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# Recent problems solved by 'stanbon'

stanbon answered: 57151 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, >>Next

 absolute-value/72721: This question is from textbook Algebra:Structure and Method Yellow paint and blue paint must be mixed in the ratio 2:3 to produce the desired shade of green paint. How much of each color should be used to produce 4 L of green paint?1 solutions Answer 51991 by stanbon(57219)   on 2007-02-28 20:29:36 (Show Source): You can put this solution on YOUR website!Yellow paint and blue paint must be mixed in the ratio 2:3 to produce the desired shade of green paint. How much of each color should be used to produce 4 L of green paint? ------- 2:3 is the same as 2x:3x EQUATION: 2x+3x=4 L 5x=4 L x=0.8 L 2x=1.6 L(amount of yellow paint) 3x=2.4 L (amount of blue paint) ------- Cheers, Stan H.
 Quadratic_Equations/72727: when solving for quadric equations how do you get x equal to zero. do you do GCF?1 solutions Answer 51990 by stanbon(57219)   on 2007-02-28 20:25:33 (Show Source): You can put this solution on YOUR website!The quadratic formula says: If ax^2+bx+c=0 then x=[-b+-sqrt(b^2-4ac)]/(2a) ------------- It is a means of determinaing the x-intercepts of a quadratic function. Why? At the x-intercepts the y-value is zero. Therefore ax^2+bx+c=0 Therefore the quadratic formula tells you the x-values that go with y=0. ------------- Cheers, Stan H.
 Inequalities/72723: Latisha has 78 soccer cards in her cellection. She wants to give n cards to each of her 3 bestfriends, and she wants to have at least 40 cards left. Write an inequality Latisha could solve to find n.1 solutions Answer 51987 by stanbon(57219)   on 2007-02-28 20:09:21 (Show Source): You can put this solution on YOUR website!Latisha has 78 soccer cards in her cellection. She wants to give n cards to each of her 3 bestfriends, and she wants to have at least 40 cards left. Write an inequality Latisha could solve to find n. ------------ 3n+40<=78 ------- Cheers, Stan H.
 Systems-of-equations/72644: This question is from textbook Beginning Algebra This problem just doesn's make any sense to me! I don't even know where to begin! Find values for m and b in the following system so that the solution to the sytsem is (-3,4). 5x+7y=b mx+y=221 solutions Answer 51952 by stanbon(57219)   on 2007-02-28 14:07:07 (Show Source): You can put this solution on YOUR website!Find values for m and b in the following system so that the solution to the sytsem is (-3,4). 5x+7y=b mx+y=22 --------- If y=4 when x=-3 you get: 5(-3)+7(4) = b m(-3)+4 =22 ---------- Then: b=-15+28 = 13 and -3m =18 m=-6 --------- Solution: b=13 and m=-6 -------- Cheers, Stan H.
 Graphs/72664: with the slop-intercept y=1/2x+5 indicate which is number is the slope and which is the y-intercept.NOTE when labeling y-intercept fill it in the blank of (0.?) to show its coorinate slope= Y-Intercept= (0, )1 solutions Answer 51951 by stanbon(57219)   on 2007-02-28 14:01:05 (Show Source): You can put this solution on YOUR website!with the slope-intercept y=(1/2)x+5, indicate which is number is the slope and which is the y-intercept.NOTE when labeling y-intercept fill it in the blank of (0.?) to show its coorinate --------- slope is 1/2 intercept is (0,5) Cheers, Stan H.
 Linear-equations/72657: This question is from textbook Beginning Algebra 1A Thanks for helping me Please solve and graph for me please. 5x + 7y =b mx + y =221 solutions Answer 51950 by stanbon(57219)   on 2007-02-28 13:23:55 (Show Source): You can put this solution on YOUR website!What is the value of "m"? of b? Can't solve or graph if you do not know these. Cheers, Stan H.
 Number-Line/72661: using number lines from-5 to 15 draw mapping diagrams to illustrate the functions x arrow 3x + 2 and x arrow4x-31 solutions Answer 51949 by stanbon(57219)   on 2007-02-28 13:19:31 (Show Source): You can put this solution on YOUR website!using number lines from-5 to 15 draw mapping diagrams to illustrate the functions x arrow 3x + 2 and x arrow4x-3 ----------------- That notation means y=3x+2 and y=4x-3 "from -5 to 15" means the domain and the range are limited to those numbers. --------- To graph y=3x+2 plot the points (0,2),(1,5) and draw a line thru them. To graph y=4x-3 plot the points (0,-3),(1,1) and draw a line thru them. --------- Cheers, Stan H.
 Polynomials-and-rational-expressions/72653: Can someone help me understand this problem Determine whether the graph of y=3x^6 - 2x^4 is symmetric with respect to the x-axis, the y-axis, and/or the origin.1 solutions Answer 51948 by stanbon(57219)   on 2007-02-28 13:13:03 (Show Source): You can put this solution on YOUR website!Determine whether the graph of y=3x^6 - 2x^4 is symmetric with respect to the x-axis, the y-axis, and/or the origin. --------------- Need to find f(-x)= 3x^6-2x^4 Need to find -f(-x) = -3x^6 +2x^4 --------- Since f(x)=f(-x) you have y-axis symmetry Since f(x) does not equal -f(-x) you do not have origin symmetry f(x) is a function so you do not have x-axis symmetry. ---------- Cheers, Stan H.
 Linear-equations/72659: This question is from textbook Beginning Algebra 1A Please help me solve, Thanks Number problems. Jill has \$3.50 in nickels and dimes. If she has 50 coins, how many of each type of coin does she have?1 solutions Answer 51947 by stanbon(57219)   on 2007-02-28 12:51:59 (Show Source): You can put this solution on YOUR website!Jill has \$3.50 in nickels and dimes. If she has 50 coins, how many of each type of coin does she have? -------- Let number of nickels be "x"; Value of these is 5x cents Number of dimes is "50-x" ; Value of these is 10(50-x)= 500-10x cents ------- EQUATION: value + value = 350 cents 5x+500-10x = 350 -5x = -150 x=30 (number of nickels) 50-x=20 (number of dimes) ------------ Cheers, Stan H.
 Expressions-with-variables/72660: This question is from textbook Beginning Algebra 1A The algebra problems I'am submitting are the ones I'am having a problem with, thanks for the help. 5x - 2y = -5 y - 5x = 31 solutions Answer 51946 by stanbon(57219)   on 2007-02-28 12:45:56 (Show Source): You can put this solution on YOUR website!5x - 2y = -5 y - 5x = 3 ------- If you add these two equations you get: -y=-2 y=2 ----------- Substitute that back to solve for "x": 2-5x=3 -5x=1 x=-1/5 ------ Check the solution in the other equation: 5(-1/5) - 2(2) = -5 -1 - 4 = -5 -5=-5 -------- Cheers, Stan H.
 Polynomials-and-rational-expressions/72654: Can I get help with this problem Write an equation for a function that has the shape of y=x^3 but shifted left 3 units and up 4 units.1 solutions Answer 51945 by stanbon(57219)   on 2007-02-28 12:41:42 (Show Source): You can put this solution on YOUR website!Write an equation for a function that has the shape of y=x^3 but shifted left 3 units and up 4 units ---------- To shift left 3 put (x+3) in place of "x". You get y=(x+3)^3 To go up 4 units you must raise the value of y by 4. Y was (x+3)^3; you add 4 to get y=(x+3)^3 + 4 Cheers, Stan H.
 Percentage-and-ratio-word-problems/72636: In the first year Ashok's salary was increased by 15%.In second year the salary increased by 20%.In third year the salary increased by 25%.If it is increased by 205 every year,Ashok would have got Rs.600 less than today's salary.What was Ashok's salary before first year?1 solutions Answer 51938 by stanbon(57219)   on 2007-02-28 10:54:29 (Show Source): You can put this solution on YOUR website!In the first year Ashok's salary was increased by 15%.In second year the salary increased by 20%.In third year the salary increased by 25%.If it is increased by 205 every year,Ashok would have got Rs.600 less than today's salary.What was Ashok's salary before first year? -------------- Let "x" be the first year salary. I am going to assume that "today's salary" means his salary after all the raises. EQUATION: x(1.15)(1.20)(1.25) =x+3(205)+600 1.725x = x+615+600 1.725x = x+1215 0.725x = 1215 x=\$1,675.86 Cheers, Stan H.
 Radicals/72640: x -2 -1 0 1 2 y .25 .5 1 2 4 Given the table above, graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph, and also the domain and range of the entire function. Graph Graph Type Explanation Domain Range 1 solutions Answer 51936 by stanbon(57219)   on 2007-02-28 10:41:24 (Show Source): You can put this solution on YOUR website!y=2^x Exponential Domain: all Real numbers Range: all Real that are greater than zero Cheers, Stan H.
 Inequalities/72623: 2-(2/3-X)+1/6=-x+5/9 We are supposed to find the solution. Please help me with the steps. There are several more problems like this on my work. 1 solutions Answer 51917 by stanbon(57219)   on 2007-02-28 08:31:25 (Show Source): You can put this solution on YOUR website!2-(2/3-X)+1/6=-x+5/9 -------- 2-(2/3)+x+(1/6) = -x + (5/9) (4/3) + x + (1/6) = -x +(5/9) 9/6 +2x = 5/9 2x = (5/9)-(9/6) 2x = (5/9)-(3/2) 2x = -17/18 x = -17/36 -------- Cheers, Stan H.
 Numeric_Fractions/72598: This question is from textbook If you need to mix 5L of fluid containing 25%alcohol and you have one that cotains 50%alcohol and another with 15%alcohol how much of each do you need to mix.1 solutions Answer 51897 by stanbon(57219)   on 2007-02-27 22:41:40 (Show Source): You can put this solution on YOUR website!If you need to mix 5L of fluid containing 25%alcohol and you have one that cotains 50%alcohol and another with 15%alcohol how much of each do you need to mix. --------- Amt of 50% solution is "x" L; Amt of alcohol is 0.5(x)= 0.5x L Amt of 15% solution is "5-x"L; Amt of alcohol is 0.15(5-x)= 0.75-0.15x L ----------- Amt of 25% mix is 5 L; amt of alcohol is (1/4)5= 1.25 L -------- EQUATION: alcohol + alcohol = 1.25 0.50x + 0.75-0.15x = 1.25 Multiply thru by 100 to get: 50x + 75 - 15x =125 35x=50 x=10/7 = 1.43 L (amt of 50% solution) 5-x=3.57 L )amt of 15% solution) ------------- Cheers, Stan H.
 Rational-functions/72589: I have checked all possible answers and heeeeeers my question. someone please explain how do I need to do this. You guys/gals are all I have in helping me. for f(x) = 1/x^2 -2x -8, find the interval(s) where f(x) < 0. -4, 2 -2, 4 2, 4 2, 8 Thank you if you can take the time to teach me.1 solutions Answer 51896 by stanbon(57219)   on 2007-02-27 22:21:41 (Show Source): You can put this solution on YOUR website!f(x) = 1/x^2 -2x -8, find the interval(s) where f(x) < 0. f(x) = 1/[(x-4)(x-2)] F(x) will be<0 when [(x-4)(x-2)] is less than zero and x is not 2 or 4. ===== When is (x-4)(x-2)<0 ?? Draw a number line and mark x=2 and x=4 on it. That establishes three intervals. Find the intervals which make (x-4)(x-2)<0 Check interval (-inf,2); select x=-100; you get (100-4)(100-2)>0 Therefore the interval is NOT part of the solution. Check interval (2.4); select x=3; you get (3-4)(3-2)<0 Therefore the interval is part of the solution. Check interval (4,inf); select x=100; you get (100-4)(100-2)>0 Therefore the interval is NOT part of the solution. --------- Solution summary: (2,4) Cheers, Stan H.
 Square-cubic-other-roots/72586: x - square root of x = 0, solve for all values of x that satisfies the equation show work1 solutions Answer 51895 by stanbon(57219)   on 2007-02-27 21:59:47 (Show Source): You can put this solution on YOUR website!x - square root of x = 0, Add sqrt(x) to both sides sqrt(x) = x Square both sides to get: x=x^2 x^2-x=0 x(x-1)=0 x=0 or x=1 Both are good answers. ------- Cheers, Stan H.
 Pythagorean-theorem/72587: a right triangle the sides are related by pythagorean theorem, c^2=a^2+b^2 where c is the hypotenuse . find the hypotenuse when the other 2 sides measurements are 3 feet and 4 feet show work please1 solutions Answer 51893 by stanbon(57219)   on 2007-02-27 21:53:49 (Show Source): You can put this solution on YOUR website!Pythagoras determined (hypotenuse)^2 = (side 1)^2 + (side 2)^2 h^2 = 3^2 + 4^2 h^2 = 9 + 16 h^2 = 25 hypotenuse = 5 -------- Cheers, Stan H.
 Radicals/72577: I need help solving this problem: 3^√x^2 = 4 "^" it means it's an exponent.... so it is 3 cubed to the square root of X squared = 4" 1 solutions Answer 51889 by stanbon(57219)   on 2007-02-27 21:44:39 (Show Source): You can put this solution on YOUR website!I need help solving this problem: 3^√x^2 = 4 "^" it means it's an exponent.... so it is 3 cubed to the square root of X squared = 4" ------------ It looks like you have posted two problems: 1st: 3^(sqrt(x^2) = 4 3^x = 4 Take the log to get: x(log3) = log4 x= (log4)/(log3) x= 1.262 ---------------- 2nd: 3 cubed to the square root of X squared = 4" (3^3)^(sqrt(x^2)) = 4 27^x = 4 Take the log of both sides to get: xlog27=log4 x=(log4)/(log27) x=0.42062 ------------------ Cheers, Stan
 Linear-equations/72490: Determine if the two equations are parellel, perpendicular or neither 2/5x - 1/3y = 7/8 1/3x - 2/4y = -72 This is not from a book1 solutions Answer 51865 by stanbon(57219)   on 2007-02-27 19:59:39 (Show Source): You can put this solution on YOUR website!Determine if the two equations are parellel, perpendicular or neither 2/5x - 1/3y = 7/8 1/3x - 2/4y = -72 --------- Put each equation in slope-intercept form: y = ((2/5)/(1/3))x -[(7/8)/(1/3)] y = (6/5)x -(21/8) ------------ y= [(1/3)/(1/2)]x + [72/(1/2) y= (2/3)x +144 ------------- They are neither parallel or perpendicular as they have different slopes and different y-intercepts. -------------. Cheers, Stan H.
 Probability-and-statistics/72535: Two number cubes are rolled and the first cube shows a 3. Find the probability that you obtain a sum of 7.1 solutions Answer 51863 by stanbon(57219)   on 2007-02-27 19:29:23 (Show Source): You can put this solution on YOUR website!Two number cubes are rolled and the first cube shows a 3. Find the probability that you obtain a sum of 7. --------- Rolling two dice gives 6*6=36 possible results. Of those results these are the ones whose sum is 7:1,6) 2,5) 3,4) 4,3) 5,2) 6,1 So the probability = 6/36 or 1/6 ---------- Cheers, Stan H.
 Polynomials-and-rational-expressions/72550: How much 18% acid solution must be mixed with 38% acid solution to create 75 oz of 25% acid solution? Using variables x & y, write two equations. 1 solutions Answer 51862 by stanbon(57219)   on 2007-02-27 19:08:26 (Show Source): You can put this solution on YOUR website!How much 18% acid solution must be mixed with 38% acid solution to create 75 oz of 25% acid solution? Using variables x & y, write two equations. ---------------------- x+y=75 0.18x+0.38y= 0.25*75 ============= Cheers, Stan H.
 Numbers_Word_Problems/72541: I am having a hard time figuring out this word problem: The sum of three numbers is 98. The sum of the first and second is two more than the third number, and the second is for more than the first. Find the numbers. So far I have figured out the equations but can't seem to put them together to solve the equation: x+y+z=98 x+y=2+z y=4+x 1 solutions Answer 51858 by stanbon(57219)   on 2007-02-27 18:40:37 (Show Source): You can put this solution on YOUR website!x+y+z=98 x+y=2+z y=4+x ----------- Try substitution from the bottom of the list. I end up with x+4++x+2x+2=98 4x+6=98 4x=92 x=23 y=27 z=48 ----------- Cheers, Stan H.
 Equations/72547: I need to help my child factor. Here are few problems that need to be factored: 8y-5 5y-15 10y-5 x^(2)+2x thank you 1 solutions Answer 51853 by stanbon(57219)   on 2007-02-27 18:31:16 (Show Source): You can put this solution on YOUR website!Here are few problems that need to be factored: 8y-5= 8(y-(5/8)) This could also be factored as: 5((8/5)y-1) --------- 5y-15= 5(y-3) This could also be factored as: 15((1/3)y-1) --------- 10y-5= 5(2y-1) This could also be factored as: 10(y-(1/2)) ---------- x^(2)+2x = x(x+2) ========= Cheers, Stan H. --------
 Percentage-and-ratio-word-problems/72542: A 35 meter wooden pole is cut into two parts that have the ratio of 5 to 2. How much longer is the longer part than the smaller part?1 solutions Answer 51851 by stanbon(57219)   on 2007-02-27 18:21:35 (Show Source): You can put this solution on YOUR website!A 35 meter wooden pole is cut into two parts that have the ratio of 5 to 2. How much longer is the longer part than the smaller part? --------- 5:2 is the same as 5x:2x EQUATION: 5x+2x=35 7x=35 x=5 The smaller part is 2x= 10 feet Cheers, Stan H.
 Linear-equations/72546: 1) find the slope: and y intercept of the graph of 2x+5y=10 2) A recent survey of the stuednt body showed that 124 out of 200 students were in favor of keeping the nutrition break between 2nd and 3rd hours. Based on these results, predict how many of the 1450 students prefer to keep the nutrition break? 3) graph: y>-1x+2 31 solutions Answer 51849 by stanbon(57219)   on 2007-02-27 18:16:46 (Show Source): You can put this solution on YOUR website!1) find the slope: and y intercept of the graph of 2x+5y=10 ------- Put in slope-intercept form by solving for "y": y=(-2/5)x+2 The slope is -2/5 ---------------------------- 2) A recent survey of the stuednt body showed that 124 out of 200 students were in favor of keeping the nutrition break between 2nd and 3rd hours. Based on these results, predict how many of the 1450 students prefer to keep the nutrition break? x/1450 = 124/200 x = 1450(124/200) x = 899 ---------------- 3) graph: y>(-1/3)x+2 You need to graph the EQUALITY which is the boundary of the INEQUALITY. To graph y=(-1/3)x+2 Let x=0, then y=2 giving you point (0,2) Let x=3, then y=1 giving you point (3,1) Plot those points; draw a dashed line thru them; that is the boundary. --------- Now, the graph of the INEQUALITY is above the boundary because you want the "Y" values to be y>(-1/3)x+2 -------- -------- Cheers, Stan H.
 Exponential-and-logarithmic-functions/72545: 3/2 to the fifth root 1 solutions Answer 51848 by stanbon(57219)   on 2007-02-27 18:03:09 (Show Source): You can put this solution on YOUR website!Are you sure you mean 5th root of 2/3 ??/ -------- If you do you need to multiply numerator and denominator by 3^4 to get: [(2*3^4)^(1/5)]/3 Another way to say this is "5th root of (2*3^4)"divided by 3 --------------- Cheers, Stan H.
 Equations/72543: My son is working with monomial quotients using a table to organize work when dividing monomials. I would like to check his home work so could you please work this and give steps. I really would appreciate it. -3g^3h 12g^2 there is a line between the two but i couldn't figure out how to get it there.1 solutions Answer 51847 by stanbon(57219)   on 2007-02-27 17:52:06 (Show Source): You can put this solution on YOUR website![-3g^3h] / [12g^2] I'll break it up so you can see the pieces: = (-3/12)(g^3h/g^2) = (-1/4)(g^(3h-2)) ------------ Cheers, Stan H.
 Rational-functions/72496: I have a hard time with word problems. A right triangle is a triangle with one angle measuring 90°. In a right triangle, the sides are related by Pythagorean Theorem, where c is the hypotenuse (the side opposite the 90° angle). Find the hypotenuse when the other 2 sides’ measurements are 3 feet and 4 feet. Thank you,1 solutions Answer 51826 by stanbon(57219)   on 2007-02-27 15:50:26 (Show Source): You can put this solution on YOUR website!Find the hypotenuse when the other 2 sides’ measurements are 3 feet and 4 feet. ---------- Pythagoras determined (hypotenuse)^2 = (side 1)^2 + (side 2)^2 h^2 = 3^2 + 4^2 h^2 = 9 + 16 h^2 = 25 hypotenuse = 5 -------- Cheers, Stan H.
 logarithm/72498: Can you prove the Property: Loga^x= log10^x/log10^a1 solutions Answer 51824 by stanbon(57219)   on 2007-02-27 15:46:13 (Show Source): You can put this solution on YOUR website!prove the Property: Loga^x= log10^x/log10^a ----------- Let log(base a)x = W Then a^W = x Take the log(base 10) of both sides to get: wlog(base 10)a = log(base 10)x Substitute for w to get: [log(base a)x][log(base 10)a = log(base 10)x Divide both sides by log(base 10)a to get: log(base a)x = [log(base 10)x]/[log(base 10)a -------- Cheers, Stan H.
 Polynomials-and-rational-expressions/72504: I do not want the answer to this problem straight away. I would like to see how it works, the process and what is happening in that process. Is saht acceptable? (-2)^-5 Our instructor handed out worksheets and this is one of the problems on it.1 solutions Answer 51822 by stanbon(57219)   on 2007-02-27 15:33:20 (Show Source): You can put this solution on YOUR website!(-2)^-5 ------- The exponent contains two instruction: 1. raise to the 5th power 2. invert You may perform them in any order. If you invert first you get: [1/(-2)]^5 Then raise to the 5th power to get: 1/-32 ----------- If you raise to the 5th power first you get: (-32)^-1 Then invert to get: 1/-32 ------------ Either way is correct: Cheers, Stan H.