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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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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149, >>Next

 Functions/103625: Find the domain of the function: f(x)= square root of (2x-8) ...then write your solution in interval notation1 solutions Answer 75346 by stanbon(57203)   on 2007-10-11 11:56:57 (Show Source): You can put this solution on YOUR website!Find the domain of the function: f(x)= square root of (2x-8) -------------- 2x-8 must be >= zero -------- 2x-8 >=0 2x >=8 x >= 4 -------- Domain is all Real Numbers greater than or equal to four. [4,inf) ================ Cheers, Stan H.
 Travel_Word_Problems/103623: It takes 175 seconds for Sarah to walk from her house to the store and back. Going there she walks at 3 ft/sec and on the way back at 4 ft/sec. How long did it take her to walk to the store?1 solutions Answer 75340 by stanbon(57203)   on 2007-10-11 11:22:26 (Show Source): You can put this solution on YOUR website!It takes 175 seconds for Sarah to walk from her house to the store and back. Going there she walks at 3 ft/sec and on the way back at 4 ft/sec. How long did it take her to walk to the store? -------------------- Sara to store DATA: Rate = 3 ft/sec ; distance = x ft ; time = x/3 seconds ---------------------- Sara from store DATA: Rate = 4 ft/sec ; distance = x ft ; time = x/4 seconds ------------------------- EQUATION: time to + time from = 175 x/3 + x/4 = 175 Multiply thru by 12 to get rid of the denominators: 4x + 3x = 12*175 7x = 12*175 x = 300 ft (distance to the store) ------------------------- x/3 = 100 seconds (time to get to the store) ================= Cheers, Stan H.
 Polynomials-and-rational-expressions/103613: (((8/2m-4 + 3/5m-10=1/5)))1 solutions Answer 75335 by stanbon(57203)   on 2007-10-11 11:05:02 (Show Source): You can put this solution on YOUR website!8/(2m-4) + 3/(5m-10) = 1/5 Factor the denominators: 8/[2(m-2)] + 3/[5(x-2)] = 1/5 ---------------------------------- Least common multiple of the denominators is 10(x-2) --------------------- Multiply thru by the lcm to get: 8*5 + 3*2 = 2(x-2) 13 + 6 = 2x-4 2x = 23 x = 23/2 =================== Cheers, Stan H.
 expressions/103620: John is traveling to a meeting that is 28 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time?1 solutions Answer 75334 by stanbon(57203)   on 2007-10-11 10:59:29 (Show Source): You can put this solution on YOUR website!John is traveling to a meeting that is 28 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time? -------------- distance = 28 miles ; time = (1/2) hour EQUATION: rate = distance/time = 28/(1/2) = 56 mph He needs to average 56 mph ======================= Cheers, Stan H.
 Distributive-associative-commutative-properties/103582: What property is m[t+(-t)]= mt+m(-t) , m[t+(-t)]=m(-t+t), and m[t+(-t)] = [t+(-t)]m1 solutions Answer 75332 by stanbon(57203)   on 2007-10-11 10:56:55 (Show Source): You can put this solution on YOUR website!What property is m[t+(-t)]= mt+m(-t) The distributive property -------------------------------- m[t+(-t)]=m(-t+t) The commutative property allows you to change t+(-t) to (-t+t) ------------------------ and m[t+(-t)] = [t+(-t)]m The commutative property allows you to swithc the order of the factors. ------------- Cheers, Stan H.
 absolute-value/103621: please i was hoping maybe you may help my with this equasion. (6+2*8-4) --------- 2 i think i got it 8*4 32 =9 --- --- 2 2 thank you1 solutions Answer 75331 by stanbon(57203)   on 2007-10-11 10:42:00 (Show Source): You can put this solution on YOUR website!(6+2*8-4) --------- 2 ====================== = (6+16-4)/2 = (18)/2 = 9 ========== Cheers, Stan H.
 Graphs/103601: What does my teacher mean when she says "Tell how each of the following may be graphed by "shifting" the graph of y=/x/. Then sketch the graph for each." y = /x + 2/ - 1 y = /x - 3/ - 2 y = /x - 1/ + 2 y = -/x + 2/ + 11 solutions Answer 75325 by stanbon(57203)   on 2007-10-11 09:09:16 (Show Source): You can put this solution on YOUR website!"Tell how each of the following may be graphed by "shifting" the graph of y=/x/. Then sketch the graph for each." ----------------- Graph y = |x| ------------------------------- y = /x + 2/ - 1 The "x+2" moves the graph 2 to the left; The -1 moves the graph 1 down; You get: ----------------------- y = /x - 3/ - 2 The "x-3" moves the original graph 3 to the right: The -2 moves it down 2 You get: -------------------- y = /x - 1/ + 2 One to the right, then up 2. ----------------- y = -/x + 2/ + 1 Two to the left, then flip it over the x-axis, then up 1. ============= Cheers, Stan H.
 Unit_Conversion_Word_Problems/103561: leah travels 22 feet per second on her bicycle. how many miles per hour does she travel. 1 solutions Answer 75287 by stanbon(57203)   on 2007-10-10 21:29:07 (Show Source): You can put this solution on YOUR website!(22 ft/sec)*(3600 sec/1 hr)(1 mile/5280 ft) ------------- the ft cancel ; the sec cancel; you are left with = [22*3600*1]/[1*1*5280](miles/hr) = 15 mph ================= Cheers, Stan H.
 Linear-equations/103560: Graph the following equation, using the intercept method. 2x+3y=61 solutions Answer 75285 by stanbon(57203)   on 2007-10-10 21:25:05 (Show Source): You can put this solution on YOUR website!Graph the following equation, using the intercept method. 2x+3y=6 --------------------- If x=0, y = 2 If y=0, x = 3 ----------------- Plot the two points (0,2), (3,0) Draw a line thru them. Graph: ==================== Cheers, Stan H.
 Polynomials-and-rational-expressions/103526: Can you please help me to factor this Polynomial expression.12ax^3+20bx^2+32cx 1 solutions Answer 75281 by stanbon(57203)   on 2007-10-10 21:16:34 (Show Source): You can put this solution on YOUR website!factor this Polynomial expression.12ax^3+20bx^2+32cx ---------= = 4x(3ax^2 + 5bx +8c) ========================== Cheers, Stan H.
 Quadratic_Equations/103555: 0.478 using scientific notation1 solutions Answer 75280 by stanbon(57203)   on 2007-10-10 21:12:37 (Show Source): You can put this solution on YOUR website!0.478 using scientific notation ------------------------- = 4.78x10^-1 ================ Cheers, Stan H.
 Exponents-negative-and-fractional/103534: HELLO,HOW DO YOU CHANGE FROM EXPONENTIAL TO RADICAL FORM AND FROM RADICAL TO EXPONENTIAL. CAN YOU GIVE SOME EXAMPLES? THANKS!!!!1 solutions Answer 75279 by stanbon(57203)   on 2007-10-10 21:11:11 (Show Source): You can put this solution on YOUR website!5^(2/3) = cube root of 5^2 ------------- 7^(1/2) = sqrt(7) ------------------- 10^(-5/2) = 1/[sqrt(10^5)] ================== Cheers, Stan H.
 Angles/103554: This question is from textbook the measure of the supplement of an angle is 30 degrees less than 5 times the measure of the compliment find 2/5 the measure of the compliment1 solutions Answer 75277 by stanbon(57203)   on 2007-10-10 21:04:13 (Show Source): You can put this solution on YOUR website!the measure of the supplement of an angle is 30 degrees less than 5 times the measure of the compliment find 2/5 the measure of the compliment --------------- Let the angle be "x"; supplement is "180-x"; complement is "90-x" ------------------------ EQUATION: 180-x = 5(90-x)-30 180-x = 450-5x-30 4x = 240 x = 60 degrees complement = 90-x = 30 degrees -------------------------- (2/5)30 = 12 degrees ================ Cheers, Stan H.
 Equations/103553: This question is from textbook Texas Algebra 1 3-4q=10q+101 solutions Answer 75274 by stanbon(57203)   on 2007-10-10 20:59:37 (Show Source): You can put this solution on YOUR website!3-4q=10q+10 Add 4q to both sides to get: 14q = -13 Divide both sides by 14 to get: q = -13/14 ============ Cheers, Stan H.
 Travel_Word_Problems/103550: A cyclist rides D km at a rate of X km/hr and returns D km at a rate of Y km/hr. Write an expression representing the average rate in terms of X,Y and D. Simplify this expression if you can. rate=distance/time Total distance = 2D rate=Total Distance/Total Time I can't figure out how to get the total time in terms of X and Y. Can you help? Thanks! 1 solutions Answer 75273 by stanbon(57203)   on 2007-10-10 20:57:46 (Show Source): You can put this solution on YOUR website!A cyclist rides D km at a rate of X km/hr and returns D km at a rate of Y km/hr. Write an expression representing the average rate in terms of X,Y and D. Simplify this expression if you can. --------------------- 1st ride DATA; Rate = X km/h ; Distance = D miles ; Time = D/R = D/X hrs ---------------- Return ride DATA: Rate = Y km/h ; Distance = D miles ; Time = D/R = D/Y hrs ------------------ Average Rate = (total distance) / (total time) = 2D/[D/X + D/Y] = 2D/[D(Y+X)/XY] = 2XY/(X+Y) ================= Cheers, Stan H.
 Equations/103509: 2x^2+6x+9=0 (finding the value of the discriminant) How many real solutions are there of this equation? I have no idea how to do this question. Please help me1 solutions Answer 75251 by stanbon(57203)   on 2007-10-10 19:48:05 (Show Source): You can put this solution on YOUR website!2x^2+6x+9=0 (finding the value of the discriminant) How many real solutions are there of this equation? ------------- You have a quadratic equation with a=2, b=6, c=9 ----------- The discriminant is b^2-4ac. ------------------------- Your Problem: b^2-4ac = 36-4*2*9 = -36 --------------- Since the result is negative, there are no Real Number solutions to your problem. ======================== Cheers, Stan H.
 Linear-equations/103507: Find the equation that defines the relations below: (-3,0) (-2,4) (-1,2) (0,0) (1,4) (2,20)1 solutions Answer 75248 by stanbon(57203)   on 2007-10-10 19:44:06 (Show Source): You can put this solution on YOUR website!Find the equation that defines the relations below: (-3,0) (-2,4) (-1,2) (0,0) (1,4) (2,20) ------------------------------ I used the TI calculator Cubic Regression function to find f(x) = x^3 + 3x^2 as a function that generates these ordered pairs. ========================== Cheers, Stan H.
 Quadratic_Equations/103489: Can someone offer some assistance to a 49 year old algebra student? ([2a^2b]/[3x^2y])^3 times ([-6xy^2]/[a^3b])^21 solutions Answer 75243 by stanbon(57203)   on 2007-10-10 19:24:55 (Show Source): You can put this solution on YOUR website!([2a^2b]/[3x^2y])^3 times ([-6xy^2]/[a^3b])^2 ---------------------- =([8a^6b^3] / [27x^6y^3]) * ([36x^2y^4] / [a^6b^2]) Get the ab's together and the xy's together: =([8a^6b^3] / [a^6b^2]) * ([36x^2y^4] / [27x^6y^3]) Cancel where you can to get: = (8b)*(4y/3x^4) = [32by/3x^4] ======================== Cheers, Stan H.
 Exponents-negative-and-fractional/103490: -34 = r/-3 -34 x -3 = r/-3 x -3 102 = r is this correct...Thanks1 solutions Answer 75237 by stanbon(57203)   on 2007-10-10 19:10:28 (Show Source): You can put this solution on YOUR website!The answer is correct. Cheers, Stan H>
 Polynomials-and-rational-expressions/103491: A parsec is approximately meters. How many meters are there in parsecs1 solutions Answer 75236 by stanbon(57203)   on 2007-10-10 19:08:00 (Show Source): You can put this solution on YOUR website!A parsec is approx 3.1x10^16 meters.How many meters are there in 8x10^13 parsecs ---------------------- (8x10^13 p)*(3.1x10^16 m/p) = (8*3.1x10^29) = 24.8x10^29 = 2.48x10^30 meters ======================== Cheers, Stan H.
 Radicals/103454: express as a mixed radical a) square root 98 b) -5 square root 32 how do i solve these types of questions thanks1 solutions Answer 75235 by stanbon(57203)   on 2007-10-10 19:01:54 (Show Source): You can put this solution on YOUR website!express as a mixed radical a) square root 98 = sqrt(49*2) = 7sqrt(2) ---------------------------------------------- b) -5 square root 32 = -5sqrt(16*2) = -5*4sqrt(2) = -20sqrt(2) ====================== Cheers, Stan H.
 Rate-of-work-word-problems/103421: Jim can fill a pool carring buckets of water in 30 minutes. Sue can do the same job in 45 minutes, and Tony can do the same job in 1 1/2 hours. How quickly can the three fill the pool together? I have tried soo many ways, and even my toutor could not remember how to do these problems. Please if any way possible, give a solution and a reasoning of how you got your answer. Thank you.1 solutions Answer 75213 by stanbon(57203)   on 2007-10-10 16:03:06 (Show Source): You can put this solution on YOUR website!Jim can fill a pool carring buckets of water in 30 minutes. Sue can do the same job in 45 minutes, and Tony can do the same job in 1 1/2 hours. How quickly can the three fill the pool together? --------------------------------- Jim Rate = 1/30 job/min Sue Rate = 1/45 job/min Tony Rate= 1/90 job/min Together Rate = 1/x job min -------------------------------- EQUATION: 1/30 + 1/45 + 1/90 = 1/x 3x + 2x + x = = 90 6x = 90 x = 15 min (Time for them to do the job together) ====================================== Cheers, Stan H.
 Graphs/103413: This question is from textbook Algebra and Trigonometry I have the following problem. I will be honest, it is for homework, so the answer is not in the back of the book. I am just trying to understand how to properly solve it. y = (x^2 - 4)/2x^4 I tried to simplify this on the website and it gave me y - (x^2 - 4)/2x^4 = 0 I am suppose to state what the intercept is and what it is symmetric to (y-axis, x-axis and/or origin) Here is what I did. y = (x^2 - 4)/2x^4 y = (x^2 - 4)/(x^2)(2x^2) - I broke apart the 2x^4 y = -4/2x^2 - I thought the x^2 on the bottom of the fraction cancelled out the top. After that, I did not know what else to do. I could multiply both sides by 2x^2, but that did not seem to get me anywhere, so I started by making a list of the possible values of x and y. Here is what I came up with. x = 2, y = -1/2 x = -2, y = -1/2 x = 1, y = -2 I plotted these and my answer was the following: 1. I could not find an intercept. I don't see where either can equal 0, unless they both equal 0. 2. They would be symmetric to the y-axis. Am I correct? My main goal is to find out what else to do with the equation. I'm lost. Thanks for your help in advance.1 solutions Answer 75211 by stanbon(57203)   on 2007-10-10 15:59:24 (Show Source): You can put this solution on YOUR website!simplify this on the website and it gave me y - (x^2 - 4)/2x^4 = 0 I am suppose to state what the intercept is and what it is symmetric to (y-axis, x-axis and/or origin) ------------------------------------- y - (x^2 - 4)/2x^4 = 0 --------------- Intercepts: Since x cannot be zero, no y-intercepts. If y=0, x=+2 or x=-2 are the x-intercepts. ----------------------- Symmetry: f(x)=f(-x) so the function is even and therefore symmetric to the y-axis. -------------------------- Cheers, Stan H.
 Quadratic_Equations/103417: This question is from textbook I have these two quadratic equations that I have to solve. and I know how to factor and I'm aware of the zero product property...but I'm not sure that regular factoring is the right way to solve this problem. Can you help me out, please? 1 solutions Answer 75208 by stanbon(57203)   on 2007-10-10 15:46:56 (Show Source): You can put this solution on YOUR website!5x^2 + x + 2 = 0 Use the quadratic formula to get: x = [-1 +- sqrt(1-4*5*2)]/10 x = [-1 +- sqrt(-39)]/10 x = [-1 + isqrt(39)]/10 or x = [-1 - isqrt(39)]/10 ---------------------------------- and 2x^2 + 6x + 12 = 0 x^2+3x+6=0 x = [-3 +- sqrt(9-4*1*6)]/2 x = [-3 + isqrt(15)]/2 or x = [-3 -isqrt(15)]/2 -------------------------------------- Cheers, Stan H.
 Polynomials-and-rational-expressions/103419: This question is from textbook Beginning Algebra Hello. A square has sides of length 3x-2 cm. Express the area of the square as a polynomial. I think it is supposed to be like this, can you check my work and let me know if it correct, or if not where I went wrong? (3x-2)^2 =3x^2 - 2(3x)(2)+2^2 =9x-12x+4 Is this correct? 1 solutions Answer 75206 by stanbon(57203)   on 2007-10-10 15:41:24 (Show Source): You can put this solution on YOUR website!(3x-2)^2 =(3x)^2 - 2(3x)(2)+2^2 =9x^2-12x+4 ------------- Cheers, Stan H.
 Square-cubic-other-roots/103418: solve the following quadratic equations by factoring or by any other techniques (x-1)^2=71 solutions Answer 75205 by stanbon(57203)   on 2007-10-10 15:39:30 (Show Source): You can put this solution on YOUR website!(x-1)^2=7 x-1 = sqrt7 or x-1=-sqrt7 x = 1+sqrt7 or x = 1-sqrt7 =================== Cheers, Stan H.
 Polynomials-and-rational-expressions/103378: This question is from textbook Beginning Algebra Hello. I would like some help not only in finding the answer for this particular problem, but understanding the steps taken in solving the equation. I am not very good at understanding fractions. (x/2 + 2/3)(2x/3 - 2/5) Sorry, these are supposed to be fractions. If you could let me know what your doing step by step, it would better help me understand, so that I can work on my homework question using the same format. 1 solutions Answer 75178 by stanbon(57203)   on 2007-10-10 11:50:19 (Show Source): You can put this solution on YOUR website!(x/2 + 2/3)(2x/3 - 2/5) Use FOIL: F: (x/2)(2x/3) = 2x^2/6 = x^2/3 O: (x/2)(-2/5) = -(1/5)x I: (2/3)(2x/3) = (4/9)x L: (2/3)(-2/5) = -4/15 ------------------------- Combine to get: (1/3)x^2 + [(-1/5)+(4/9)]x - 4/15 = (1/3)x^2 -(11/45)x -(4/15) ================= Cheers, Stan H.
 Functions/103358: This is coming from the University of Houston online textbook, section 3.6 #39, if that helps anyone else. I'm not sure how to get "fog" when there is a number to multiply by. Given the functions f (x) = x2 + 2 and g(x) = 5x − 8 , find: (a) f (g(1)) (b) g(f (1)) (c) f (g(x)) (d) g(f (x)) (e) f ( f (1)) (f) g(g(1)) (g) f ( f (x)) (h) g(g(x)) 1 solutions Answer 75177 by stanbon(57203)   on 2007-10-10 11:41:39 (Show Source): You can put this solution on YOUR website! Given the functions f (x) = x2 + 2 and g(x) = 5x − 8 , find: (a) f (g(1)) = f[5*1-8] = f[-3] = (-3)^2+2 = 11 (b) g(f (1)) = g[1+2] = g[3] = 5*3-8 = 7 (c) f (g(x)) = f[5x-8]= (5x-8)^2+2 = 25x^2-80x+66 -------- I'll leave the rest for you. -------------------------- Cheers, Stan H. (d) g(f (x)) (e) f ( f (1)) (f) g(g(1)) (g) f ( f (x)) (h) g(g(x))
 Linear-equations/103376: the postive y values of the graph y=-3-4x fall in which quadrant?1 solutions Answer 75176 by stanbon(57203)   on 2007-10-10 11:34:46 (Show Source): You can put this solution on YOUR website!the postive y values of the graph y=-3-4x fall in which quadrant? Plot a couple of points; Draw the graph of the line and see where the y-values are positive. ------------- Graph: ================= Looks like the line has positive y-values in the 2nd quadrant. ================= Cheers, Stan H.