Tutor:

New! Get regular updates about newly solved problems via algebra.com's RSS system.

---

Recent problems solved by 'solver91311'

solver91311 answered: 16860 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

Geometry_Word_Problems/184689: how many square inches of velvet fabric is needed to cover a shoe box that is 10 inches in width and 6 inches in length and 5 inches in height? 1 solutions Answer 138604 by solver91311(16872)   on 2009-03-02 23:14:45 (Show Source): You can put this solution on YOUR website! To cover the entire box, you have two rectangles that are 6 by 5, two that are 6 by 10, and two that are 5 by 10. Calculate the area of all six rectangles and then add the areas to get the total surface area. John

Equations/184677: Hello. I'm needing some help factoring out this trinomial. a^6-2+a^3 thanks! 1 solutions Answer 138603 by solver91311(16872)   on 2009-03-02 23:11:28 (Show Source): You can put this solution on YOUR website! Let then But since But is the difference of two cubes, so since: We can say: If you are factoring over the rational numbers then the complete factorization is: However, if you are allowed to consider irrational factors you could also say: John

Polynomials-and-rational-expressions/184661: Melanie can paint a certain barn by herself in x days. Her helper, Melissa can paint the same barn by herself in 2x days. Write a rational expression for the fraction of the barn that they complete in one day by working together. Evaluate the expression for x=5. 1 solutions Answer 138583 by solver91311(16872)   on 2009-03-02 21:22:14 (Show Source): You can put this solution on YOUR website! Melanie can paint a certain barn by herself in x days, so she can paint th of the barn in 1 day. Likewise her helper can paint th of the barn in 1 day. Together, they can paint: th of the barn in 1 day. So together they take: days to paint the barn. Just substitute 5 for x to evaluate for 5 days. In general if A takes x time periods to do a job, and B takes y time periods to do the same job, then working together they can complete the job in: time periods. John

Exponential-and-logarithmic-functions/184660: what does this represent 1 solutions Answer 138580 by solver91311(16872)   on 2009-03-02 21:11:21 (Show Source): You can put this solution on YOUR website! so John

Quadratic_Equations/184643: 4x^2 - 8x - 5=0 answer x= -1/2 or 5/2 need a full break down of how my text book got this answer 1 solutions Answer 138578 by solver91311(16872)   on 2009-03-02 21:07:22 (Show Source): You can put this solution on YOUR website! Note that: So this factors: Using the Zero Product Rule: or John

Linear-equations/184650: Write an equation in standard form with integer coefficients for the line with slope 13/19 going through the point (-2,-1) What is the equation of the line 1 solutions Answer 138575 by solver91311(16872)   on 2009-03-02 21:00:26 (Show Source): You can put this solution on YOUR website! You need the Point-Slope form of the equation of a straight line: Just substitute the coordinates of your given point for and and your slope number for m. Then rearrange your equation into standard form: Hint: Multiply by 19 first. John

absolute-value/184644: Did I do this absolute problem correct? Ab.value(5x)+9=19 5x=10 x=2 or 5x=-10 x=-2 Thanks 1 solutions Answer 138573 by solver91311(16872)   on 2009-03-02 20:55:25 (Show Source): You can put this solution on YOUR website! Couldn't have done it better myself. Good job. John

Average/184653: Solve x^2 + 7 = 43 ?? 1 solutions Answer 138572 by solver91311(16872)   on 2009-03-02 20:53:24 (Show Source): You can put this solution on YOUR website! Add -7 to both sides and then take the square root. Remember to consider both the positive and negative square root. John

Average/184654: Solve (x – 5)2 = 3 1 solutions Answer 138571 by solver91311(16872)   on 2009-03-02 20:51:42 (Show Source): You can put this solution on YOUR website! Take the square root of both sides remembering to consider both the positive and negative roots. Add 5 to both sides: John

Average/184655: Solve x2 + 16x + 69 = 6 1 solutions Answer 138570 by solver91311(16872)   on 2009-03-02 20:48:28 (Show Source): You can put this solution on YOUR website! Add -6 to both sides: Then solve by factoring. Hint: and John

logarithm/184633: Solve for N Log base 4 (Log base 3 (log base 2 N))=1 1 solutions Answer 138569 by solver91311(16872)   on 2009-03-02 20:45:50 (Show Source): You can put this solution on YOUR website! Remember that: So: So: And: So: And finally: A very large number indeed. 2,417,851,639,229,258,349,412,352 John

Linear_Equations_And_Systems_Word_Problems/184635: The line Ax + By =8 passes through the points (2,1) and (4,-2). Find the values of A & B. Show work please. 1 solutions Answer 138564 by solver91311(16872)   on 2009-03-02 20:15:15 (Show Source): You can put this solution on YOUR website! You need to use the Two-Point form of the equation of a straight line because you are given two ordered pairs to define your line. Where and are your given points. It really doesn't matter which point you select as #1 and #2, so I just selected: and giving us: Now all you have to do is the arithmetic and algebraic manipulation to put the equation into the requested form, namely: John

Linear-systems/184629: I need help to solve this problem. Solve the systems of equations by substitutions 5x + y = 9 y=4x Type an ordered pair. 1 solutions Answer 138562 by solver91311(16872)   on 2009-03-02 20:05:43 (Show Source): You can put this solution on YOUR website! Since you have an equation that expresses y in terms of x, just substitute the expression containing x into the other equation, thus: Solve for x to get your x-coordinate, and then substitute that value back into either of the equations and solve for the y-coordinate. Express your answer as (x,y) once you have the proper values. John

Graphs/184630: Find the slope of the line if it exist. Type as integer or fraction. Simplifiy. Use N for no solution. (2,1) (2,-4) 1 solutions Answer 138561 by solver91311(16872)   on 2009-03-02 20:01:06 (Show Source): You can put this solution on YOUR website! The slope number is a fraction where the numerator is the difference in the y values and the denominator is the difference in x values. Remember, any fraction with a denominator of zero is undefined. John

Graphs/184625: Find the domain and the range. {(8,5),(-4,-5),(7,4),(4,7)} 1 solutions Answer 138560 by solver91311(16872)   on 2009-03-02 19:58:48 (Show Source): You can put this solution on YOUR website! The domain is the set of x-coordinates. The range is the set of y-coordinates. John

Graphs/184628: Graph the linear equation. x=3 1 solutions Answer 138559 by solver91311(16872)   on 2009-03-02 19:57:02 (Show Source): You can put this solution on YOUR website! The graph consists of all ordered pairs such that x = 3 and y is any real number. John

Probability-and-statistics/184624: If there is a 30% chance of snow today and a 20% chance of snow tomorrow, what is the probability that both days will go by without any snow falling? 1 solutions Answer 138558 by solver91311(16872)   on 2009-03-02 19:54:59 (Show Source): You can put this solution on YOUR website! A 30% chance of snow today and a 20% chance of snow tomorrow means that there is a 70% chance of no snow today and an 80% chance of no snow tomorrow, so: John

Probability-and-statistics/184623: What is the probability of rolling three 6s in a row, using a standard 6-sided die? 1 solutions Answer 138557 by solver91311(16872)   on 2009-03-02 19:52:26 (Show Source): You can put this solution on YOUR website! John

Quadratic_Equations/184612: Linear System Extension Thinking & Inquiry Questions 8. A triangle is formed by the intersection of the lines 2x+3y=14, 4x-5y=-16, and the x-axis. Find the area of the triangle Could you help me please with this question because i am really confused. Thank you very much!!! 1 solutions Answer 138556 by solver91311(16872)   on 2009-03-02 19:48:49 (Show Source): You can put this solution on YOUR website! Since the x axis forms one side of the triangle, use that as the base. Find the x-intercepts of each of the two equations by substituting 0 for y in each of them. Then the length of the base of the triangle will be the magnitude of the difference between these x-intercepts. Next find the point of intersection of the two lines represented by the two given equations by solving the 2-equation, 2-variable linear system. This one lends itself readily to solution by elimination if you go for eliminating the x term. Once you have that point of intersection, the y-coordinate will be the height of the triangle. Now that you know the length of the base and the height, just use the triangle area formula: John

Quadratic_Equations/184560: I'm can't figure out how to create a quadratic equation out of the vertex and a point that it must pass through. All i've managed so far is some trial and error and come up with this. y=2(x+2)²+4 From the vertex of (-2,4) and passing through (-1,8). I have been fiddling around with it and have two ideas how to proceed. I could change (x+2) to something else to move it along the x axis or change the first part of it to change the fatness or whichever you want to call it of the parabola. Regardless i figure there is a better way to do it other then trial and error, if it has been answered before i'm sorry I didn't see it. I'm self taught and this is the first time I really have had any problem. -Thanks 1 solutions Answer 138539 by solver91311(16872)   on 2009-03-02 18:06:50 (Show Source): You can put this solution on YOUR website! If you have three points on a parabola, you can determine the equation of the parabola by substituting the coordinates of your points into: Giving you three simultaneous linear equations that can be solved for the values of the coefficients A, B, and C. But you only have two points, namely the vertex and one other point. However, if you use the properties of symmetry for a parabola, you can easily develop the coordinates of the third point. Your only problem is that you must decide whether your parabola's axis of symmetry is vertical, giving you an equation where y is defined in terms of x, or whether the axis is horizontal, giving you an equation where x is defined in terms of y. If (-2, 4) is the vertex and (-1,8) is a point on the parabola with a vertical axis of symmetry, there is another point on the parabola with a y value of 8 and the x value that produces it will be equidistant from the vertex on the other side of the vertex from (-1,8), namely (-3, 8). If this is the case, then: Solve this system by your favorite method; either Gaussian Elimination or Cramer's Rule should do. The solution set will give you the three required coefficients. If you think your parabola has a horizontal axis, then your third point is (-1, 0), and you will use: to set up your three equations. In the absence of any evidence as to the orientation of the axis of symmetry, you might consider doing the problem both ways. John

Graphs/184558: I'm not sure about this. Graph the linear equation by finding and plotting its intercepts. y=-5x Thanks 1 solutions Answer 138532 by solver91311(16872)   on 2009-03-02 17:26:24 (Show Source): You can put this solution on YOUR website! The process for finding the intercepts requires substituting 0 for each of the variables and then determining the value of the other variable to give you two points: (a,0) which is the x-intercept (the point where the graph intersects the x-axis and (0,b) which is the y-intercept. This would give you two points that will define the line that is the graph of your equation. For this equation: and The problem you have with the given equation is that the x- and y-intercepts are the same point, namely the origin (0,0), and one point is insufficient to define a line. Consequently, just finding the intercepts is not enough to create the graph of this equation. To find a second point on the line, you need to find a point that is not an intercept. Select a value for x other than 0, substitute that value, and determine the resulting value for y. The selected value and the resulting value can be formed into an ordered pair that you can graph to establish your second point. (I chose 1 as a value for x, but you could choose anything you like so long as it is not 0) Now you have two points, (0,0) and (1,-5). Plot them then draw a line through them to give you your graph. John

Exponential-and-logarithmic-functions/184514: A plane's air speed is 450 km/h, With a tail wind , the plane traveled 1050 km/h. On the return trip, the plane flew witha head wind that was 20km.h less than the tail wind. If the total flying time was 4.6 h, find the speed of the head wind 1 solutions Answer 138499 by solver91311(16872)   on 2009-03-02 12:57:07 (Show Source): You can put this solution on YOUR website! This makes no sense at all. If the plane has an air speed of 450 km/h, and the plane traveled at 1050 km/h with a tail wind then the tail wind had to be 600 km/h. The fastest wind ever recorded in a hurricane is 190 miles per hour which is about 305 km/h hence a 600 km/h tail wind is utterly absurd. Check your work and repost your question written properly please. John

Problems-with-consecutive-odd-even-integers/184506: four times the smallest of three consecutive odd integers is 236 more than the sum of the two integers. find the integers. 1 solutions Answer 138493 by solver91311(16872)   on 2009-03-02 12:33:55 (Show Source): You can put this solution on YOUR website! The only way your question makes any sense at all is if you left out the word other when you typed your question. I suspect your question is supposed to be: "Four times the smallest of three consecutive odd integers is 236 more than the sum of the other two integers. Find the integers." In the future, please take more care when you post. We tutors do enough work just answering the questions you guys pose without having to guess at what you mean. Having vented my spleen, let's answer the question that I think you meant to ask. Let the smallest odd integer be x. Then the next consecutive odd integer must be x + 2. And the next consecutive odd integer after that must be x + 2 + 2 = x + 4. Four times the smallest is "is" means equals The sum of the other two is: 236 more than that is: Putting it all together: Solve for x to get the smallest integer. Add 2 to get then next one, and add 2 more to get the largest one. John

Mixture_Word_Problems/184467: A school district is combining 2 schools that will have a total of 1000 students, 42% of whom are african american. 90% of one school is african american and 10% of the other is african american. How may students are in each school. I've tried solving it several different ways x/2 + 420 = 1000 and x + y - 420 = 1000 for example and just can't figure this out! Please help - thank you very much! 1 solutions Answer 138466 by solver91311(16872)   on 2009-03-02 02:42:01 (Show Source): You can put this solution on YOUR website! If 42% of the new school is african-american, then out of the 1000 students at the new school, 420 are african-american. If x represents the number of students at one school and y represents the number of students at the second school. We can establish three things: 1. The sum of the students from the 2 schools must equal 1000: (1) 2. 90% of the first school is african-american, so you can say the number of african american students at school 1 is: 3. Likewise, the number of african american students at the second school is: And we know that 420 is the sum of the african-americans at both schools, so: (2) Now (1) and (2) form a system of linear equations that can be solved by either substitution or elimination. John

Square-cubic-other-roots/184453: This question is from textbook Blitzer 3 square root minus 4 equal 2 1 solutions Answer 138465 by solver91311(16872)   on 2009-03-02 02:27:43 (Show Source): You can put this solution on YOUR website! What you said was: Which is an utterly false statement because a complex number with a non-zero imaginary component cannot be equal to a real number. What you really might have meant was: In which case: Divide both sides by 3: Square both sides: Add 4 to both sides: John

Triangles/184450: How do you find out if two triangles are similar? I know that the triangles' angles must be congruent, and their sides must be proportional. How do you determine if the sides are proportional? Here is the problem: Are any of these triangles similar? If so, write the appropriate similarity statement. 1st triangle-CAB CA=4; CB=4; AB=5/angles A and B are congruent. 2nd triangle-PRQ PR=8; RQ not listed; QP=10 3rd triangle-XYZ XZ=8; XY not listed; ZX=8 On triangles PRQ and XYZ, angles Z and P are congruent. 1 solutions Answer 138464 by solver91311(16872)   on 2009-03-02 02:17:36 (Show Source): You can put this solution on YOUR website! If you have two triangles that have 2 congruent angles, then the third angles must be congruent because the angles of a triangle always sum to 180. If you have three congruent angles, then the sides must be related with a common constant of proportionality and therefore are at least similar (congruent if the constant of proportionality is 1) John

Polygons/184462: How do I find a missin angle in a heptagon? I am given angles 142 130 122 105 and 110 1 solutions Answer 138463 by solver91311(16872)   on 2009-03-02 01:27:37 (Show Source): You can put this solution on YOUR website! The sum of the interior angles of a n-sided polygon in degrees is given by: So any heptagon (7-sided polygon) must have interior angles whose measure totals: degrees. The only problem is, you only specified the measure of 5 of the angles. So, either you really meant hexagon, or you simply failed to specify all of the given angles. The best that can be done with the given information is to determine the sum of the two missing angles. Add the measures of the angles you have, then subtract from 1260. The result will be the sum of the two missing angles in your heptagon. On the other hand, if you actually meant hexagon, then subtract the sum of the given angles from 720. John

Polygons/184463: How do I proove that to lines are parallel if I am given a transversal and the angles that transversal is going through the lines? 1 solutions Answer 138460 by solver91311(16872)   on 2009-03-02 01:03:34 (Show Source): You can put this solution on YOUR website! Opposite interior angles formed by a transversal that intersects two lines are equal if and only if the lines are parallel. John

Graphs/184416: Solve the inequality |2x -4| < 10. Write the solution in interval notation and graph it. 1 solutions Answer 138413 by solver91311(16872)   on 2009-03-01 19:20:55 (Show Source): You can put this solution on YOUR website! Means: or Note change of inequality sense when multiplying by . So your interval is: In interval notation: (-3,7). Note use of parentheses vice square brackets because equals was not included in the original inequality relationship. You can draw your own graph. Remember to use open circles on the endpoints. John

Quadratic_Equations/184397: Use the quadratic formula to solve the equation: 3x^2-38x=101 a) 19+[664]/3 b) -19+[664] c) 19-[58]/3 d) 19+[664]/6 e) 19+[58]/3 f) 19-[664]/3 Hint: the [] stands for square root signal. And there is a chance it may be more than one answer! 1 solutions Answer 138410 by solver91311(16872)   on 2009-03-01 19:14:18 (Show Source): You can put this solution on YOUR website! In the first place, there is more than a chance that there will be two answers. There is an absolute iron-clad money-back take-it-to-the-bank guarantee that there are two answers. That is because ALL quadratic polynomials have two factors, be they real or complex. The Fundamental Theorem of Algebra tells me so. Sometimes you will have a perfect square trinomial and the factors will be the same, but there are still two factors and therefore two roots to the equation. No guarantee they will both be in your list of answers though. The first thing to do is put your equation into standard form: Quadratic Formula: Your coefficients are: So: Which gets you to two of the listed answers. By the way, those answers are not reduced to simplest terms. So the answers should be: John

Geometric_formulas/184399: The height h(in feet) of an object that is dropped from the height of s feet is given by the formula h=s-16t^s, where t is the time the object has been falling. A 5ft woman on a side walk looks directly over head and sees a window washer drop a bottle from the 3 story. How long does she have to get out of the way? Round to the nearest tenth. A story is 12ft. a) 1.9seconds b) 1.4seconds c) 1.7seconds d) 1.3seconds 1 solutions Answer 138405 by solver91311(16872)   on 2009-03-01 18:44:29 (Show Source): You can put this solution on YOUR website! To start with, your height function is incorrect. You have: Whereas it should be: Having settled that, you need to solve for t when h = 5. The only problem is the exact value of s to use. Was the window washer standing on a scaffold that was positioned between the 2nd and 3rd floor (at 24 feet) and he pushed the bottle off of the scaffold with his foot? Was he holding it above waist level with his feet on the scaffold at (maybe) 24 feet, so the bottle dropped from 28 feet? Or maybe the scaffold was half-way up the 3rd floor at 30 feet and he either kicked the bottle off the scaffold (s = 30) or dropped it from just above waist height (s = 34). It is highly unlikely that he dropped it from the full 36 feet if he was cleaning windows that extend from 24 to 36 feet. So: You can try some different values for s and see what you get. John