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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/175170: what is the remainder when d^4+2d^2+5d-10 is divided by d+4?1 solutions Answer 130253 by stanbon(57214)   on 2009-01-05 22:48:06 (Show Source): You can put this solution on YOUR website!what is the remainder when d^4+2d^2+5d-10 is divided by d+4? -------------------------------------- Find f(-4) or use synthetic division to find the remainder. ----------------------------- -4)....1....0....2....5....-10 ........1....-4...18...-67...|..258 Remainder: 258 ====================================================== Cheers, Stan H.
 Average/175173: I am in desperate need of understanding Algebra. Would you please help me!? 1). Factor Out the GCF in this expression: 〖15x〗^2 y^2-〖9xy〗^2+〖6x〗^2 y 2). Use grouping to factor each Polynomial completely: x^3+ax+3a+〖3a〗^2 3). Factor this polinomial. If it is prime, please tell me. 18z + 45 + z^2 the same with the next one: 4). 〖3x〗^3 y^2-〖3x〗^2 y^2+〖3xy〗^2 Thank you so much! 1 solutions Answer 130251 by stanbon(57214)   on 2009-01-05 22:40:08 (Show Source): You can put this solution on YOUR website!1). Factor Out the GCF in this expression: 〖15x〗^2 y^2-〖9xy〗^2+〖6x〗^2 y 2). Use grouping to factor each Polynomial completely: x^3+ax+3a+〖3a〗^2 3). Factor this polinomial. If it is prime, please tell me. 18z + 45 + z^2 the same with the next one: 4). 〖3x〗^3 y^2-〖3x〗^2 y^2+〖3xy〗^2 -------------------------------------- your posting is very confusing. Cheers, Stan H.
 Equations/175175: 8r - r/3 = 461 solutions Answer 130250 by stanbon(57214)   on 2009-01-05 22:27:49 (Show Source): You can put this solution on YOUR website!8r - r/3 = 46 24r - r = 138 23r = 138 r = 6 ================= Cheers, Stan H.
 expressions/175176: dp __ d+p d=8 and p=11 solutions Answer 130249 by stanbon(57214)   on 2009-01-05 22:22:37 (Show Source): You can put this solution on YOUR website!dp __ d+p d=8 and p=1 --------------------- (8*1)/(8+1) = 8/9 =============================================== Cheers, Stan H.
 Numbers_Word_Problems/175177: Totally confused on this word problem: The number of people infected after t days is P=200 +5t - t^2. Find the number of days until the number of people infected is 176. Can someone PLEASE help? I don't even know where to begin?1 solutions Answer 130248 by stanbon(57214)   on 2009-01-05 22:18:37 (Show Source): You can put this solution on YOUR website!The number of people infected after t days is P=200 +5t - t^2. Find the number of days until the number of people infected is 176. --------------------------------- 200 +5t - t^2 = 176 t^2 - 5t - 200 + 176 = 0 t^2 -5t - 24 = 0 Factor: (t-8)(t+3) = 0 t = 8 (# of days till 176 people are infected) ================================================ Cheers, Stan H.
 Quadratic-relations-and-conic-sections/175155: This question is from textbook In 1940, Emanual Zacchini of Italy was fired record distance of 175 feet from a cannon while performing in the untied states. Suppose his intial upward velocity was 80 feet per second. The height y can be represented by the function y=80x-16x^2, where x represents the number of seconds that have passed. a) Draw the graph of the function, relating heights Mr. Zacchini reaches to the time after he was shot from the cannon. b) How long after he was shot out of the cannon did he reach his maximum height? What was the height? 1 solutions Answer 130234 by stanbon(57214)   on 2009-01-05 20:59:57 (Show Source): You can put this solution on YOUR website!In 1940, Emanual Zacchini of Italy was fired record distance of 175 feet from a cannon while performing in the untied states. Suppose his intial upward velocity was 80 feet per second. The height y can be represented by the function y=80x-16x^2, where x represents the number of seconds that have passed. a) Draw the graph of the function, relating heights Mr. Zacchini reaches to the time after he was shot from the cannon. ------------------------------------------------------------ b) How long after he was shot out of the cannon did he reach his maximum height? maximum occurs at x = -b/2a = -80/-32 = 2.5 seconds ------------- What was the height? h(2.5) = 80*2.5 - 16(2.5)^2 = 100 ft. ============================================= Cheers, Stan H.
 Age_Word_Problems/175156: Find two consecutive integers such that four times the larger exceeds three times the smaller by 23. 1 solutions Answer 130229 by stanbon(57214)   on 2009-01-05 20:48:28 (Show Source): You can put this solution on YOUR website!Find two consecutive integers such that four times the larger exceeds three times the smaller by 23. ----------------------- 1st "x" 2nd "x+1" --------------------------- Equation: 4(x+1) - 3x = 23 x = 19 (1st) x+1 = 20 (2nd) ============================ Cheers, Stan H.
 Rational-functions/175153: how do I solve log(base6)60-log(base6)30?1 solutions Answer 130224 by stanbon(57214)   on 2009-01-05 20:43:20 (Show Source): You can put this solution on YOUR website!how do I solve log(base6)60-log(base6)30 ------------------- = [log(60)/log(6)] - [log(30)/log(6)] = [log(60)-log(30)]/log(6) = [log(60/30)]/log6 = log(2)/log(6) = 0.38685... ========================= Cheers, Stan H.
 Rational-functions/175151: how do I find y=log(base 3)243?1 solutions Answer 130218 by stanbon(57214)   on 2009-01-05 20:35:57 (Show Source): You can put this solution on YOUR website! how do I find y=log(base 3)243 ---------------- y=log(base 3)243 y = log(base 3) 3^5 y = 5log(base 3) 3 y = 5*1 y = 5 ======================================= Cheers, Stan H.
 Rational-functions/175150: what is the value of log10,6.85 to the nearest ten thousandth?1 solutions Answer 130212 by stanbon(57214)   on 2009-01-05 20:29:48 (Show Source): You can put this solution on YOUR website!the value of log10,6.85 log(base 10) 6.85 = 0.835691.... ==================================== Cheers, Stan H.
 Rational-functions/175145: what is log10,100?1 solutions Answer 130210 by stanbon(57214)   on 2009-01-05 20:25:58 (Show Source): You can put this solution on YOUR website!what is log10,100 ------------------------ If you mean log(base 10) 100, the answer is 2 ------------ If you mean log(10,100) the answer is 4.00432.... Cheers, Stan H.
 Linear-systems/175131: I need help with the following - Find the shortest distance from the point (3,1) to the line 3x+y=-2 to the nearest tenth.1 solutions Answer 130207 by stanbon(57214)   on 2009-01-05 20:22:55 (Show Source): You can put this solution on YOUR website!I need help with the following - Find the shortest distance from the point (3,1) to the line 3x+y=-2 to the nearest tenth. ----------------------- Draw the picture. Find the equation of the line perpendicular to the given line and passing thru (3,1) --------------- slope of the given line: -3 slope of the perpendicular line: 1/3 intercept for this line: 1 = (1/3)3 + b b = 0 Equation of the perpendicular line: y = (1/3)x --------------------------------- intercept of the given line and the perpendicular line: y = (1/3)x y = -3x-2 --------------- Substitute to solve for "x": (1/3)x = -3x-2 ; (8/3)x=-2;x =-3/4 Since y = (1/3)x y = (1/3)(-3/4) = -1/4 ------ So the intercept point is (-3/4,1/4) ------------------- Find the distance from (-3/4,-1/4) t0 (3,1) distance = sqrt[(1--1/4)^2 + (3--3/4)^2] = sqrt[(25/16) + (225/16)] = sqrt[250/16] = (5/4)sqrt(10) ============================================ Cheers, Stan H.
 Linear-equations/175130: This question is from textbook select any two points on the line (0,2)and(1,4)1 solutions Answer 130202 by stanbon(57214)   on 2009-01-05 19:58:49 (Show Source): You can put this solution on YOUR website!select any two points on the line (0,2)and(1,4) ------------------ slope = (4-2)/(1-0) = 2 intercept: (0,2) ---------- Equation: y = 2x + 2 ----------- Points: (1,4); (3,8) ========================== Cheers, Stan H.
 Mixture_Word_Problems/175123: How many millimeters of water must be evaporate from 160mL of a 20% iodine solution to make it a 40% iodine solution?1 solutions Answer 130201 by stanbon(57214)   on 2009-01-05 19:55:53 (Show Source): You can put this solution on YOUR website!How many millimeters of water must be evaporate from 160mL of a 20% iodine solution to make it a 40% iodine solution? ----------------------- iodine = iodine 0.2(160mL) = 0.4(160-x) 2(160) = 4(160-x) 4x = 2(160) x = 80 mL(amount of water that must be evaporated) --------------- Cheers, Stan H.
 Percentage-and-ratio-word-problems/175124: This question is from textbook write the percent as a fraction. simplify if possible 19.68% please tell me what u do so i can understand 1 solutions Answer 130200 by stanbon(57214)   on 2009-01-05 19:37:43 (Show Source): You can put this solution on YOUR website!write the percent as a fraction. simplify if possible 19.68% ----------- The % symbol means 1/100 ----------- 19.68% = 19.68(1/100) = 0.1968 = 1968/10,000 ==================================== Cheers, Stan H.
 test/175116: i have a problem with a review sheet that iam doing for my mid term here is the question multi-step problem consider some rectangles with a perimeter of 24 inches copy and complete the table the table has columns and there is 4 colums across and 7 down and from left to right it says width(in.), perimeter(in.), length(in.), and area(in.2) 1 solutions Answer 130199 by stanbon(57214)   on 2009-01-05 19:34:26 (Show Source): You can put this solution on YOUR website!i have a problem with a review sheet that i am doing for my mid term here is the question multi-step problem consider some rectangles with a perimeter of 24 inches copy and complete the table the table has columns and there is 4 columns across and 7 down and from left to right it says width(in.), perimeter(in.), length(in.), and area(in.2) ------------------------------------ Put a number in for length; the other columns values can be derived ----------------- Example: Let L = 4,perimeter=24,so W = [(24-2*4)/2] = 8,and area = 32 sq in Let L = 5,perimeter = 24,so W = [(24-2*5)/2]=6, and area = 30 sq in --- Do this for seven values of L. Cheers, Stan H.
 Linear-equations/175088: This question is from textbook Find the slope of the line at passes through (3,6) and (1,-4).1 solutions Answer 130182 by stanbon(57214)   on 2009-01-05 16:42:37 (Show Source): You can put this solution on YOUR website!Find the slope of the line at passes through (3,6) and (1,-4). ---------------------- slope = (6--4)/(3-1) = 10/2 = 5 ================================== Cheers, Stan H.
 Systems-of-equations/175082: solve the system 4x+2y=4 6x-8=-2y1 solutions Answer 130179 by stanbon(57214)   on 2009-01-05 16:19:03 (Show Source): You can put this solution on YOUR website!solve the system 4x+2y=4 6x-8=-2y ------------------------- Rearrange: 4x + 2y = 4 6x + 2y = 8 --------------- Subtract 1st from 2nd and solve for "x": 2x = 4 x = 2 --------------- Substitute to solve for "y": 4*2 + 2y = 4 2y = -4 y = -2 ==================== Cheers, Stan H.
 Linear-equations/175085: This question is from textbook The profits made by Happenin'Hats depend on the number of hats they sell. If the company's weekly expenses are \$2250 and they charge \$45 per hat,their profits "p" can be calculated by the equation: p=45n-2250,where "n" is the number of hats sold. Write this relation in functional notation.1 solutions Answer 130178 by stanbon(57214)   on 2009-01-05 16:11:44 (Show Source): You can put this solution on YOUR website!p(n) = 45n-2250 =================== Cheers, Stan H.
 Systems-of-equations/175083: solve the system x+2y=10 x+Y=61 solutions Answer 130177 by stanbon(57214)   on 2009-01-05 16:00:11 (Show Source): You can put this solution on YOUR website!solve the system x+2y=10 x+Y=6 --------- Subtract 2nd from 1st and solve for "y": y = 4 Since x+y=6 , x = 2 ================== Cheers, Stan H.
 Systems-of-equations/175084: solution to the system of inequalities y<3x-1 Y>|x-2|1 solutions Answer 130176 by stanbon(57214)   on 2009-01-05 15:56:34 (Show Source): You can put this solution on YOUR website!solution to the system of inequalities y<3x-1 Y>|x-2| ------------- Graph y = 3x-1 with a dashed line; shade the half-plane below that line. ------------- Graph y = |x-2| with a dashed "curve"; shade the area above the "curve". -------------- The solution set is the intersection of those two half-planes. --------------- =================== Cheers, Stan H.
 Expressions-with-variables/175058: can you please help me solve: ((( (x-3/2)^3 x (1/x-3)^2 )))1 solutions Answer 130174 by stanbon(57214)   on 2009-01-05 15:45:31 (Show Source): You can put this solution on YOUR website!(x-3/2)^3 x (1/x-3)^2 [(2x-3)/2]^3 x [(1-3x)/x]^2 = (1/8)[(2x)^3 - 3(2x)^2(3) + 3(2x)(3)^2 - (3)^3][(1/x)^3(1^3 -3(3x)+3(3x)^2-(3x)^3] etc. ============ Cheers, Stan H.
 Numeric_Fractions/175074: Mr.Lucero's cornbread recipe calls for 3 cups of cornmeal. He puts in 1 2/3 cups from one open bag and 2/3 cup from another open bag. How many cups of cormeal does Mr. Lucero need to add when he opens a third bag.1 solutions Answer 130173 by stanbon(57214)   on 2009-01-05 15:29:09 (Show Source): You can put this solution on YOUR website!Mr.Lucero's cornbread recipe calls for 3 cups of cornmeal. He puts in 1 2/3 cups from one open bag and 2/3 cup from another open bag. How many cups of cormeal does Mr. Lucero need to add when he opens a third bag. ----------------------------------------- 3 - (5/3 + 2/3) = 3 - 7/3 = 2/3 cups needed. ========================================= Cheers, Stan H.
 Finance/175079: Your grades on five math tests are 95,86,79,88,83. What grad do you need on the sixth test to have an average of 90%.1 solutions Answer 130172 by stanbon(57214)   on 2009-01-05 15:25:29 (Show Source): You can put this solution on YOUR website!Your grades on five math tests are 95,86,79,88,83. What grade do you need on the sixth test to have an average of 90%. -------------------- Let the grade on the 6th test be "x". EQUATION: (95+86+79+88 + 83 + x)/6 = 90 431 + x = 540 x = 109 ----------- You would need a grade of 109 on the 6th test. Cheers, Stan H.
 Travel_Word_Problems/175078: 'Jim rollerbladed the first 1,600 meters in 3 minutes. How long would it take him to rollerblade 10,000 meters?' I'm not sure if I did any of this correctly, so a step by step would be usefull, thanks.1 solutions Answer 130169 by stanbon(57214)   on 2009-01-05 15:05:21 (Show Source): You can put this solution on YOUR website!'Jim rollerbladed the first 1,600 meters in 3 minutes. How long would it take him to rollerblade 10,000 meters? ------------------------------- x/10,000 = 3/1600 x = (3/1600)*10,000 x = 18.75 minutes ============================ Cheers, Stan H.
 Divisibility_and_Prime_Numbers/175075: _ x _ x _ = 4897 The numbers must be prime numbers. You cannot use a number more than once.1 solutions Answer 130167 by stanbon(57214)   on 2009-01-05 15:00:10 (Show Source): You can put this solution on YOUR website!_ x _ x _ = 4897 The numbers must be prime numbers. ----------- Procedure: 1st take the square root of 4897 to determine the highest possible factor. sqrt(4897) is around 69. 2nd Divide by primes that are less than 69 like 67,61, etc: Results: 4897/59 = 83 3rd look for factors of 83 sqrt(83) is around 9 4th 7 and 3 are not factors of 83 -------------------- Conclusion: 4897 = 59*83 ============================== Cheers, Stan H.
 Radicals/175026: For which value(s) of k will the roots of 4x^2 + kx + 1 = 0 be real and unequal?1 solutions Answer 130126 by stanbon(57214)   on 2009-01-04 22:20:43 (Show Source): You can put this solution on YOUR website!For which value(s) of k will the roots of 4x^2 + kx + 1 = 0 be real and unequal? -------------------------- determinant = k^2 - 4*4*1 = k^2-16 --------------------------------------- To have real and unequal roots the determinant must be > 0. k^2-16 > 0 k^2 > 16 k > 4 or k < -4 ======================== Cheers, Stan H.
 Radicals/175027: For which value of k will the roots of 2x^2 + kx + 1 = 0 be real?1 solutions Answer 130125 by stanbon(57214)   on 2009-01-04 22:15:06 (Show Source): You can put this solution on YOUR website!For which value of k will the roots of 2x^2 + kx + 1 = 0 be real? ------------------------ determinant = k^2 - 4*2*1 = k^2-8 ------------------------------- For the roots to be Real the determinant must be non-negative: k^2-8 >= 0 k^2 >= 8 k >= 2sqrt(2) or k <= -2sqrt(2) ===================================== Cheers, Stan H.
 Quadratic_Equations/175029: Solve the equation and express its roots in simplest a + bi form: 2(x-3) = - 5 divided by x 1 solutions Answer 130122 by stanbon(57214)   on 2009-01-04 22:10:28 (Show Source): You can put this solution on YOUR website!2(x-3) = - 5 divided by x ------ 2x-6 = -5/x 2x^2 - 6x + 5 = 0 x = [6 +- sqrt(36 - 4*2*5)]/4 x = [6 +- sqrt(76)]/4 x = [6 + 2isqrt(19)]/4 or x = [6 + 2isqrt(19)]/4 x = (3/2) + (1/2)isqrt(19) or x = (3/2) - (1/2)isqrt(19) =============================== Cheers, Stan H.
 Mixture_Word_Problems/175008: Debbie traveled by boat 5 miles upstream to fish in her favorite spot. Because of the 4-mph current, it took her 20 minutes longer to get there than to return. How fast will her boat go in still water?1 solutions Answer 130104 by stanbon(57214)   on 2009-01-04 20:17:20 (Show Source): You can put this solution on YOUR website!Debbie traveled by boat 5 miles upstream to fish in her favorite spot. Because of the 4-mph current, it took her 20 minutes longer to get there than to return. How fast will her boat go in still water? ------------------------------------------------------ Upstream DATA: distance = 5 miles; rate = b-4 mph ; time = d/r = 5/(b-4) hrs ---------------------------------------------------------------------- Downstream DATA: distance = 5 miles; rate = b+4 mph ; time = 5/(b+4) hrs. ---------------------------------------------------------------------- Equation: uptime - downtime = 1/3 hr 5/(b-4) - 5/(b+4) = 1/3 5(b+4) - 5(b-4) = (1/3)(b^2-16) 40 = (1/3)(b^2-16) b^2 - 16 = 120 b^2 = 136 --- Positive solution: b = 11.66 mph (boat speed in quiet water) ============================== Cheers, Stan H.
 Percentage-and-ratio-word-problems/175012: There are 357 seniors in Harris High School. The ratio of boys to girls is 7:10. How many boys are in the senior class?1 solutions Answer 130103 by stanbon(57214)   on 2009-01-04 19:53:56 (Show Source): You can put this solution on YOUR website!There are 357 seniors in Harris High School. The ratio of boys to girls is 7:10. How many boys are in the senior class? -------------------- 7:10 is the same as 7x:10x where 7x represents the number of boys. -------------------- Equation: 7x + 10x = 357 17x = 357 x = 21 Then 7x = 147 (# of boys) ========================================== Cheers, Stan H. ===================================== Cheers, Stan H.