9.2 hrs E = 1.96*(5.1/sqrt(120)) = 0.9125 ---- 95% CI: 9.2 - 0.9125 < u < 9.2 + 0.9125 ======================================== 3.In a set of 10 samples of bike, the mileage were listed as follows 41, 42, 45, 42, 47, 59, 55, 60, 40, 35 What percent of samples are getting more than an average of 40 ? --------- # above 40 = 8 Total number = 10 ----------------------- Percentage = 8/10 = 80% ============================= Cheers, Stan H.

Quadratic_Equations/173626: This question is from textbook Introductory Algebra Tom Quig traveled 280 miles east of St. Louis. For most of the trip he averaged 60 mph, but for one period of time he was slowed to 10 mph due to a major accident. If the total time of travel was 8 hours, how many miles did he drive at the reduced speed? 1 solutions Answer 128477 by stanbon(57984)   on 2008-12-16 07:40:08 (Show Source): You can put this solution on YOUR website! Tom Quig traveled 280 miles east of St. Louis. For most of the trip he averaged 60 mph, but for one period of time he was slowed to 10 mph due to a major accident. If the total time of travel was 8 hours, how many miles did he drive at the reduced speed? ------------------------------ Most-trip DATA: distance = x miles ; rate = 60 mph ; time = d/r = x/60 hrs. ---------------------- Slow part DATA: distance = 280-x miles ; rate = 10 mph ; time = d/r = (280-x)/10 hrs ------------------------ EQUATION: time + time = 8 hrs. x/60 + (280-x)/10 = 8 Multiply thru by 60 to get: x + 6(280-x) = 480 -5x = 480 - 6*280 -5x = -1200 x = 240 miles (distance traveled at 60 mph) 280-x = 40 miles (distance traveled at 10 mph) ================ Cheers, Stan H.

Equations/173631: Take a look at the table below and write out an equation for f(x). x: -2, -1, 0, 1, 2 f(x): -1, 1, 3, 5, 7 1 solutions Answer 128474 by stanbon(57984)   on 2008-12-16 07:31:13 (Show Source): You can put this solution on YOUR website! Take a look at the table below and write out an equation for f(x). x: -2, -1, 0, 1, 2 f(x): -1, 1, 3, 5, 7 --------------------------- Notice that f(s) increases 2 for every increase in one of x. That tells you the slope is 2/1 = 2 ------------- Notice that when x = 0, f(x) = 3. That tells you the intercept is 3 ----------------------- So the equation is f(x) = 2x + 3 ================================== Cheers, Stan H.

logarithm/173587: A bacteria culture doubles every 15min. How long would it take for a culture of 20 bacteria to grow to a population of 163840? 1 solutions Answer 128447 by stanbon(57984)   on 2008-12-15 22:57:39 (Show Source): You can put this solution on YOUR website! A bacteria culture doubles every 15min. How long would it take for a culture of 20 bacteria to grow to a population of 163840? --------------- A(t) = Ao*2^(t/4) where t is hours. ------------------------------------- 163840 = 20*2^(t/4) 2^(t/4) = 8192 (t/4)log2 = log 8192 t/4 = [log 8192 / log 2] t/4 = 13 t = 52 hours ================= Cheers, Stan H.

logarithm/173578: Log(2x+1)+log(x-1)=log9 1 solutions Answer 128444 by stanbon(57984)   on 2008-12-15 22:51:13 (Show Source): You can put this solution on YOUR website! Log(2x+1)+log(x-1)=log9 log[(2x+1)(x-1)] = log9 (2x+1)(x-1) = 9 2x^2 - x -1 = 9 2x^2 - x - 10 = 0 2x^2 -5x + 4x - 10 = 0 x(2x-5) + 2(2x-5) = 0 (2x-5)(x+2) = 0 Realistic answer: x = 5/2 ------------- Comment: x=-2 is extraneous because it would make log(x+1) = log(-1) which has no meaning. ========================== Cheers, Stan H.

logarithm/173572: Solve y=log2(5x-4) y=3+log2(x-1) 1 solutions Answer 128441 by stanbon(57984)   on 2008-12-15 22:42:12 (Show Source): You can put this solution on YOUR website! Solve y= log2(5x-4) y= 3+log2(x-1) ------------- Substitute to get: log2 (5x-4) = 3 + log2 (x-1) log2 (5x-4) - log2 (x-1) = 3 log2 [(5x-4)/(x-1)] = 3 [(5x-4)/(x-1)] = 2^3 5x-4 = 8(x-1) 5x-4 = 8x - 8 3x = 4 x = 4/3 ================================ Cheers, Stan H.

Travel_Word_Problems/173569: Four Minutes after Monica left to go to school with her mom, her Dad realized that she had left her math homework at home. He decided to bring it to her so she would not get in trouble. Since he was driving at a speed 20 mph more than Monica's mom, he caught up with her after 8 miles from their house. What was Monica's dad's speed? 1 solutions Answer 128439 by stanbon(57984)   on 2008-12-15 22:34:05 (Show Source): You can put this solution on YOUR website! Four Minutes after Monica left to go to school with her mom, her Dad realized that she had left her math homework at home. He decided to bring it to her so she would not get in trouble. Since he was driving at a speed 20 mph more than Monica's mom, he caught up with her after 8 miles from their house. What was Monica's dad's speed? ----------------- Dad DATA: distance = 8 miles ; rate = m+20 mph ; time = 8/(m+20) hrs. ----------------------- Mom DATA: distance = 8 miles ; rate = m mph ; time = 8/m hrs. ------------------------------------------------------- Equation: Mom time - Dad time = 4 minutes = (1/15) hour 8/m - 8/(m+20) = 1/15 8*15*(m+20) - 8*15m = m(m+20) 8*16*20 = m^2 + 20m m^2 + 20m - 2400 = 0 (m+60)(m-40) = 0 Positive solution: m = 40 mph (Mom's speed) m+20 = 60 mph (Dad's speed) =========================== Cheers, Stan H.