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Recent problems solved by 'stanbon'

stanbon answered: 57182 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 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209, >>Next

Equations/87957: Word problem to solve; thanks purchased a combination of 25 air condition and heating systems for $440,000. One single AC system cost 22,000 and single heat system cost 11,000. How many of each did they buy Steps 1. assign variables 2. write algebraic model 3. solve model 4... answer Thanks bb 1 solutions Answer 63847 by stanbon(57250)   on 2007-07-11 10:34:40 (Show Source): You can put this solution on YOUR website! purchased a combination of 25 air condition and heating systems for $440,000. One single AC system cost 22,000 and single heat system cost 11,000. How many of each did they buy ----------- Let # of AC units purchased be "x"; Value of these is 22000x dollars ---------- # of heat units purchased is "25-x"; Value of these is 11000(25-x)=275000-11000x ------------------ EQUATION: value + value = 440,00 dollars 22000x + 275000 - 11000x = 440000 11000x = 165000 x = 15 (# of AC units purchased) 25-x = 10 (# of heating units purchased) ============= Cheers, Stan H.

Equations/87962: Word problem - hard one - thanks for help Okay Making 3 different kinds of missiles for defense - each one takes a different combination of alloys - aluminum, plexiglas, and titanium Missile 1 - needs 2 tons of alum, 2 tons of plex and 3 tons of titan Missile 2 - 3 tons of alum, and 1 ton of titan Missile 3 - 3 tons of plex and 1 ton alum Need to produce 800 of type 1 650 of type 2 and 350 of type 3 How many tons of each alloy will we need???? HELP!?!?!?!?!? Steps needed: 1. assign variables 2. write algebraic model 3. solve model 4. answer thank you so much - lucyloo 1 solutions Answer 63846 by stanbon(57250)   on 2007-07-11 10:28:38 (Show Source): You can put this solution on YOUR website! Making 3 different kinds of missiles for defense - each one takes a different combination of alloys - aluminum, plexiglas, and titanium Missile 1 - needs 2 tons of alum, 2 tons of plex and 3 tons of titan Missile 2 - 3 tons of alum, and 1 ton of titan Missile 3 - 3 tons of plex and 1 ton alum Need to produce 800 of type 1 650 of type 2 and 350 of type 3 How many tons of each alloy will we need? --------------- Let "a" be amt of alum; "p" be amt of plex; "t" amt of titan -------- Total alum = 800*2 + 650*3 + 350*1 = 3900 tons Total plex = 800*2 + 350*3 = 2650 tons Total titan = 800*3 + 650*1 = 3050 tons ============= Comment: I doubt this is the problem you were asked to work. Are you sure the 800, 650, and 350 are not respectively the amts of alem, plex, and titan, rather than the number of each missile type? Cheers, Stan H.

Mixture_Word_Problems/87963: This is from a worksheet: In a chemistry class, 6 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution is needed? 1 solutions Answer 63845 by stanbon(57250)   on 2007-07-11 10:13:44 (Show Source): You can put this solution on YOUR website! In a chemistry class, 6 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution is needed? ---------------- Amt of 4% solution = 6 L ; Amt of active ingredient = 0.04*6 = 0.24 L ------------- Amt of 10% solution = x L ; Amt of active ingredient = 0.10x L ----------------- Amto of 6% mixture = "6+x" L; Amt of active = 0.06(6+x)=0.36+0.06x L -------------- EQUATION: active + active = active 0.24 + 0.10x = 0.36+0.06x 0.04x = 0.12 x = 3 L (Amt of 10% solution that must be added) ============ Cheers, Stan H.

Radicals/87950: This question is from textbook algebra structure and method I'm supposed to express in simpest radical form. (square root of 3 minus square root of 5)(square root of 3 minus square root of 5). Would you use the problem solving technique of (a-b)*(a+b)=asquare-bsquarePlease help!! Thanks!!! 1 solutions Answer 63831 by stanbon(57250)   on 2007-07-11 06:15:23 (Show Source): You can put this solution on YOUR website! express in simpest radical form. (square root of 3 minus square root of 5)(square root of 3 minus square root of 5). ----------------- (sqrt3 - sqt5)(sqrt3 - sqrt5) Use FOIL to get: F: sqrt3*sqrt3 = 3 O: -sqrt5*sqrt3 = -sqrt15 I: -sqrt3*sqrt5 = sqrt 15 L: sqrt5*sqrt5 = 5 ------------ Combine these to get: 8 - 2sqrt15 =============== The form you could use here is (a-b)(a-b)=a^2-2ab+b^2 This is called "the square of a binomial". =============================== Cheers, Stan H.

Linear_Equations_And_Systems_Word_Problems/87928: How can you prove that a point (x, y) is not located on a line of a given equation. Show example to explain. 1 solutions Answer 63804 by stanbon(57250)   on 2007-07-10 22:13:01 (Show Source): You can put this solution on YOUR website! How can you prove that a point (x, y) is not located on a line of a given equation. Show example to explain. ------------------------ Is the point (1,5) on the line y = 3x + 7 ------------- Substitute x=1 and y=5 into the equation to see if you get a true statement. 5 = 3*1 + 7 5 = 3 + 7 5 = 10 ----------------- That's not true. That point is not on that line. --------------- Cheers, Stan H.

logarithm/87924: I need help with a question that says: solve each of the following for x *1/8=4^(6x+2) *(1/4)^x=256 *log10x=4 1 solutions Answer 63803 by stanbon(57250)   on 2007-07-10 22:07:19 (Show Source): You can put this solution on YOUR website! solve each of the following for x *1/8=4^(6x+2) 2^-3 = 2^(2(6x+2)) -3 = 12x+4 12x = -7 x = -7/12 ---------------------- *(1/4)^x=256 2^-2x = 2^8 -2x = 8 x = -4 -------------------------- *log10x=4 Question: Does this mean log(10x) or log(base 10)x ? =================== Cheers, Stan H.

logarithm/87926: I need help with this: expand the logarithm logb squareroot (55/86) 1 solutions Answer 63799 by stanbon(57250)   on 2007-07-10 21:59:13 (Show Source): You can put this solution on YOUR website! expand the logarithm logb squareroot (55/86) ----------- Comment: All these logs are base b. --------------- = (1/2)[log(55/86)] = (1/2)[log55 - log86] ================ Cheers, Stan H.

logarithm/87927: I need help with this homework: evaluate the logarithm using the change-of-base formula *log2 17.95 *log7 (2/3) 1 solutions Answer 63798 by stanbon(57250)   on 2007-07-10 21:56:10 (Show Source): You can put this solution on YOUR website! evaluate the logarithm using the change-of-base formula *log2 17.95 = [log17.95]/[log2] = 4.1659... ---------------------------------------------- *log7 (2/3) = [log(2/3)]/[log7] = -0.208368 ---------------------- Cheers, Stan H.

Geometry_Word_Problems/87923: This question is from textbook Introductory and Intermediate Algebra Could you please help with the following problem: A picture 9 inches wide and 12 inches long is surrounded by a frame of uniform width. The area of the frame only is 162 square inches. Find the width of the frame. Thank you very much for any help you can provide. 1 solutions Answer 63796 by stanbon(57250)   on 2007-07-10 21:49:25 (Show Source): You can put this solution on YOUR website! A picture 9 inches wide and 12 inches long is surrounded by a frame of uniform width. The area of the frame only is 162 square inches. Find the width of the frame. ------------- Draw the picture of the frame around the picture. ---------------------------- Let the width of the frame be "x"inches. ----------------------------- Area of picture with frame around is length*width Width = 9 + 2x inches length = 12 + 2x inches --------- Larger area = (9+2x)(12+2x) =2(9+2x)(6+x) =2[54+21x+2x^2] =4x^2 + 42x + 108 --------------- Area of frame = larger area - 9*12 = 4x^2 + 42x +108 - 108 = 4x^2 + 42x ------------------- Area of frame = 162 sq. in. 4x^2+42x= 162 2x^2 + 21x -81 = 0 x = [-21+33]/4 = 3 or x = [-21-33]/4 = -54/4 = -27/2 ---------------------- Realistic Answer: width = 3 inches ============================ Cheers, Stan H.

Mixture_Word_Problems/87918: This question is from textbook How many litres of water must be added to 50 L of a 30% acid solution in order to produce a 20% acid solution? 1 solutions Answer 63790 by stanbon(57250)   on 2007-07-10 20:42:21 (Show Source): You can put this solution on YOUR website! How many litres of water must be added to 50 L of a 30% acid solution in order to produce a 20% acid solution? ---------------- Amt of 30% solution = 50 L; amt of active ingredient = 0.30*50 = 15 L ------------------ Amt of water added = x L ; amt of active ingredient = 0x = 0 ------------------------- Amt of 20% solution = (50+x) L; amt of active ingredient = 0.2(50+x) = 10+0.2x L ---------------------------- EQUATION: active + active = active 15 + 0 = 10 + 0.2x 5 = 0.2x x= 25 L (amount of water that must be added) ============= Cheers, Stan H.

Expressions-with-variables/87919: On september 11, 2003, the Minneapolis Star Tribune compared the price of Glad wrap to Press 'n Seal. A roll of Glad wrap sells for $2.99, A roll of Press n' Seal sells for $3.79 or 5 cents a squeare foot. Press's Seal for 10/3 times as much per square foot as Glad wrap. What is the price of Glad wrap per square foot? 1 solutions Answer 63789 by stanbon(57250)   on 2007-07-10 20:27:06 (Show Source): You can put this solution on YOUR website! A roll of Glad wrap sells for $2.99, A roll of Press n' Seal sells for $3.79 or 5 cents a square foot. Press's Seal for 10/3 times as much per square foot as Glad wrap. What is the price of Glad wrap per square foot? -------------- EQUATION: PS =(10/3)GW 5 cents/sq. ft = (10/3)GW GW = 5/(10/3) = = 15/10 = 1.5 cents/sq.ft =============== Cheers, Stan H.

Mixture_Word_Problems/87916: Okay, I am taking an online Math class and have come across all of the types of work problems, Mystery #s, Money, Mixture & Motion problems. I am so stuck on this Mixture Problem. : Ms. Post wants to mix 2 kinds of cereal. Type A sells at $2.20/lb and Type B sells at $4.20/lb. How many lbs of Type A should she use if she wants a 20 lb mixture selling at $3.00/lb.? Well, I tried using problems in my lesson as an example for the chart. This is what I came up with and am pretty sure I got it wrong... 2.20x+4.20(20-x)=3.00(20) 2.20x+84-4.20x=60 +4.20x -84= 6.4x divided by itself, cancelling the 6.4, then dividing -24 by the 6.4, I ended up w/ x=-3.75 ** I'm pretty sure I got this wrong. SO could you please help me so I can finish my work? Thanks very much for anything you can give me.!!! 1 solutions Answer 63788 by stanbon(57250)   on 2007-07-10 20:06:47 (Show Source): You can put this solution on YOUR website! Ms. Post wants to mix 2 kinds of cereal. Type A sells at $2.20/lb and Type B sells at $4.20/lb. How many lbs of Type A should she use if she wants a 20 lb mixture selling at $3.00/lb.? ----------------- Let amt of Type A be "x" ; value of this is 220x cents ----------------------------------- Amt of Type B is "20-x" ; value of this is 420(20-x) = 8400-420x cents ----------------------- Amt of mixture is 20 lbs. ; value of this is 300*20= 6000 cents ======================== EQUATION: value + value = value 220x + 8400-420x = 6000 -200x = -2400 x = 12 lbs (amount of Type A cereal) 20-x = 8 lbs (amount of Type B cereal) ====================== Cheers, Stan H.

Probability-and-statistics/87915: The probability that Robin Hood hits a target is 5/6. The probability that Little John hits a target is 1/7. If Robin Hood and Little John each shoot one arrow at the target, what is the probability that they both miss?: 1 solutions Answer 63786 by stanbon(57250)   on 2007-07-10 19:32:24 (Show Source): You can put this solution on YOUR website! The probability that Robin Hood hits a target is 5/6. The probability that Little John hits a target is 1/7. If Robin Hood and Little John each shoot one arrow at the target, what is the probability that they both miss?: ------------- The events are independent so P(A AND B) = [Prob(A)*Prob(B) Prob(miss AND miss) = (1/6)(6/7) = 1/7 =============== Cheers, Stan H.

test/87910: Which does not represent a possible intersection of two spheres? choices 0 points 1 point 2 points infinitely many points 1 solutions Answer 63784 by stanbon(57250)   on 2007-07-10 19:06:10 (Show Source): You can put this solution on YOUR website! Answer: 2 points The intersection has to be nothing, one point, a circle, or a sphere. ========== Cheers, Stan H.

Matrices-and-determiminant/87893: how do you find the determinant of a 4 by 4 matrix? 1 solutions Answer 63783 by stanbon(57250)   on 2007-07-10 19:03:55 (Show Source): You can put this solution on YOUR website! Finding the determinant of a 4x4 matrix is a complicated process unless you have a calculator that can do it for you. The following site shows how to find the determinant of a 3x3 and then a 4x4. Cheers, Stan H. http://www.richland.edu/james/lecture/m116/matrices/determinant.html

Quadratic_Equations/87887: complete the square x^2-14x=51 x= ? and ? 1 solutions Answer 63778 by stanbon(57250)   on 2007-07-10 18:50:46 (Show Source): You can put this solution on YOUR website! complete the square x^2-14x=51 x^2-14x+(14/2)^2 = 51+(14/2)^2 (x-7)^2 = 51 + 49 x-7 = +-10 x= 10+7= 17 or x= -10+7=-3 ==================== Cheers, Stan H.

Geometry_Word_Problems/87905: The measure of an angle is 2/3 the measure of its supplement. Find the measure of the angle and its supplement. my equation for this is x + (2x)/3 = 180 and my answer is 108 and 72 ( is it correct?) 1 solutions Answer 63776 by stanbon(57250)   on 2007-07-10 18:45:16 (Show Source): You can put this solution on YOUR website! The measure of an angle is 2/3 the measure of its supplement. Find the measure of the angle and its supplement. -------------- Let the angle be "x"; its supplement is "180-x". EQUATION: x = (2/3)(180-x) x = 120-(2/3)x (5/3)x = 120 x = 120(3/5) x = 72 degrees (one of the angles) 180-x = 108 degrees (the other angle) ============== Cheers, Stan H.

Quadratic_Equations/87906: This question is from textbook Elementary and Intermediate Algebra Please help me solve this problem: 108. Racquestball. The volume of rubber(in cubic centimeters) ina hollow rubber ball used in racquetball is given by V= 4/3 pie R^3- 4/3 pie r^3 where the inside radius is r centimeters and the outside radius is R centimeters Thank you... 1 solutions Answer 63772 by stanbon(57250)   on 2007-07-10 18:36:54 (Show Source): You can put this solution on YOUR website! Racquestball. The volume of rubber(in cubic centimeters) in a hollow rubber ball used in racquetball is given by V= 4/3 pie R^3- 4/3 pie r^3 where the inside radius is r centimeters and the outside radius is R centimeters ---------------- a Rewrite the formula by factoring the right-hand side completely. V= 4/3 pie R^3- 4/3 pie r^3 V = (4/3)pi[R^3 - r^3] ----------------------- b The accompanying graph shows the relationship between r and V when R=3. Use the graph to estimate the value of r for which V=100 cm^3 ------ Comment: Will look at the graph later. =========== Cheers, Stan H.

Exponents-negative-and-fractional/87891: 7/2x+1/2x=3x+3/2+5/2x= 1 solutions Answer 63771 by stanbon(57250)   on 2007-07-10 18:33:52 (Show Source): You can put this solution on YOUR website! [7/2x]+[1/2x]=[(3x+3)/2]+[5/2x] [7/2x]+[1/2x]=[x(3x+3)/2x]+[5/2x] [7+1]/2x = [3x^2+3x+5]/2x 3x^2+3x+5 = 8 3x^2+3x-3 = 0 x^2+x-1 = 0 x = [-1+-sqrt(1-4*1*-1)]/2 x = [-1 +- sqrt5]/2 x= [-1+srt5]/2 or x= [-1-sqrt5]/2 ===================== Cheers, Stan H.

Geometric_formulas/87904: how exactly do i get orderded pairs for the eguation it was an equation y=-x2+3x+3 then i the farthest i gotten on my formula is -3+- the square root of 21 divided by -2 1 solutions Answer 63769 by stanbon(57250)   on 2007-07-10 18:22:12 (Show Source): You can put this solution on YOUR website! how exactly do i get ordered pairs for the eguation it was an equation y=-x^2+3x+3 then i the farthest i gotten on my formula is -3+- the square root of 21 divided by -2 -------------- It looks like you were trying to apply the quadratic formula. But that is not the easiest way to find ordered pairs. ----------- Getting ordered Pairs: 1st: pick a value for "x". 2nd: substitute that value of x into the equation to find the corresponding value for y. ---------- For example: If x=0, y= -0^2+4*0+3 = 3, giving you the ordered pair (0,3) If x=1, y= -1^2+4*1+3 = 6, giving you the ordered pair (1,6) etc. ========= Cheers, Stan H.

test/87903: Describe the locus of all points in space that are 5 cm from point P. choices: circle P with a radius of 5 cm cube with 5 cm sides sphere P with a radius of 5 cm cube with 5 cm sides 1 solutions Answer 63767 by stanbon(57250)   on 2007-07-10 18:15:50 (Show Source): You can put this solution on YOUR website! Describe the locus of all points in space that are 5 cm from point P. choices: Answer: sphere P with a radius =========== Cheers, Stan H.

Geometry_Word_Problems/87901: Two angles are complementary. One-half the measure of the larger angle exceeds one-fourth the measure of the smaller by 30. Find the measure of the angle, the measure of its supplement and the measure of its complement. 1 solutions Answer 63766 by stanbon(57250)   on 2007-07-10 18:07:29 (Show Source): You can put this solution on YOUR website! Two angles are complementary. One-half the measure of the larger angle exceeds one-fourth the measure of the smaller by 30. Find the measure of the angle, the measure of its supplement and the measure of its complement. ------------------------------- Let one of the angles be "x"; the other is "90-x". EQUATION: (1/2)x = (1/4)(90-x)+30 Multiply thru by 4 to get: 2x = (90-x) + 120 3x = 210 x = 70 (measure of one of the angles) 90-x = 20 ( measure of the other angle) =============== Cheers, Stan H.

Polynomials-and-rational-expressions/87797: This question is from textbook elementary and intermediate alebra Please help me solve this equation. Thank you. Find the LCD for the given rational expressions, and convert each rational expression into an equalivalent rational expression with the LCD as the denominator. 3/4b^2-9,2b/2b+3,-5/2b^2-3b 1 solutions Answer 63704 by stanbon(57250)   on 2007-07-10 07:50:22 (Show Source): You can put this solution on YOUR website! Find the LCD for the given rational expressions, and convert each rational expression into an equalivalent rational expression with the LCD as the denominator. 3/4b^2-9,2b/2b+3,-5/2b^2-3b --------------------------- Factor each denominator: 4b^2-9 = (2b-3)(2b+3) 2b+3 2b^2-3b = b(2b-3) ---------------------- Form the LCD: LCD = b(2b+3)(2b-3) --------------------- Convert each fraction: 3/(4b^2-9) = [3*b]/LCD 2b/2b+3 = [2b^2(2x-3)]/LCD -5/2b^2-3b = -5(b+3)/LCD ========================= Cheers, Stan H.

Linear-equations/87804: Could you please help me understand and solve this equation? Write an equation of the line containing the given points and perpendicular to the given line express answer y=mx+b (8,9) 4x+y=9 The equation of the line is y= 1 solutions Answer 63703 by stanbon(57250)   on 2007-07-10 07:41:37 (Show Source): You can put this solution on YOUR website! Write an equation of the line containing the given points and perpendicular to the given line express answer y=mx+b (8,9) 4x+y=9 --------- The given line can be written as y = -4x+9 So it has slope = -4. -------------- Any line perpendicular to it must have slope m=1/4 --------------- Your equation will have the form y=mx+b where m=1/4, and y=9 when x=8. So 9 = (1/4)8+b 9 = 2 + b b=7 ----------- Your equation is y=(1/4)x+7 ----------------- ==================== Cheers, Stan H.

Age_Word_Problems/87802: Can you help me, please??? this is our assignment and I can't figure it out.. The question is : Henry's father is now twice as old as Henry. Sixteen years ago, he was four times as old. How old is each now? Thank you. . 1 solutions Answer 63702 by stanbon(57250)   on 2007-07-10 07:33:29 (Show Source): You can put this solution on YOUR website! Henry's father is now twice as old as Henry. Sixteen years ago, he was four times as old. How old is each now? ------------ NOW DATA: Let Henry's age be "x" ; Father is "2x". -------------- 16 yrs. ago DATA: Henry was x-16 ; Father was 2x-16 ----------------- EQUATION: Father was four times as old. 2x-16 = 4(x-16) 2x-16 = 4x-64 2x = 48 x=24 (Henry's age NOW) 2x=48 (Father's age NOW) ==================== Cheers, Stan H.

Linear-equations/87807: I think I have the answer correct on the equation, but I am not certain. Find the domain of the function p(x)=/x+9/ Answer: x/x is a real number 1 solutions Answer 63700 by stanbon(57250)   on 2007-07-10 07:24:30 (Show Source): You can put this solution on YOUR website! Correct; Domain is all Real Numbers. Cheers, Stan H.

Graphs/87779: Write the equation of the line with given slope and y-intercept. Then graph each line using the slope and y-intercept. For Problems 16, 18 and 20, refer to Examples 3 and 4 (pp 606-607) for solutions of similar problems. Since you’re given one point already (the y-intercept), you only need to find the coordinates of one additional point on the line to be able to graph the solution! Slope: -2; y-intercept: (0, 4) Slope: 5; y-intercept: (0, -2) Slope: - ; y-intercept: (0, 8) 1 solutions Answer 63671 by stanbon(57250)   on 2007-07-09 22:59:10 (Show Source): You can put this solution on YOUR website! Slope: -2; y-intercept: (0, 4) y = -2x + 4 ---------------------------------------------- Slope: 5; y-intercept: (0, -2) y = 5x -2 --------------------------------------------- Slope: -? ; y-intercept: (0, 8) y = ?x +8 ============================== Cheers Stan H.

Polynomials-and-rational-expressions/87774: Find the following product of So far i have gotten the following answer but I don't understand how to combine the like terms. My Answer: Please let me know if I am correct so far. Thank You 1 solutions Answer 63664 by stanbon(57250)   on 2007-07-09 22:04:28 (Show Source): You can put this solution on YOUR website! Find the following product of (x-2)^3 = 3C3x^3 + 3C2x^2(-2) + 3C1x(-2)^2 + 3C0(-2)^3 = x^3 -6x^2 + 12x -8 =============== Cheers Stan H.

Polynomials-and-rational-expressions/87769: How do I factor this completely? y^4Z^4-81z^4 Thank you in advance!!!!1 1 solutions Answer 63659 by stanbon(57250)   on 2007-07-09 20:55:17 (Show Source): You can put this solution on YOUR website! factor this completely? y^4Z^4-81z^4 --------- = z^4(y^4 - 81) = z^4(y^2+9)(y^2-9) = z^4(y^2+9)(y+3)(y-3) ==================== Cheers, Stan H.

Inequalities/87747: This is a tough question. Please Help. Solve x/(x – 5) < 2 1 solutions Answer 63658 by stanbon(57250)   on 2007-07-09 20:50:06 (Show Source): You can put this solution on YOUR website! Solve x/(x – 5) < 2 ------------ Rewrite as: [x/(x-5)] - 2 < 0 Rewrite with a common denominator: [x/(x-5)] - [2(x-5)/(x-5)] <0 Combine the numerators: to get: [x-2(x-5)]/(x-5) < 0 [-(x-10)]/[(x-5)] < 0 ---------------- The numerator is zero when x=10 The denominator is zero when x=5 Both of these are NOT part of the solution. -------------- Draw a number line; plot points x=5 and x=10 This breaks the number line into three intervals. --------------- Determine which interval(s) are part of the solution set: Pick a sample value from each interval and check it in the INEQUALITY, as follows: In the interval (-inf,5) pick x=0; then -(0-10)/(0-5)=-2 which is < 0 Therefore all x values in that interval are part of the solution set. --------------- In the interval (5,10) pick x = 8; then -(8-10)/(8-5)>0 Therefore no values in that interval are part of the solution set. ---------------- In the interval (10,inf) pick x=100; then -(100-10)/(100-5)<0 Therefore all x values in that interval are part of the solution set. ---------------------- Conclusion: The solution is all x-values in (-inf,5) OR (10,inf) ======================= Cheers, Stan H.

Points-lines-and-rays/87759: sketch two lines that lie in a planebut do not intercept 1 solutions Answer 63648 by stanbon(57250)   on 2007-07-09 20:22:20 (Show Source): You can put this solution on YOUR website! Draw two parallel lines. Example: railroad tracks. Cheers, Stan H.