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# Recent problems solved by 'stanbon'

stanbon answered: 57214 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 , 57210..57239, >>Next

 Equations/644579: write an equation in slope-intercept form for a line with a slope of -4 and y-intercept of 9.1 solutions Answer 405146 by stanbon(57282)   on 2012-09-02 16:16:56 (Show Source): You can put this solution on YOUR website!write an equation in slope-intercept form for a line with a slope of -4 and y-intercept of 9. ------- y = mx + b m is the slope = -4 b is the y-intercept = 9 ------- y = -4x + 9 ======================= Cheers, Stan H.
 Travel_Word_Problems/644568: Can you show me the steps to solving this and how to set up an equation to solve it? Sarah and John are driving in opposite direction on a straight road. John is driving fifteen miles per hour faster than Sarah. After three hours they are 375 miles apart. How fast were Sarah and John traveling?1 solutions Answer 405141 by stanbon(57282)   on 2012-09-02 16:13:43 (Show Source): You can put this solution on YOUR website!Sarah and John are driving in opposite direction on a straight road. John is driving fifteen miles per hour faster than Sarah. After three hours they are 375 miles apart. How fast were Sarah and John traveling? ---- You want to solve for "rate". ---- Sarah DATA: rate = x mph ; time = 3 hours ; distance = 3x miles -------------- John DATA: rate = x+15 mph ; time = 3 hours ; distance = 3(x+15) miles ------------------------- Equation: distance + distance = 375 miles 3x + 3(x+15) = 375 3x + 3x + 45 = 375 6x = 330 x = 55 mph (Sarah's rate) x+15 = 70 mph (John's rate) ========================== Cheers, Stan H. ===============
 Trigonometry-basics/644572: List the domain and range. Is it a function? {(3,6);(5,6);(4,6);(-3,6)}1 solutions Answer 405136 by stanbon(57282)   on 2012-09-02 15:59:38 (Show Source): You can put this solution on YOUR website!List the domain and range. Is it a function? {(3,6);(5,6);(4,6);(-3,6)} --- Yes, it is a function. ------------ Domain: {3,5,4,-3} Range: {6} Cheers, Stan H.
 Trigonometry-basics/644571: List domain and range. Is it a function? {(2,0);(-2,1);(2,3);(3,3)}1 solutions Answer 405133 by stanbon(57282)   on 2012-09-02 15:53:39 (Show Source): You can put this solution on YOUR website!List domain and range. Is it a function? {(2,0);(-2,1);(2,3);(3,3)} ------- Not a function because 2 has two correspondiing y-values. ----- Domain: {2,-2,3} Range: {0,1,3} ======================== Cheers, Stan H. ====================
 Radicals/644563: Hello! I have been working on simplifying radical expressions and I have been stumped on one question. That question is.... (4√6x)(2√18x) I have tried: 8√108x(squared) 8√36x times √3x 48 √x times √3x The real answer is: 48x√3 but I am really confused as to how to get that answer. Thanks so much for your time!1 solutions Answer 405128 by stanbon(57282)   on 2012-09-02 15:49:52 (Show Source): You can put this solution on YOUR website!(4√6x)(2√18x) I have tried: 8√108x^2 8√36x^2 * √3 48x*√3 ------------ Cheers, Stan H.
 absolute-value/644550: To say that [x+7]<= 5 is the same as saying x is in the closed interval [A,B] A where is: and where B is: Plaese help me! I do not understand this at all!1 solutions Answer 405119 by stanbon(57282)   on 2012-09-02 15:41:30 (Show Source): You can put this solution on YOUR website!To say that [x+7]<= 5 is the same as saying x is in the closed interval [A,B] A where is: and where B is: ----- |x+7| <= 5 means -5<= x+7 <=5 -- Subtracting 7 along the line you get: -12 <= x <= -2 --- So, A = -12 and B = -2 ========================== Cheers, Stan H. ==============
 Mixture_Word_Problems/644556: a paint mixture contains 15 gallons of base for every gallon of color. In 1440 gallons of paint how many gallons of color are there?1 solutions Answer 405115 by stanbon(57282)   on 2012-09-02 15:33:59 (Show Source): You can put this solution on YOUR website!a paint mixture contains 15 gallons of base for every gallon of color. In 1440 gallons of paint how many gallons of color are there? ----- base and color are in a ratio of 14:1 or 14x:x, where color is "x": ------------------ Equation: 14x + x = 1440 15x = 1440 x = 96 (gallons of color) ====================== Cheers, Stan H. ===============
 Unit_Conversion_Word_Problems/644559: This is what my lab sheet states. Measure the width of a standard 8.5.X 11 inch page using a meter stick. Record your measurement in Millimeters,Centimeters, and Meters.What formula.should I be.using to figure this out? Thank you in advanced.1 solutions Answer 405113 by stanbon(57282)   on 2012-09-02 15:28:44 (Show Source): You can put this solution on YOUR website!This is what my lab sheet states. Measure the width of a standard 8.5.X 11 inch page using a meter stick. Record your measurement in Millimeters,Centimeters, and Meters.What formula.should I be.using to figure this out? Thank you in advanced. ---- Don't use any formula. Just use a ruler that has metric measure. Cheers, Stan H.
 Expressions-with-variables/644558: what is the answer to the following system of equations: y=2x-2 4x+3y=141 solutions Answer 405110 by stanbon(57282)   on 2012-09-02 15:24:55 (Show Source): You can put this solution on YOUR website!what is the answer to the following system of equations: y=2x-2 4x+3y=14 ---- Substitute for "y" and solve for "x": 4x + 3(2x-2) = 14 4x + 6x - 6 = 14 10x = 20 x = 2 ------- Solve for "y: y = 2x-2 y = 2*2-2 = 2 ---- Cheers, Stan H.
 Geometry_proofs/644444: what is the largest number of different regions into which the plane can be divided by n lines?1 solutions Answer 405053 by stanbon(57282)   on 2012-09-02 10:40:29 (Show Source): You can put this solution on YOUR website!what is the largest number of different regions into which the plane can be divided by n lines? --- Use Google to search for "number of lines and regions". Ans: 1 + [n(n+1)/2] ======================== Cheers, Stan H. ==================
 Linear-equations/644450: the distance between 2 stations is 300 km.Two motorcyclists start simultaneously from these stations and move towards each other.The speed of one of them is 7 km/h more than that of the other.If the distance between them after 2 hours of their start is 34 km, find the speed of each motorcyclists. 1 solutions Answer 405051 by stanbon(57282)   on 2012-09-02 10:19:10 (Show Source): You can put this solution on YOUR website! the distance between 2 stations is 300 km.Two motorcyclists start simultaneously from these stations and move towards each other.The speed of one of them is 7 km/h more than that of the other.If the distance between them after 2 hours of their start is 34 km, find the speed of each motorcyclists. ------------------- Faster-cyclist DATA: rate = x + 7 km/h ; time = 2 hrs ; distance = 2(x+7) km ----- Slower-cyclist DATA: rate = x km/h ; time = 2 hrs ; distance = 2x km ---- Equation: 2(x+7) + 2x + 34 = 300 2x+14 + 2x = 66 4x = 52 x = 13 km/h speed of the slower x + 7 = 20 km/h speed of the faster ====================================== Cheers, Stan H. ============
 Linear-equations/644451: x/(x^2-9)+4/(x+3)=3/(x^2-9)1 solutions Answer 405049 by stanbon(57282)   on 2012-09-02 10:12:25 (Show Source): You can put this solution on YOUR website! x/(x^2-9)+4/(x+3)=3/(x^2-9) ---- Note: x^2-9 = (x-3)(x+3) ---------------- Multiply thru by x^2-9 to get: x + 4(x-3) = 3 --- 5x-12 = 3 5x = 15 x = 3 ============ Cheers, Stan H. ==========
 Permutations/644453: A manager has a panel of 11 players to choose from . He must pick a team of 6 players to play in a match. Two of the other players melissa and amy both like the same boy so cannot stand each other . They cannot play together on the same team . How many different teams can be selected if melissa and amy cannot both be on the same team1 solutions Answer 405048 by stanbon(57282)   on 2012-09-02 10:09:56 (Show Source): You can put this solution on YOUR website!A manager has a panel of 11 players to choose from . He must pick a team of 6 players to play in a match. Two of the other players melissa and amy both like the same boy so cannot stand each other . They cannot play together on the same team . How many different teams can be selected if melissa and amy cannot both be on the same team ---- # of teams with melissa and without amy: 10C6 = 210 --- # of teams with amy and without melissa: 10C6 = 210 ----- # of teams without both on the same team: 420 ================ Cheers, Stan H. =================
 Linear-equations/644452: in 1980, the median family income was 18,000 and in 2000 it was 41,000 I need to know what the m= and what would be the median family income 2002 1 solutions Answer 405047 by stanbon(57282)   on 2012-09-02 10:06:33 (Show Source): You can put this solution on YOUR website! in 1980, the median family income was 18,000 and in 2000 it was 41,000 I need to know what the m= and what would be the median family income 2002 ---- Let "x" be the number of years after 1980. ---- You have 2 points: (0,18000) and (20,41000) ---- Find an equation thru those two points: slope = (41000-18000)/(20-0) = 23000/20 = 1150 --- Intercept = f(0) = 18000 ------- Equation: f(x) = 1150x + 18000 ---- Income in 2002 -- f(22) = 1150*22 + 18000 f(22) = \$43300 ===================== Cheers, Stan H.
 Functions/644362: What is the rule for this function: Domain:0,1,2,3 Range:3,7,9,11 y= Please and thank you1 solutions Answer 405011 by stanbon(57282)   on 2012-09-02 00:13:45 (Show Source): You can put this solution on YOUR website!What is the rule for this function: Domain:0,1,2,3 Range:3,7,9,11 y = mx + b ---- Find m and find b. -------- m = (7-3)/(1-0) = 4 ----- b = f(0) = 3 ------- Equation: y = 4x +3 -------- Cheers, Stan H.
 Functions/644377: Find the domain of g(x)= x/x^2+x-6 Write in English and in interval symbolism.1 solutions Answer 405004 by stanbon(57282)   on 2012-09-01 23:39:35 (Show Source): You can put this solution on YOUR website!Find the domain of g(x)= x/x^2+x-6 Write in English and in interval symbolism. -------- The denominator cannot be zero. Solve: x^2 + x -6 = 0 (x+3)(x-2) = 0 x = -3 or x = 2 ---- Domain is "All Real Numbers except x = -3, x = 2. ---- (-00,-3)U(-3,2)U(2,+oo) ============================ Cheers, Stan H.
 Geometry_Word_Problems/644367: The base of a triangle is 10 inches more than 2 times the height. If the area of the triangle is 14 square inches, find the base and height.1 solutions Answer 404998 by stanbon(57282)   on 2012-09-01 23:15:44 (Show Source): You can put this solution on YOUR website!The base of a triangle is 10 inches more than 2 times the height. If the area of the triangle is 14 square inches, find the base and height. ------ Let the height be "x": Then the base is "2x+10" --- Area = (1/2)(base)(height) --- 14 = (1/2)(2x+10)(x) ----- 2x^2 + 10x - 28= 0 --- x^2 + 5x - 14 = 9 (x+7)(x-2) = 9 Positive solution: x = 2(height) 2x+10 = 14 (base) =================== Cheers, Stan H.
 Polynomials-and-rational-expressions/644368: Simplify the expression x+√5 x-√5 x+41 solutions Answer 404987 by stanbon(57282)   on 2012-09-01 21:45:02 (Show Source): You can put this solution on YOUR website!Simplify the expression x+√5x -√5x +4 ------- = x + 4 ================= Cheers, Stan H. =================
 Polynomials-and-rational-expressions/644366: solving equations and inequalities x+1/3X-1 + 2X+1/3X-2 = -11 solutions Answer 404986 by stanbon(57282)   on 2012-09-01 21:42:12 (Show Source): You can put this solution on YOUR website!solving equations and inequalities x+1/3X-1 + 2X+1/3X-2 = -1 ---- Multiply thru by (3X-1)(3X-2) to get: (x+1)(3x-2) + (2x+1)(3x-1) = -(3x-1)(3x-2) ---------------------------------------------- 3x^2 +x -2 + 6x^2 +x -1 = -9x^2 + 9x -2 ------------------------------------------- 9x^2 + 2x -3 = -9x^2 + 9x -2 ------- 18x^2 - 7x -1 = 0 18x^2 -9x+2x -1 = 0 --- 9x(2x-1) + (2x-1) = 0 ------ (2x-1)(9x+1) = 0 ------- x = 1/2 or x = -1/9 ========================== Cheers, Stan H.
 Graphs/644365: Use graphs to find the set. (-9, 0) ∩ [-1, 9]1 solutions Answer 404985 by stanbon(57282)   on 2012-09-01 21:34:47 (Show Source): You can put this solution on YOUR website!Use graphs to find the set. (-9, 0) ∩ [-1, 9] = [-1,0] =========================== Cheers, Stan H. =================
 Linear-equations/644361: I am not sure if this is the correct category. But please help me solve this. This is the question: Graph the equation using the most appropriate method. Be sure to include key points. F(x)= I'm not really sure how to get the points from this equation.1 solutions Answer 404984 by stanbon(57282)   on 2012-09-01 21:30:39 (Show Source): You can put this solution on YOUR website!Graph the equation using the most appropriate method. Be sure to include key points. F(x)={1/2}(x+3)^2 ---- If x = -3, y = 0 That is the x-intercept. ----------------------------- If x = 0, y = 9/2 That is the y-intercept ------ Plot those 2 points to see where it would be good to have a 3rd point. ---- Try x = -6, then y = (1/2)(9) = 9/2 --- Plot that point and you should see the shape of the parabola. If not, plot a few more points. =============== =================== Cheers, Stan H.
 Numbers_Word_Problems/644358: One number is 6 less than another number. If the sum of the two numbers is 150, find the numbers1 solutions Answer 404983 by stanbon(57282)   on 2012-09-01 21:16:35 (Show Source): You can put this solution on YOUR website!One number is 6 less than another number. If the sum of the two numbers is 150, find the numbers -------------------- x = y-6 x + y = 150 ---- Rearrange: x - y = -6 x + y = 150 ---- 2x = 144 x = 72 --- Solve for "y": x + y = 150 72 + y = 150 y = 78 ====================== Cheers, Stan H.
 Systems-of-equations/644359: please solve the systems of linear equations: y= (1/2) y= cosx1 solutions Answer 404982 by stanbon(57282)   on 2012-09-01 21:12:29 (Show Source): You can put this solution on YOUR website!please solve the systems of linear equations: y= (1/2) y= cosx ---- cos(x) = 1/2 --- x = 60 degrees or pi/3 y = 1/2 ----------------- Cheers, Stan H.
 Functions/644356: I need help with figuring out the rule for this function: Domain: 1,2,3,4 Range: 3,7,11,15 y= Please and thank you1 solutions Answer 404981 by stanbon(57282)   on 2012-09-01 21:10:00 (Show Source): You can put this solution on YOUR website!help with figuring out the rule for this function: Domain: 1,2,3,4 Range: 3,7,11,15 ----- slope = (7-3)/(2-1) = 4 ----- Note that if x = 0, y would be -1: --- Equation: y = 4x - 1 ------------------ Cheers, Stan H. ======================
 Polynomials-and-rational-expressions/644228: Suppose that R(x)is a polynomial of degree whose coefficients are real numbers. Also suppose that R(x) has the following zeros. -2,3,8,-4+4i _ (a) Find another zero of R(x).? (b) What is the maximum number of real zeros that R(x) can have? ? (c) What is the maximum number of nonreal zeros that R(x)can have?1 solutions Answer 404927 by stanbon(57282)   on 2012-09-01 13:57:26 (Show Source): You can put this solution on YOUR website!Suppose that R(x)is a polynomial of degree?? whose coefficients are real numbers. Also suppose that R(x) has the following zeros. -2,3,8,-4+4i _ (a) Find another zero of R(x).? Ans: -4-4i ------------------------ (b) What is the maximum number of real zeros that R(x) can have? ? You did not show the degree of the polynomial. If it is "n", the max number of Real must be n-2. ------------------------------------- (c) What is the maximum number of nonreal zeros that R(x)can have? ???? Cheers, Stan H.
 Mixture_Word_Problems/644255: David's Salarywas raised was 1st raised by 8% and after 6 months again rasised by 10% ,what is the net percent increase in his salary thanks in Advance for the help and please clarify step by step Best Regards Luay1 solutions Answer 404926 by stanbon(57282)   on 2012-09-01 13:52:38 (Show Source): You can put this solution on YOUR website!David's Salarywas raised was 1st raised by 8% and after 6 months again rasised by 10% ,what is the net percent increase in his salary thanks in Advance for the help and please clarify step by step ----- Let initial salary be "x": --- After 1st raise it is 1.08x --- After 6 months it is 1.1(1.08x) = 1.188x ------ Net percent increase is 18.8% ================================== Cheers, Stan H.
 Rectangles/644262: Calculate the area of a rectangle with a length of 12.0 cm and a width of 86.0 mm. 1 solutions Answer 404924 by stanbon(57282)   on 2012-09-01 13:40:54 (Show Source): You can put this solution on YOUR website! Calculate the area of a rectangle with a length of 12.0 cm and a width of 86.0 mm. ------ 12 cm = 120 mm --- Area = 120 mm *86 mm = 10320 mm^2 ---- OR -------- 86 mm = 8.6 cm Area = 8.6 cm * 12 cm = 103.2 cm^2 --------------- Cheers, Stan H.
 Inequalities/644261: Please help me find the answer. Use the addition property and\or multiplication property to find a and b If -2 is less than x which is less then 0, then a is less then 3x+5 which is less than b1 solutions Answer 404923 by stanbon(57282)   on 2012-09-01 13:37:11 (Show Source): You can put this solution on YOUR website!If -2 is less than x which is less then 0, then a is less then 3x+5 which is less than b ---- Problem: If -2 < x < 0, then a < 3x+5 < b ---- Solution to find "a" and "b": ----- If -2 < x < 0, then -6 < 3x < 0 ------------------------------- and -1 < 3x+5 < 5 --- So a = -6 and b = 5 -------------------- Cheers, Stan H.
 Linear-equations/644246: If a girl works for 8 min. and her brother works for 15 min, they can wash the front windows of their house. Also, if the girl works for 12 min and her brother works for 10 min, they can wash the same windows. How long will it take each person alone to wash the windows? (Hint: If it takes t minutes for a person to do a job alone, then in 1 min, the person can do 1/t of the job).1 solutions Answer 404906 by stanbon(57282)   on 2012-09-01 12:15:55 (Show Source): You can put this solution on YOUR website!If a girl works for 8 min. and her brother works for 15 min, they can wash the front windows of their house. Also, if the girl works for 12 min and her brother works for 10 min, they can wash the same windows. How long will it take each person alone to wash the windows? (Hint: If it takes t minutes for a person to do a job alone, then in 1 min, the person can do 1/t of the job). ---- Let the girl's rate be "g" and the brother's rate be "b". ---- Equation: 8g + 15b = 1 job 12g+ 10b = 1 job --------------------- 80g + 150b = 10 180g + 150b = 15 ---- 100g = 5 g = 1/20 (girl's rate) 1/g = 20 minutes (time for the girl to do the job alone) ------ Solve for "b": 80(1/20) + 150b = 10 150b = 6 b = 1/25 1/b = 25 minutes (time for the brother to do the job alone) ============== Cheers, Stan H.
 Inequalities/644245: Solve this compound inequality: 3x-3>3 or x-4<=36-3x Please explain this to me! Thank you!1 solutions Answer 404904 by stanbon(57282)   on 2012-09-01 12:06:40 (Show Source): You can put this solution on YOUR website!Solve this compound inequality: 3x-3>3 or x-4<=36-3x --- 3x > 6 or 4x < 40 ---- x > 2 or x < 10 ----------------- x is "All Real Numbers". =========== Cheers, Stan H. =============
 Inequalities/644244: How do I solve tis compound inequality?: 3x<6 or -2x>8 Thank you!1 solutions Answer 404903 by stanbon(57282)   on 2012-09-01 12:03:58 (Show Source): You can put this solution on YOUR website!solve tis compound inequality?: 3x<6 or -2x>8 ---- x < 2 or x < -4 ---- Ans: x < 2 =============== Cheers, Stan H.