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# Recent problems solved by 'stanbon'

stanbon answered: 57146 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, >>Next

 Complex_Numbers/88519: how do you simplfy i to the 91th power1 solutions Answer 64388 by stanbon(57214)   on 2007-07-15 20:59:45 (Show Source): You can put this solution on YOUR website!how do you simplfy i to the 91th power --------- i^4 =1 and 91 = 4(22)+3 So i^91 = i^(4*22+ 3) = i^(4*22)*i^3 = 1^22*i^3 = i^3 = -i =========== Cheers, Stan H.
 Sequences-and-series/88545: if a[1]=4 and d=-2, what are the first four terms of the arithmetic sequence?1 solutions Answer 64382 by stanbon(57214)   on 2007-07-15 19:55:10 (Show Source): You can put this solution on YOUR website!if a[1]=4 and d=-2, what are the first four terms of the arithmetic sequence? 4,4-2=2, 2-2=0, 0-2=-2 ================================== Cheers, Stan H.
 Sequences-and-series/88544: find the value of a[3] if: n=3 and a[n] =2n-3/n i dont know why the n-th numbers are not comming out right, but i think the answer is 6 can someone help with this, thanks!1 solutions Answer 64381 by stanbon(57214)   on 2007-07-15 19:51:29 (Show Source): You can put this solution on YOUR website!find the value of a[3] if: n=3 and a[n] =2n-3/n a(3) = 2*3 - 3/3 a(3) = 6-1 a(3) = 5 ============ Cheers, Stan H.
 Linear-equations/88531: Déjà vu strikes again! Problem 36 follows the trend with the equation: f(x) = 5x – 1 but complicates it by giving you the following instead of a real number (good thing Part (b) of Example 6 on p 657 does something very similar): 36) f(a – 2) 1 solutions Answer 64380 by stanbon(57214)   on 2007-07-15 19:43:54 (Show Source): You can put this solution on YOUR website!f(x) = 5x – 1 but complicates it by giving you the following instead of a real number (good thing Part (b) of Example 6 on p 657 does something very similar): 36) f(a – 2) ------------------- f(a-2) = 5(a-2)-1 =5a-11 ================= Cheers, Stan H.
 Polynomials-and-rational-expressions/88540: I am having a problems with these two problems and wondering if there was someone that could guide me on how to solve this problem. Thank you Solve the following equation for X. 2/5=X-2/20 1 solutions Answer 64379 by stanbon(57214)   on 2007-07-15 19:28:15 (Show Source): You can put this solution on YOUR website!Solve the following equation for X. 2/5=X-2/20 Multiply both sides by 20 to get of the denominators: 8 = 20x - 2 20x = 10 x=1/2 ================ Cheers, Stan H.
 logarithm/88534: This question is from textbook modeling, functiongs, and graphs How to solve 22) 2^x-1 = 8^-2x 33) write a formula y= -3+f(x-2) 48) write in logarithmic form 127= 2 (10^0.5x)- 17.3 1 solutions Answer 64376 by stanbon(57214)   on 2007-07-15 19:18:12 (Show Source): You can put this solution on YOUR website!solve 22) 2^x-1 = 8^-2x 2^(x-1) = 2^[3(-2x) 2^(x-1) = 2^-6x The exponents must be equal: x-1 = -6x 7x = 1 x = 1/7 --------------------------- 33) write a formula y= -3+f(x-2) Comment: that doesn't make any sense. ------------------ 48) write in logarithmic form 127= 2 (10^0.5x)- 17.3 144.3 = 2(10^0.5x) 72.15 = 10^0.5x Take the log of both sides to get: 0.5x = log72.15 0.5x = 1.858236... x = 3.71647... =============== Cheers, Stan H.
 Quadratic_Equations/88505: 12x^3 +7x^2-5x=0 a. solve by factoring b. what are the solutions(roots)1 solutions Answer 64349 by stanbon(57214)   on 2007-07-15 15:10:36 (Show Source): You can put this solution on YOUR website!12x^3 +7x^2-5x=0 a. solve by factoring x(12x^2+7x-5) = 0 b. what are the solutions(roots) x=0 is a root 12x^2+7x-5 = 0 x= [-7+-sqrt(49-4*12*-5)]/24 x= [-7+-sqrt289]/24 x= [[-7+-17]/24 x= -1 or x= 5/12 ================== Cheers, Stan H.
 Inequalities/88504: x/2-2(x-3) > 11 solutions Answer 64348 by stanbon(57214)   on 2007-07-15 15:00:28 (Show Source): You can put this solution on YOUR website!x/2-2(x-3) > 1 Multiply thru by 2 to get: x - 4(x-3) > 2 x-4x+12 >2 -3x > -10 x<10/3 ====================================== Cheers, Stan H.
 Equations/88503: find the value of c such that the graph of 3x+c=5y has an intercept of (-4,0)1 solutions Answer 64346 by stanbon(57214)   on 2007-07-15 14:53:40 (Show Source): You can put this solution on YOUR website!find the value of c such that the graph of 3x+c=5y has an intercept of (-4,0) -------------- 3*-12+c = 5*0 -36+c=0 c=36 ================ Cheers, Stan H.
 Equations/88502: write the equation of the line parallel to the y-axis that passes thru 2,51 solutions Answer 64345 by stanbon(57214)   on 2007-07-15 14:49:27 (Show Source): You can put this solution on YOUR website!x=2 is a vertical line parallel to the y-axis. Cheers, Stan H.
 Inequalities/88500: Zoning laws in Harrington prohibit displaying signs with areas exceeding 12 square ft. If Flo's Marina is ordering a triangular sigh with an 8 foot base, how tall can the sign be? Define the variable, write an inequality and solve1 solutions Answer 64344 by stanbon(57214)   on 2007-07-15 14:47:04 (Show Source): You can put this solution on YOUR website!Zoning laws in Harrington prohibit displaying signs with areas exceeding 12 square ft. If Flo's Marina is ordering a triangular sigh with an 8 foot base, how tall can the sign be? -------------- Area = (1/2)(base)(height) 12 + (1/2)*8*h h = 24/8= 3 feet ===================== Cheers, Stan H.
 Polynomials-and-rational-expressions/88498: Hello, Here is what I am currently working on and I am not sure if I am doing this right. Thank you for your help Given that either 2 or -2 is a solution to each of the following, solve each equation x^3-2x^2-6x+12=0 This is what I have done 2/1 -2 -6 -12 /- 2 0 0 ----------- 1 0 0 0 2 is a solution -2 is not a solution How do I solve the equation? Thank you 1 solutions Answer 64342 by stanbon(57214)   on 2007-07-15 14:43:14 (Show Source): You can put this solution on YOUR website!Given that either 2 or -2 is a solution to each of the following, solve each equation x^3-2x^2-6x+12=0 2/....1.... -2.... -6....+12 ...............2......0.....-12 ........1......0......-6..|..0 =============== Remainder is zero, so x=2 is a zero. Quotient is x^2-6 Other zeroes are +sqrt6 and -sqrt6 ============ Cheers, Stan H.
 logarithm/88497: 2. For the given equation log base y (x-1)+ log base y ( x^2+x+1)= 1 A) solve for y. B)Let y= f(x)and find f^-1 (x) Thank you1 solutions Answer 64340 by stanbon(57214)   on 2007-07-15 14:33:54 (Show Source): You can put this solution on YOUR website!2. For the given equation log base y (x-1)+ log base y ( x^2+x+1)= 1 A) solve for y. = log(base y) (x-1)(x^2+x+1) = 1 y = (x-1)(x^2+x+1) y = x^3+x^2-x^2+x-x-1 = x^3-1 ---------------- B)Let y= f(x)and find f^-1 (x) y = x^3-1 Interchange x and y to get x = y^3-1 Sove for y as follows: y^3=x+1 y = (x+1)^(1/3) That is f^-1(x) ================ Cheers, Stan H.
 logarithm/88476: USe the properties of logarithms to expand log2 x^4(x + 3). I don't get this at all. I need some major help!1 solutions Answer 64330 by stanbon(57214)   on 2007-07-15 11:32:28 (Show Source): You can put this solution on YOUR website!expand log2 x^4(x + 3). = log2(x^4) + log2(x+3) = 4log2(x) + log2(x+3) ============== Cheers, Stan H.
 Equations/88486: This question is from textbook Elementary Algebra I am having trouble with Equations, Iequalities, and Problem Solving can you help? please. 2x + 7 + 3x = 321 solutions Answer 64329 by stanbon(57214)   on 2007-07-15 11:29:25 (Show Source): You can put this solution on YOUR website!2x + 7 + 3x = 32 Add the "like" terms to get: 5x + 7 = 32 Subtract 7 from both sides to get 5x = 25 Divide both sides by 5 to get: x = 5 ============ Cheers, Stan H.
 Geometry_Word_Problems/88464: the total measure of two sides of a triangle is less than 90.the third angle is more than the sum of the measures of first two angles.what will be the measure of each angle.1 solutions Answer 64315 by stanbon(57214)   on 2007-07-14 22:53:46 (Show Source): You can put this solution on YOUR website!the total measure of two sides of a triangle is less than 90.the third angle is more than the sum of the measures of first two angles.what will be the measure of each angle. --------- a+b<90 C>A+B --------- There is not enough information to proceed. Cheers, Stan H.
 expressions/88458: Good day to all,I need some help with some problems,the first one is,Simplify:x(4x^2+3x-5)-2(4-x^2).The next one is,Find the product:(b+2)(b+6).The third one is,Find the product:(7x+1)(x^2+1).And the last one is,Find the product:(2x+6)(x-10).Thanks to whoever can help me.1 solutions Answer 64313 by stanbon(57214)   on 2007-07-14 22:47:59 (Show Source): You can put this solution on YOUR website!some problems,the first one is,Simplify:x(4x^2+3x-5)-2(4-x^2). = 4x^3+3x^2-5x-8+2x^2 = 4x^2 + 5x^2 -5x -8 --------------------------- The next one is,Find the product:(b+2)(b+6). (b+2)(b+6) = b(b+6)+2(b+6) = b^2+6b+2b+12 = b^2+8b+12 --------------------------- The third one is,Find the product:(7x+1)(x^2+1). = 7x(x^2+1) + 1(x^2+1) = 7x^3+7x+x^2+1 = 7x^3+x^2+7x+1 ------------------ And the last one is,Find the product:(2x+6)(x-10). = 2x(x-10)+6(x-10) = 2x^2-20x+6x-10 = -2x^2-14x-10 -------------------------- Cheers, Stan H.
 Linear-equations/88462: solve the system by addition -3x+7y=2 x+2y=-181 solutions Answer 64312 by stanbon(57214)   on 2007-07-14 22:26:04 (Show Source): You can put this solution on YOUR website!-3x+7y=2 x+2y=-18 ---------- Multiply thru the 2nd equation by 3 to get: 3x+6y=-54 Add that to the 1st equation to get rid of the x terms: 13y = -52 y = -4 ---------- Substitute that value of y into x+2y=18 to solve for x: x - 8 = -18 x = -10 --------------- Check the answers in -3x+7y=2 30-28=2 2 = 2 ================= Cheers, Stan H
 Numbers_Word_Problems/88463: The perimeter of a rectangle is 3 more than three times its width.Find the length and width of the rectangle.1 solutions Answer 64310 by stanbon(57214)   on 2007-07-14 22:19:10 (Show Source): You can put this solution on YOUR website!The perimeter of a rectangle is 3 more than three times its width. Find the length and width of the rectangle. ---------------- Let the width be "x". Perimeter = 3x+3 --------------------- Perimeter = 2*length + 2*width 3x+3 = 2*length + 2*x 2*length = x+3 length = (1/2)(x+3 width = x ================== Cheers, Stan H.
 Percentage-and-ratio-word-problems/88440: A woman has an estate of \$10,000. She leaves 2/5 to a charity. Of the remainder, 2/3 goes to her son. How much does her son get?1 solutions Answer 64300 by stanbon(57214)   on 2007-07-14 19:23:44 (Show Source): You can put this solution on YOUR website!A woman has an estate of \$10,000. She leaves 2/5 to a charity. Of the remainder, 2/3 goes to her son. How much does her son get? --------------- 1 - 2/5 -(2/3)(3/5) = (15/15) - (6/15) - (6/15) = 3/15 = 1/5 ---------- (1/5)*10,000 = \$2000 (amt. her son gets) ============================= Cheers, Stan H.
 Percentage-and-ratio-word-problems/88441: At one Kennel, 11/18 of the dogs are small, 1/9 are medium size, and the rest are large. What fraction of the dogs are large?1 solutions Answer 64298 by stanbon(57214)   on 2007-07-14 19:19:05 (Show Source): You can put this solution on YOUR website!At one Kennel, 11/18 of the dogs are small, 1/9 are medium size, and the rest are large. What fraction of the dogs are large? -------------- 1 - (11/18) - (2/18) = (18/18) - (11/18) - (2/18) = 5/18 of the dogs are large =========== Cheers, Stan H.
 Quadratic_Equations/88446: I cannot figure out how to solve this quadratic equation. Solve for x: 2x^2 + 3bx + b^2 = 0 Thank you, Melody Salzer1 solutions Answer 64296 by stanbon(57214)   on 2007-07-14 19:15:41 (Show Source): You can put this solution on YOUR website!Solve for x: 2x^2 + 3bx + b^2 = 0 ------------ Use the quadratic formula to get: x = [-3b+-sqrt(9b^2-4*2*b^2)]/4 x = [-3b +-sqrt(b^2)]/4 x = [-3b+-b]/4 x = -b or x = -b/2 ================== Cheers, Stan H.
 Sequences-and-series/88447: What is the sum of the first 50 natural numbers?1 solutions Answer 64294 by stanbon(57214)   on 2007-07-14 19:11:19 (Show Source): You can put this solution on YOUR website!What is the sum of the first 50 natural numbers? ----------- This is a arithmetic sequence. Formula for the sum of n terms. S(n) = (n/2)(first + last) Your Problem: S(50) = (50)/2(1+50) S(50) = 25*51 = 1275 ============== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/88433: A girl buys three apples and seven oranges for \$4.56. If an orange costs \$0.28 more than an apple, how much does each fruit cost?1 solutions Answer 64282 by stanbon(57214)   on 2007-07-14 16:29:41 (Show Source): You can put this solution on YOUR website!A girl buys three apples and seven oranges for \$4.56. If an orange costs \$0.28 more than an apple, how much does each fruit cost? ---------- # of apples is 3; price per apple is x cents ; value of three apples = 3x cents # of oranges is 7; price per orange is "x+28"; value of oranges = 7x+196 cents ------------ EQUATION: value + value = 456 cents 3x + 7x+196 = 456 10x = 260 x = 26 cents (price of an apple) x+28 = 54 cents (price of an orange) ================ Cheers, Stan H.
 Polynomials-and-rational-expressions/88435: Hello, I am having diffuclties understanding this problem. Find all real and imaginary zeros for each polynomial factor. f(x) = 2x^2-1=0 Here is the work that I have started with but I am unsure if I am doing this properly 2x^2-1=0 +1 = +1 2x^2=1 ------ 2 x^2=1/2 would my answer be x= square root of +1/2 and square root of -1/2? Thank you for your help1 solutions Answer 64281 by stanbon(57214)   on 2007-07-14 16:20:32 (Show Source): You can put this solution on YOUR website!Find all real and imaginary zeros for each polynomial factor. f(x) = 2x^2-1=0 2x^2-1=0 2x^2 = 1 x^2 = 1/2 x = sqrt(1/2) or x = -sqrt(1/2) x = (sqrt2/20 or x = (-sqrt2)/2 =========== Cheers, Stan H.
 Polynomials-and-rational-expressions/88436: I am having some difficulties with this problem Find all real and imaginary zeros for each polynomial function f(x)=5 Since there are no other portions of the problem are all real and imaginary zeros 5 and -5? I am very confused by this problem. Thank you for your help. 1 solutions Answer 64280 by stanbon(57214)   on 2007-07-14 16:17:11 (Show Source): You can put this solution on YOUR website!Find all real and imaginary zeros for each polynomial function f(x)=5 ----------- It has no real and no imaginary zeroes. No matter what you try y=5: never zero. ============== Cheers, stan H.
 Polynomials-and-rational-expressions/88437: Hello I am working with the Descartes rule of signs. I am supposed to discuss the possibilities for the roots of the equation. Do not solve the equation. THE EQUATION IS x^5+x^3+5x=0 Here is my answer Pos: 3......0 Neg: 0......3 Imag: Am I even close on this problem? Thank you1 solutions Answer 64279 by stanbon(57214)   on 2007-07-14 16:15:04 (Show Source): You can put this solution on YOUR website!discuss the possibilities for the roots of the equation. Do not solve the equation. THE EQUATION IS x^5+x^3+5x=0 --------- # of changes of sign for f(x) is zero # of positive roots = zero --------- f(-x)=-x^5-x^3-5x # of changes of sign of f(-x) is zero # of negative roots = 0 The equation can be written as x(x^4+x^2+5)=0 So, it has a zero at x=0. The remaining four roots are imaginary. ============== Cheers, Stan H.
 Radicals/88438: 3square of 27 + square root of 8 - 2square root of 751 solutions Answer 64278 by stanbon(57214)   on 2007-07-14 16:02:34 (Show Source): You can put this solution on YOUR website!3square of 27 + square root of 8 - 2square root of 75 --------------- cube rt of 27 + sqrt8 - 2sqrt75 =3 + 2sqrt2 -2*5sqrt3 =3 +2sqrt2 - 10sqrt3 ================ Cheers, Stan H.
 test/88432: 8x . x^2-4 ____ _____ = 3x-6 2x+4 Please help solve this, i already know the answer, I need an explanation!1 solutions Answer 64275 by stanbon(57214)   on 2007-07-14 14:15:33 (Show Source): You can put this solution on YOUR website!8x . x^2-4 ____ _____ = 3x-6 2x+4 ---------------- [8x/(3(x-2))] * [(x-2)(x+2)/2(x+2)] Cancel the (x+2) factors to get = [8x/(3(x-2))] * [(x-2)/2] Cancel the (x-2) factors to get: = [8x/(3)] * [1/2] Cancel the "2" factors to get: = 4x/3 Cheers, Stan H.
 Polynomials-and-rational-expressions/88430: Hi, I'm trying to understand the topic of Degree of polynomials but I don't quite get it, and I'm stuck in this problem, how can I determine the degree of this polynomial? 8x3 + 6x2y + 4xy3 - 2y4 1 solutions Answer 64272 by stanbon(57214)   on 2007-07-14 13:38:22 (Show Source): You can put this solution on YOUR website!For polynomials in two or more variables, the degree of a term is the sum of the exponents of the variables in the term; the degree of the polynomial is again the maximum of the degrees of all terms in the polynomial. For example, the polynomial x^2y^2 + 3x^3 + 4y has degree 4, the same degree as the term x^2y^2. However, a polynomial in variables x and y, is a polynomial in x with coefficients which are polynomials in y, and also a polynomial in y with coefficients which are polynomials in x. x^2y^2 + 3x^3 + 4y = (3)x^3 + (y^2)x^2 + (4y) = (x^2)y^2 + (4)y + (3x^3) This polynomial has degree 3 in x and degree 2 in y. ----------------- Your Problem: 8x^3 + 6x^2y + 4xy^3 - 2y^4 has degree 4 As a polynomial in y it has degree 4 As a polynomial in x it has degree 3 ============== Cheers, Stan H.
 Linear-equations/88426: This question is from textbook What is a super imposed line and what are unique solutions?1 solutions Answer 64271 by stanbon(57214)   on 2007-07-14 13:30:35 (Show Source): You can put this solution on YOUR website!What is a super imposed line and what are unique solutions? If you have a system of two linear equations that are really the same equation the two graphs will be two lines, one superimposed on the other, and the solution for the system of equations will be the set of all points on the line. ----------- If you have a system of two linear equations that have different line graphs and those lines are not parallel, the solution for the system will be the unique point of intersection of the two lines. =============== Cheers, Stan H.