Algebra ->  Tutoring on algebra.com -> See tutors' answers!      Log On

 Tutoring Home For Students Tools for Tutors Our Tutors Register Recently Solved
 By Tutor
| By Problem Number |

Tutor:

Recent problems solved by 'solver91311'

solver91311 answered: 16882 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 , 4740..4769 , 4770..4799 , 4800..4829 , 4830..4859 , 4860..4889 , 4890..4919 , 4920..4949 , 4950..4979 , 4980..5009 , 5010..5039 , 5040..5069 , 5070..5099 , 5100..5129 , 5130..5159 , 5160..5189 , 5190..5219 , 5220..5249 , 5250..5279 , 5280..5309 , 5310..5339 , 5340..5369 , 5370..5399 , 5400..5429 , 5430..5459 , 5460..5489 , 5490..5519 , 5520..5549 , 5550..5579 , 5580..5609 , 5610..5639 , 5640..5669 , 5670..5699 , 5700..5729 , 5730..5759 , 5760..5789 , 5790..5819 , 5820..5849 , 5850..5879 , 5880..5909 , 5910..5939 , 5940..5969 , 5970..5999 , 6000..6029 , 6030..6059 , 6060..6089 , 6090..6119 , 6120..6149 , 6150..6179 , 6180..6209 , 6210..6239 , 6240..6269 , 6270..6299 , 6300..6329 , 6330..6359 , 6360..6389 , 6390..6419 , 6420..6449 , 6450..6479 , 6480..6509 , 6510..6539 , 6540..6569 , 6570..6599 , 6600..6629 , 6630..6659 , 6660..6689 , 6690..6719 , 6720..6749 , 6750..6779 , 6780..6809 , 6810..6839 , 6840..6869 , 6870..6899 , 6900..6929 , 6930..6959 , 6960..6989 , 6990..7019 , 7020..7049 , 7050..7079 , 7080..7109 , 7110..7139 , 7140..7169 , 7170..7199 , 7200..7229 , 7230..7259 , 7260..7289 , 7290..7319 , 7320..7349 , 7350..7379 , 7380..7409 , 7410..7439 , 7440..7469 , 7470..7499 , 7500..7529 , 7530..7559 , 7560..7589 , 7590..7619 , 7620..7649 , 7650..7679 , 7680..7709 , 7710..7739 , 7740..7769 , 7770..7799 , 7800..7829 , 7830..7859 , 7860..7889 , 7890..7919 , 7920..7949 , 7950..7979 , 7980..8009 , 8010..8039 , 8040..8069 , 8070..8099 , 8100..8129 , 8130..8159 , 8160..8189 , 8190..8219 , 8220..8249 , 8250..8279 , 8280..8309 , 8310..8339 , 8340..8369 , 8370..8399 , 8400..8429 , 8430..8459 , 8460..8489 , 8490..8519 , 8520..8549 , 8550..8579 , 8580..8609 , 8610..8639 , 8640..8669 , 8670..8699 , 8700..8729 , 8730..8759 , 8760..8789 , 8790..8819 , 8820..8849 , 8850..8879 , 8880..8909 , 8910..8939 , 8940..8969 , 8970..8999 , 9000..9029 , 9030..9059 , 9060..9089 , 9090..9119 , 9120..9149 , 9150..9179 , 9180..9209 , 9210..9239 , 9240..9269 , 9270..9299 , 9300..9329 , 9330..9359 , 9360..9389 , 9390..9419 , 9420..9449 , 9450..9479 , 9480..9509 , 9510..9539 , 9540..9569 , 9570..9599 , 9600..9629 , 9630..9659 , 9660..9689 , 9690..9719 , 9720..9749 , 9750..9779 , 9780..9809 , 9810..9839 , 9840..9869 , 9870..9899 , 9900..9929 , 9930..9959 , 9960..9989 , 9990..10019 , 10020..10049 , 10050..10079 , 10080..10109 , 10110..10139 , 10140..10169 , 10170..10199 , 10200..10229 , 10230..10259 , 10260..10289 , 10290..10319 , 10320..10349 , 10350..10379 , 10380..10409 , 10410..10439 , 10440..10469 , 10470..10499 , 10500..10529 , 10530..10559 , 10560..10589 , 10590..10619 , 10620..10649 , 10650..10679 , 10680..10709 , 10710..10739 , 10740..10769 , 10770..10799 , 10800..10829 , 10830..10859 , 10860..10889 , 10890..10919 , 10920..10949 , 10950..10979 , 10980..11009 , 11010..11039 , 11040..11069 , 11070..11099 , 11100..11129 , 11130..11159 , 11160..11189 , 11190..11219 , 11220..11249 , 11250..11279 , 11280..11309 , 11310..11339 , 11340..11369 , 11370..11399 , 11400..11429 , 11430..11459 , 11460..11489 , 11490..11519 , 11520..11549 , 11550..11579 , 11580..11609 , 11610..11639 , 11640..11669 , 11670..11699 , 11700..11729 , 11730..11759 , 11760..11789 , 11790..11819 , 11820..11849 , 11850..11879 , 11880..11909 , 11910..11939 , 11940..11969 , 11970..11999 , 12000..12029 , 12030..12059 , 12060..12089 , 12090..12119 , 12120..12149 , 12150..12179 , 12180..12209 , 12210..12239 , 12240..12269 , 12270..12299 , 12300..12329 , 12330..12359 , 12360..12389 , 12390..12419 , 12420..12449 , 12450..12479 , 12480..12509 , 12510..12539 , 12540..12569 , 12570..12599 , 12600..12629 , 12630..12659 , 12660..12689 , 12690..12719 , 12720..12749 , 12750..12779 , 12780..12809 , 12810..12839 , 12840..12869 , 12870..12899 , 12900..12929 , 12930..12959 , 12960..12989 , 12990..13019 , 13020..13049 , 13050..13079 , 13080..13109 , 13110..13139 , 13140..13169 , 13170..13199 , 13200..13229 , 13230..13259 , 13260..13289 , 13290..13319 , 13320..13349 , 13350..13379 , 13380..13409 , 13410..13439 , 13440..13469 , 13470..13499 , 13500..13529 , 13530..13559 , 13560..13589 , 13590..13619 , 13620..13649 , 13650..13679 , 13680..13709 , 13710..13739 , 13740..13769 , 13770..13799 , 13800..13829 , 13830..13859 , 13860..13889 , 13890..13919 , 13920..13949 , 13950..13979 , 13980..14009 , 14010..14039 , 14040..14069 , 14070..14099 , 14100..14129 , 14130..14159 , 14160..14189 , 14190..14219 , 14220..14249 , 14250..14279 , 14280..14309 , 14310..14339 , 14340..14369 , 14370..14399 , 14400..14429 , 14430..14459 , 14460..14489 , 14490..14519 , 14520..14549 , 14550..14579 , 14580..14609 , 14610..14639 , 14640..14669 , 14670..14699 , 14700..14729 , 14730..14759 , 14760..14789 , 14790..14819 , 14820..14849 , 14850..14879 , 14880..14909 , 14910..14939 , 14940..14969 , 14970..14999 , 15000..15029 , 15030..15059 , 15060..15089 , 15090..15119 , 15120..15149 , 15150..15179 , 15180..15209 , 15210..15239 , 15240..15269 , 15270..15299 , 15300..15329 , 15330..15359 , 15360..15389 , 15390..15419 , 15420..15449 , 15450..15479 , 15480..15509 , 15510..15539 , 15540..15569 , 15570..15599 , 15600..15629 , 15630..15659 , 15660..15689 , 15690..15719 , 15720..15749 , 15750..15779 , 15780..15809 , 15810..15839 , 15840..15869 , 15870..15899 , 15900..15929 , 15930..15959 , 15960..15989 , 15990..16019 , 16020..16049 , 16050..16079 , 16080..16109 , 16110..16139 , 16140..16169 , 16170..16199 , 16200..16229 , 16230..16259 , 16260..16289 , 16290..16319 , 16320..16349 , 16350..16379 , 16380..16409 , 16410..16439 , 16440..16469 , 16470..16499 , 16500..16529 , 16530..16559 , 16560..16589 , 16590..16619 , 16620..16649 , 16650..16679 , 16680..16709 , 16710..16739 , 16740..16769 , 16770..16799 , 16800..16829 , 16830..16859 , 16860..16889, >>Next

 Finance/203764: Geometry A square pool has side length p. The border of the pool is 1 ft wide. The combined area of the border and the pool is 400 ft^2. Find the length and the area of the pool. 1 solutions Answer 153734 by solver91311(16897)   on 2009-07-21 13:16:29 (Show Source): You can put this solution on YOUR website! If the pool is square and the border is uniformly 1 foot wide all the way around, then the side length of the outside edge of the border must be The overall area must then be Solve for (exclude the negative root) and John
 Travel_Word_Problems/203758: Please help me solve, Iam unsure how to set up the problem... it shows in the book but I cannot understand the explanation #6. If a car travels 1/100 kilometer each second, how many kilometers does it travel in an hour? I tried this 1/100*120 seconds... this is not right, I dont understand why.1 solutions Answer 153732 by solver91311(16897)   on 2009-07-21 12:54:28 (Show Source): You can put this solution on YOUR website! I'm not exactly sure how you derived the 120 in , but I suspect that you added 60 seconds per minute to 60 minutes per hour. That makes as much sense as adding 3 apples to 4 math homework assignments -- which is to say no sense at all. Each minute consists of 60 seconds. So, the first minute is 60 seconds, and the second minute has 60 seconds, so 2 minutes has seconds. 3 minutes would be seconds, and so on. But an hour has 60 minutes, so an hour is , for 60 terms of 60 each which is the same as So what you need is: John
 Polygons/203689: how many diagonals can be drawn from each vertex of a decagon?1 solutions Answer 153676 by solver91311(16897)   on 2009-07-20 21:43:27 (Show Source): You can put this solution on YOUR website! One less than the number of vertices, which is the same as the number of sides. John
 Geometric_formulas/203316: This question is from textbook Elementary and Intermediate Algebra Needn help finding the area of a square. The problem states: Find a polynomial A(x) that represents the area of the shaded region in the accompanying figure. There is a picture of this square with the variables and shading, I have included my book info so that you can see what I am talking about thanks. My try: (x+2)^2?1 solutions Answer 153396 by solver91311(16897)   on 2009-07-17 00:39:07 (Show Source): You can put this solution on YOUR website! Nice of you to leave your book info. Not that it will do any good. There are hundreds of Algebra texts in current use, each of which has a price tag of $50 to$150. You do the math. You have to describe your figure so that we can understand what it looks like. John
 Quadratic_Equations/203276: -2x^2+x-5=0 how do you solve this equation?1 solutions Answer 153395 by solver91311(16897)   on 2009-07-17 00:33:50 (Show Source): You can put this solution on YOUR website! Use the quadratic equation. John
 Graphs/203285: Question 7 (Multiple Choice Worth 1 points) Choose the best directions for graphing the equation y= (1/2)x + 1. a.Graph the point (0,1) and count up 1 and to the right 2 to find another point on the line. b.Graph the point (1,0) and count up 1 and to the right 2 to find another point on the line. c.Graph the point (0,1) and count to the right 1 and up 2 to find another point on the line. d.Graph the point (1,0) and count to the right 1 and up 2 to find another point on the line. -------------------------------------------------------------------------------- Question 8 (Multiple Choice Worth 1 points) What kind of line is created when you graph the equation x=2? a.Horizontal line b.Oblique line c.Vertical line d.No line is created. -------------------------------------------------------------------------------- Question 9 (Multiple Choice Worth 1 points) What is the slope of the line x=2? a.Zero b.Undefined c.2 d.Not enough information. -------------------------------------------------------------------------------- Question 10 (Multiple Choice Worth 1 points) What is the slope of the line y= -3? a.Zero b.Undefined c.-3 d.Not enough information. -------------------------------------------------------------------------------- Question 11 (Multiple Choice Worth 1 points) Choose the equation that is written in standard form. a.y= -3x +4 b.2y = x+8 c.x = 3y-6 d.4x -2y = 10 -------------------------------------------------------------------------------- Question 12 (Multiple Choice Worth 1 points) Find the x intercept of the graph represented by the equation 3x + 4y = 12. a.(0,3) b.(3,0) c.(4,0) d.(0,4) -------------------------------------------------------------------------------- Question 13 (Multiple Choice Worth 1 points) Find the y intercept of the graph represented by the equation 3x + 4y = 12. a.(0,3) b.(3,0) c.(4,0) d.(0,4) -------------------------------------------------------------------------------- Question 14 (Multiple Choice Worth 1 points) Choose ALL the points that are solutions to the equation y= 2x -5. a.(0,-5) b.(1,3) c.(-1,-7) d.(1/2, -4) -------------------------------------------------------------------------------- Question 15 (Multiple Choice Worth 1 points) Choose the equation of the line with a slope of 2/3 and y passing through the point (6,-2). a.y= (2/3)x -6 b.y= (2/3)x -2 c.y= (2/3) x -4 d.y = (3/2) x -6 -------------------------------------------------------------------------------- Question 16 (Multiple Choice Worth 1 points) Choose the equation of the line passing through the points (-2,3) and (-4,1). a.y = x -1 b.y = (-1/3)x + 7/3 c.y= x-4 d.y = x + 5 -------------------------------------------------------------------------------- Question 17 (Multiple Choice Worth 1 points) Choose the equation of the vertical line passing through the point (-2,1). a.x = -2 b.x = 1 c.y = -2 d.y = 1 -------------------------------------------------------------------------------- Question 18 (Multiple Choice Worth 1 points) Choose the equation of the line passing through the points (3,4) and (1,-6). a.y = 5x - 19 b.y = (1/5)x + 15/5 c.y = (1/5)x - 2 d.y = 5x - 11 -------------------------------------------------------------------------------- Question 19 (Multiple Choice Worth 1 points) Choose the ordered pair that is the solution to the following system of equations: y= 2x + 1 and y = x -5. a.(-6, -1) b.(-6,-11) c.(4,9) d.(4,-1) -------------------------------------------------------------------------------- Question 20 (Multiple Choice Worth 1 points) Choose the orderred pair that is the solution to the following system of equations: -3x + y = 4 and -7x + y = 12. a.(-2,-2) b.(-2,2) c.(2,-2) d.(2,2) -------------------------------------------------------------------------------- Question 21 (Multiple Choice Worth 1 points) Choose the ordered pair that is the solution to the following system of equations: 5x - 2y = 3 and 3x + 4y = 7. a.(1,-1) b.(-1,1) c.(-1,-1) d.(1,1) -------------------------------------------------------------------------------- Question 22 (Essay Worth 1 points) Give an ordered pair that is the solution to the equation y = 5x + 2. -------------------------------------------------------------------------------- Question 23 (Multiple Choice Worth 1 points) Choose the equation of the line that is perpendicular to the line shown in the graph and passes through the point shown in the graph. a.y = x - ll b.y= 3x – 11 c.y = -3x - 11 d.y = -x + 11 -------------------------------------------------------------------------------- Question 24 (Multiple Choice Worth 1 points) Choose the equation of the line that is perpendicular to the line shown in the graph and passes through the point shown in the graph. a.y = 2x + 7 b.y = -2x + 10 c.y = 2x - 10 -------------------------------------------------------------------------------- Question 25 (Multiple Choice Worth 1 points) The figure shown below looks like a trapezoid. By definition, a trapezoid is a four-sided figure with at least two parallel sides. Choose the best description below of how to determine whether the figure shown is or is not a trapezoid. a.Find the slope of the line between point (-9,5) and point (-3,8). Then find the slope of the line between point (4,-1) and point (3,5). If the slopes are opposite reciprocals, then the figure is a trapezoid. b.Find the slope of the line between point (-3,8) and point (3,5). Then find the slope of the line between point (-9,5) and point (4,-1). If the slopes are the same, then the figure is a trapezoid. c.Find the slope of the line between point (-9,5) and point (3,5). Then find the slope of the line between point (-3,8) and point (4,-1). If the slopes are the same, then the figure is a trapezoid. d.Find the slope of the line between point (-3,8) and point (3,5). Then find the slope of the line between point (-9,5) and point (4,-1). If the slopes are opposite reciprocals, then the figure is a trapezoid. : Question 7 (Multiple Choice Worth 1 points) Choose the best directions for graphing the equation y= (1/2)x + 1. a.Graph the point (0,1) and count up 1 and to the right 2 to find another point on the line. b.Graph the point (1,0) and count up 1 and to the right 2 to find another point on the line. c.Graph the point (0,1) and count to the right 1 and up 2 to find another point on the line. d.Graph the point (1,0) and count to the right 1 and up 2 to find another point on the line. 1 solutions Answer 153393 by solver91311(16897)   on 2009-07-17 00:20:31 (Show Source): You can put this solution on YOUR website!No, we are not going to take your test or do your entire assignment for you.
 Graphs/203289: Question 1 (Multiple Choice Worth 3 points) Given y = 2x – 4, choose the statement that accurately describes this line. a.The slope is 2 and the y intercept is 4. b.The slope is 2 and the y intercept is -4. c.The slope is 4 and the y intercept is 2. d.The slope is -4 and they y intercept is 2. -------------------------------------------------------------------------------- Question 2 (Multiple Choice Worth 3 points) The slope of the line that passes through (2, -4) and (-6, 2) is: a.-4/3 b.3/2 c.1/4 d.-3/4 -------------------------------------------------------------------------------- Question 3 (Multiple Choice Worth 3 points) Complete this sentence with the correct choice: y = 4 is a horizontal line with ________. a.undefined slope. b.a slope of 4. c.a slope of 0. d.None of the above will make a true statement. -------------------------------------------------------------------------------- Question 4 (Multiple Choice Worth 3 points) What would be the missing piece of information given the following information: Find the slope of the line that passes through the points (2, 6) and (4, 10). m = ? a.2 b.6 c.1 d.9 -------------------------------------------------------------------------------- Question 5 (Multiple Choice Worth 3 points) What would be the missing piece of information given the following information: Find the equation of the line that passes through the points (2, 6) and (4, 10). y = 2x + ? a.4 b.2 c.7 d.5 -------------------------------------------------------------------------------- Question 6 (Multiple Choice Worth 3 points) What would be the missing piece of information given the following information: Find the equation of the line that passes through the points (3, -1) and (2, 5). y = -6x + ? a.17 b.15 c,20 d.11 -------------------------------------------------------------------------------- Question 7 (Multiple Choice Worth 2 points) How would you would graph the linear equation y = -2x + 6? a.First plot the point (6,0) and then count up two and to the right 1. b.First plot the point (6,0) and then count down two and to the right 1 c.First plot the point (0,6) and then count up two and to the right 1 d.First plot the point (0,6) and then count down two and to the right 1 1 solutions Answer 153392 by solver91311(16897)   on 2009-07-17 00:18:30 (Show Source): You can put this solution on YOUR website!No, we are not going to take your test or do your entire assignment for you.
 Permutations/203313: Two cards are drawn without replacement from an ordinary deck of 52 playing cards. What is the probability of drawing an ace and a king? I have: 4/52 x 4/51 = 4/663 is this permutation correct?1 solutions Answer 153391 by solver91311(16897)   on 2009-07-17 00:16:35 (Show Source): You can put this solution on YOUR website!It is not a permutation, but it is the correct answer to your problem.
 Probability-and-statistics/203178: Given: A= {1,3, 5, 7} B= {c, d} S= {x e I 0 < x <10 } u {x x is a letter of the word dice} Find each of the following stes. a) A' b) B' c) A u B' d) (A u B) I am sorry I don't have all the write keys for the union and the funky looking E/ = and I don't know the correct term for it either. All I really need to know is what A' means. Thank you!1 solutions Answer 153320 by solver91311(16897)   on 2009-07-15 20:21:59 (Show Source): You can put this solution on YOUR website! You didn't specify, but I suspect that is your universe set. It has to be, otherwise expressions like don't make any sense. Given that S is the Universe set, , read 'the complement of A', means "everything that is in S that is NOT in A". The union of two sets is everything that is in one set and everything in the other set as well. It will be helpful to first enumerate . First we have a set of integers, larger than zero but less than ten, so: and then we have the letters of the word 'dice': Put them all together: From that set, cross out each element of and you are left with the complement of , or You should be able to figure out the rest. Notation: means "such that", means "is an element of", is the set of integers. John
 Average/203208: This question is from textbook Elementary and intermediate algebra Find the domain of each rational expression a^2-b^2/a-b1 solutions Answer 153319 by solver91311(16897)   on 2009-07-15 19:53:13 (Show Source): You can put this solution on YOUR website! The variables can be anything you like so long as they aren't equal to each other making the denominator of the expression equal to zero. John
 Functions/203212: Given f(x)=2x+3 and g(x)=x^2-3x+4 find following: 1. f(3) 2. g(-2) 3. f(b) 4. g(a+3) 5. (f+g)(x) Thank you!1 solutions Answer 153318 by solver91311(16897)   on 2009-07-15 19:49:04 (Show Source): You can put this solution on YOUR website! and are functions, the notation and mean "the value of the function (or ) at ". So if then , that is, the value of the function at 1. , the value of the function at , and so on. You just substitute the given value, whatever it is, for the independent variable in the function definition. Finally, . You just need to simplify the new expression. John
 Trigonometry-basics/203165: 2/(x-2)*2 1. what is the vertical asymptote 2. horizontal symptoto 3. what are the zeros if any ?1 solutions Answer 153317 by solver91311(16897)   on 2009-07-15 19:36:57 (Show Source): You can put this solution on YOUR website! There is a vertical asymptote at where is any value that would make the denominator zero, provided that it doesn't make the numerator zero also. Compare the degree of the numerator polynomial to the degree of the denominator polynomial. If the degree of the denominator is greater than the degree of the numerator, then there is a horizontal asymptote at . If the degree of the numerator and denominator are the same, then there is a horizontal asymptote at where is the lead coefficient of the numerator and is the lead coefficient of the denominator. If the degree of the numerator is larger than the degree of the denominator by 1 then there is an oblique asymptote whose equation is the quotient excluding any remainder obtained by performing polynomial long division of the numerator by the denominator. In order for a rational expression to be equal to zero, there must be a value of the variable that makes the numerator equal to zero. So to answer your question, you must ask yourself "Is there any value of the variable that will cause 2 to be equal to zero?" If there are, then those values are the zeros of the rational expression. If not, then there are no zeros. John
 Rectangles/203193: the diagonals of the following rectangle have which coordinates for their point of intersection? -2,7 1,9 5,3 2,1 a. 1,5 b.1.5,5 c.1.5,3 d.0.5,41 solutions Answer 153316 by solver91311(16897)   on 2009-07-15 19:18:31 (Show Source): You can put this solution on YOUR website! The diagonals of a rectangle bisect each other, so the point of intersection is the midpoint of either diagonal. Apply the midpoint formulas to the coordinates of either of the two sets of points that define the ends of either of the diagonals. and Where and are the ends of one of the diagonals. John
 test/203167: Hi, Need some help on this question. It's a practice test question and I'm a bit confused. Graph the following system and solve the linear programming problem: Maximize: P=7x+10y subject to: {2x+5y<=80 {4x+3y<=104 x>=0; y>=0 Thank you!1 solutions Answer 153284 by solver91311(16897)   on 2009-07-15 14:43:48 (Show Source): You can put this solution on YOUR website! Graph the two lines. Note that (0,0) is in the solution set for both of them, hence the solution set for each of the inequalities is the half-plane region below and to the left of the graphed line. The two non-negative constraints further bound the area of feasibility to above and to the right of the coordinate axes. See graph: Considering the two non-negative constraints, the area of feasibility is the quadrilateral region bounded by the two coordinate axes, the green graph line on the top and the red graph line on the right. The proof is beyond the scope of this discussion, so take it on faith that the optimum point will be one of the vertices of the feasibility area, namely: (0,0), (0,16), (26,0), or (20, 8). Substitute the coordinate values for the 4 possible optimum points into your objective function and see which one has the maximum result. You can calculate the other two and decide which is maximum. John
 real-numbers/203104: This question is from textbook Intermediate Algebra -25, -28/7, -18/5, -Pi, -0.763, -0.333..., 0, 1/10, 2/7, Pi/4, sqrt3, 9, 52.8, 283/5 From the above list, list all the irrational numbers. I think that -Pi is one of them? 1 solutions Answer 153251 by solver91311(16897)   on 2009-07-15 00:18:48 (Show Source): You can put this solution on YOUR website! A rational number is any number that can be expressed as the quotient of two integers. That does not include , , or from your list. Everything else can. is also trancendental, meaning that there is no polynomial equation that has as a root. on the other hand is algebraic, since is one of the roots of John
 Linear_Equations_And_Systems_Word_Problems/203111: find two consecutive integers whose sum is 89. to solve this problem, let x be the smaller of these integers. what's the larger of these two consecutive integers? write an equation that says that this sum is equal to 89. sole this equation What are the two numbers?1 solutions Answer 153245 by solver91311(16897)   on 2009-07-14 23:03:05 (Show Source): You can put this solution on YOUR website! Let represent the smaller integer. Consecutive means following one after the other in order. So the next consecutive integer must be So John
 Geometry_Word_Problems/203070: A rectangular track was being built so that the length of one of the short sides was half the length of one of the long sides. The track was supposed to be 300 yards around. At the last minute, the plans for the track were changed and a semicircle was added at each of the short ends. What is the distance around the track after the plans were modified? I know that the width of the rectangular part of the track is 50, and the length is 100. (2x+2x+x+x=300 -> 6x=300 -> x = 50) Don't know what to do from here.1 solutions Answer 153232 by solver91311(16897)   on 2009-07-14 19:35:04 (Show Source): You can put this solution on YOUR website! You are adding a semi-circle at each end. Two semi-circles make a whole circle. The diameter of the circle is the short side of the track. So you are subtracting the two short sides and adding the circumference of the circle. . I would leave the answer in terms of because that is the exact answer. But if you must have a number, use 3.14 for -- that is plenty close enough. John
 Polynomials-and-rational-expressions/203020: Find the zeros of all the polynomial functions. Multiply the binomials together. You may use special products, and you may multiply conjugate pairs together first. 1. (x-3i)(x+3i)(x-5)(x+4) 2. (x+3i)(x-3i)(x-2)(x+1) 3. (x+6)(x-7)(x-8)(x+4)(x-1) 4. (x+1)(x+2)(x-3)(x-4)(x+i)(x-i) 5. (x+2+i)(x+2-i)(x-i)(x+i) 6. (x-1+i)(x-1-i)(x+3)(x-5) 7. (x+i)(x-i)(x+1)(x-1)(x+3) 8. (x-i)(x+i)(x-3i)(x+3i)(x+2)(x-2)1 solutions Answer 153161 by solver91311(16897)   on 2009-07-14 00:24:21 (Show Source): You can put this solution on YOUR website! If you think you are going to get someone to do your entire homework assignment for you, let me disabuse you of such a notion right now. I'll do one, and you can do the rest. is a conjugate pair, so the product is the difference of two squares (remembering that ): Multiply the other two factors using FOIL: Now multiply the two partial products: John
 Linear-equations/203012: Two perpendicular lines intersect on the x-axis. The equation of one line is 3x-5y+6=0. What is the equation of the other line?1 solutions Answer 153160 by solver91311(16897)   on 2009-07-14 00:11:03 (Show Source): You can put this solution on YOUR website! Solve the given equation for , that is put it into form. Then determine the slope of the given line by inspection of the coefficient on . Knowing the slope of the given line will tell you the slope of the perpendicular line, because: Since the two lines intersect on the -axis, you can find the point of intersection by determining the -intercept of the given equation. Substitute 0 for in the original equation and then do the arithmetic to solve for . The -intercept is a point of the form where is the value you just calculated. With the slope of the desired line and the -intercept point use the point-slope form to derived the desired equation: where is the given point and is the slope determined above. John
 Linear-equations/203013: What is the equation for the line which contains the point (3,-1)1 solutions Answer 153159 by solver91311(16897)   on 2009-07-13 23:52:52 (Show Source): You can put this solution on YOUR website! There are an infinite number of different lines that pass through any one given point. There is no answer to your question as posed. John
 Graphs/203015: Write an equation of the line containing the given points and parallel to the given line. (7, -8); 6x-7y=5 The equation of the line is y= ??????1 solutions Answer 153158 by solver91311(16897)   on 2009-07-13 23:50:23 (Show Source): You can put this solution on YOUR website! Solve the given equation for , that is put it into form. Then determine the slope of the given line by inspection of the coefficient on . Knowing the slope of the given line will tell you the slope of the parallel line, because: Now that you have the slope of the desired line, you can use that and the given point in the point-slope form to derived the desired equation: where is the given point and is the slope determined above. John
 Inverses/203021: If two numbers are opposite of each other, are their reciprocals also opposite of each other?1 solutions Answer 153157 by solver91311(16897)   on 2009-07-13 23:40:23 (Show Source): You can put this solution on YOUR website! and are opposites. is the reciprocal of and is the reciprocal of So what do you think? John
 Radicals/203016: What does the radical sign tell you to do if, for example you have: 7√2. Does the sign mean multiply 7 by 2, and you'll get your answer? 1 solutions Answer 153156 by solver91311(16897)   on 2009-07-13 23:29:13 (Show Source): You can put this solution on YOUR website! In a word, no. The radical sign tells you to take the square root of the quantity inside of it. The square root is that number, when multiplied by itself results in the quantity under the radical. For example, because As to the example you gave, , the only way to exactly represent this quantity is just like it is, . That's because is an irrational number; it cannot be represented as the quotient of two integers. You can approximate it with a decimal representation to as many digits of precision as you like, but you can never represent it exactly except by writing . John
 test/202891: Let p, q, and r be the following statements: p: It is raining. q: The clouds are dark. r: The temperature is dropping. Translate the following statements into English (a) p upside down v r (b) ~p upsidedown v (q v r) (c) q arrow r (d) (~ rupside down v~ q) arrow ~ p1 solutions Answer 153133 by solver91311(16897)   on 2009-07-13 17:31:51 (Show Source): You can put this solution on YOUR website! The 'upsidedown v', means "and" in English. Replace every instance of with the word "and". The 'v' symbol, means "or" in English. Replace every instance of with the word "or". The tilde, (~) means "not" in English. Where ever you see the (~) symbol in front of a statement, insert the word "not" into the statement at a place where it makes sense. For example would be "It is not raining" (rather than "Not it is raining", "It not is raining", or "It is raining not"). An arrow that has an arrowhead only on the right means "if. . .then" Put the statement that precedes the arrow after the 'if' and before the 'then', and put the statement that follows the arrow after the 'then'. A double headed arrow means "if and only if", and the statement to the left of the double headed arrow would come first, then "if and only if" followed by the statement to the right of the arrow. Otherwise, replace the variables , , and with the statements that define them. John
 Numbers_Word_Problems/202916: Four girls, Ann, Bobbie, Cathy, and Deb, have $1100; Ann has a certain sum, Bobbie has twice as much as Ann, Cathy has$800, and Deb has $200 more than Cathy; how many dollars has Ann?1 solutions Answer 153125 by solver91311(16897) on 2009-07-13 16:59:05 (Show Source): You can put this solution on YOUR website! Whoever made up this problem must be a member of Congress. If Cathy has$800 and Deb has $200 more than that, then Deb and Cathy together have$1800, which is $700 more than the 4 girls started with in the first place. No solution to the problem as stated. John  Miscellaneous_Word_Problems/202964: Suppose that$1000 is invested in a savings account where interest is compounded continuously at 4.5% per year. Write down the equation P(t) for the balance in the account after t years.1 solutions Answer 153124 by solver91311(16897)   on 2009-07-13 16:53:13 (Show Source): You can put this solution on YOUR website! For continuous compounding So: John
 Equations/202973: The sum of two numbers is 6 less than twice the first number. Their difference is 10 less than four times the second number. Find each of the numbers.1 solutions Answer 153121 by solver91311(16897)   on 2009-07-13 16:47:40 (Show Source): You can put this solution on YOUR website! Let represent the first number. Let represent the second number. Then: and Solve the system for the ordered pair solution Hint: Solving the second equation for is a simple matter and leads you directly to a solution by substitution. John
 Expressions-with-variables/202976: Pre-Algebra (24n). What does "n" represent?1 solutions Answer 153120 by solver91311(16897)   on 2009-07-13 16:43:02 (Show Source): You can put this solution on YOUR website! Generally, some natural number (positive integers, either including or excluding 0 depending on who you talk to). But without any other contextual clues, it could be anything. John
 Probability-and-statistics/202971: X- and y-intercepts of a line given the equation in standard form. Find both the x-intercept and the y-intercept of the line given by the equation 1.8x-9.4y-6.6 =0 Round your answers to decimal places. x-intercepts:___ y-intercepts:___1 solutions Answer 153114 by solver91311(16897)   on 2009-07-13 16:00:13 (Show Source): You can put this solution on YOUR website! Substitute 0 for and do the arithmetic to get the -intercept. Then substitute 0 for and do the arithmetic to get the -intercept. John
 logarithm/202963: Find (f o g)(x), where f(x)=sqrt(x) and g(x)=1/x1 solutions Answer 153112 by solver91311(16897)   on 2009-07-13 15:56:29 (Show Source): You can put this solution on YOUR website! John
 Geometry_Word_Problems/202969: Area of a painting. A rectangular painting with a width of x centimeters has an area of x^2+ 50x square centimeters. Find a binomial that represents the length. 1 solutions Answer 153109 by solver91311(16897)   on 2009-07-13 15:40:53 (Show Source): You can put this solution on YOUR website! Area is length times width, so factor the width () out of the area expression. John