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Recent problems solved by 'stanbon'

stanbon answered: 57178 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

Quadratic_Equations/89086: Find the axis of symmetry. y = x^2 + 7x + 10 1 solutions Answer 64758 by stanbon(57246)   on 2007-07-19 10:31:00 (Show Source): You can put this solution on YOUR website! Find the axis of symmetry. y = x^2 + 7x + 10 ----------- Complete the square on the xFind the axis of symmetry. y = x^2 + 7x + 10-terms. x^2+7x+(7/2)^2 = y-10+(7/2)^2 Factor to get: (x+(7/2))^2 = y+(9/4) Vertex is at (-7/2,-9/4) so axis of symmetry is x=-7/2 ------------- Cheers, Stan H.

Quadratic_Equations/89087: Describe what the graph of the following equation would look like, by providing a set of five x/y values centered around the axis of symmetry, stating the x-intercepts, and explaining whether the parabola would open up or open down and how you know. y = x^2 – 1 1 solutions Answer 64749 by stanbon(57246)   on 2007-07-19 09:55:11 (Show Source): You can put this solution on YOUR website! Describe what the graph of the following equation would look like, by providing a set of five x/y values centered around the axis of symmetry, stating the x-intercepts, and explaining whether the parabola would open up or open down and how you know. y = x^2 – 1 If x=0, y=-1 If x=1, y=0 If x=2, y=3 If x=-1,y=0 If x=-2,y=3 -------------------- opens up because the points go up centered at (0,-1) ------------------ Cheers, Stan H.

Vectors/89040: Can someone tell me if this is correct, and also I need to round it to the nearest tenth but I don't know how.......A plane with an airspeed of 450 mph if flying in the direction N35degrees West....im supposed to express the vector in terms of i&j...... my answer is -450sin35i + 450cos35j 1 solutions Answer 64724 by stanbon(57246)   on 2007-07-18 23:34:49 (Show Source): You can put this solution on YOUR website! I think N35 degrees W is an angle of 135 degrees If your i corresponds to horizontal motion and your j corresponds to vertical motion you might want an answer of 450(icos(135) + jsin(135)) ------------ Cheers, Stan H.

Polynomials-and-rational-expressions/89042: From a worksheet: the directions are to simplfy. I can't create this problem exactly for you the way it is on the worksheet, but hopefully you will know what it is. I know that it is dealing with rationalizing denominators, but I don't understand it. 1/2-2sqt3 On the worksheet, the 1 is the numerator. Then on the bottom is 2-2, then the square root sign followed by 3. 1 solutions Answer 64723 by stanbon(57246)   on 2007-07-18 23:28:33 (Show Source): You can put this solution on YOUR website! Rationalize the denominator if you have the 1 is the numerator. Then on the bottom is 2-2, then the square root sign followed by 3. -------- 1/(2-2sqrt(3)) Rewrite as follows: 1/[2(1-sqrt3)] Multiply numerator and denominator by (1+sqrt3) to get: (1+sqrt3)/[2(1-sqrt3)(1+sqrt3)] = (1+sqrt3)/[2(1^2-(sqrt3)^2)] = (1+sqrt3)/[2(1-3)] = (1+sqrt3)/4 =========== Cheers, stan H.

expressions/89004: Hello out there,I need some help with some problems,the first one is,Factor.Write prime if the expression cannot be factored:49y^2-25.The next one is,Factor.Write prime if the expression cannot be factored:4x^2-24x+36.The next one is,Factor.Write prime if the expression cannot be factored:16e^2-4.And the last one is,Factor.Write prime if the expression cannot be factored:4k^2+20k+25.Thanks to whoever can help. 1 solutions Answer 64721 by stanbon(57246)   on 2007-07-18 23:20:03 (Show Source): You can put this solution on YOUR website! first one is,Factor.Write prime if the expression cannot be factored: 49y^2-25 = (7y-5)(7y+5) -------------- The next one is,Factor.Write prime if the expression cannot be factored: 4x^2-24x+36 = 4(x^2-6x+9) = 4(x-3)(x-3) ----------------- The next one is,Factor.Write prime if the expression cannot be factored: 16e^2-4 = (4e-2)(4e+2) ----------------- And the last one is,Factor.Write prime if the expression cannot be factored: 4k^2+20k+25 = (2k+5)(2k+5) =============== Cheers, Stan H.

Coordinate-system/89037: By looking at the graph of a line, how can you tell if its slope is negative? 1 solutions Answer 64717 by stanbon(57246)   on 2007-07-18 22:37:39 (Show Source): You can put this solution on YOUR website! As x increases (goes to the right) y decreases (goes down). Cheers, Stan H.

Linear-equations/89010: Let y vary directly with x, with a constant of variation k=3. Graph the equation of variation. 1 solutions Answer 64716 by stanbon(57246)   on 2007-07-18 22:35:25 (Show Source): You can put this solution on YOUR website! Let y vary directly with x, with a constant of variation k=3. Graph the equation of variation. ------------- y=3x Cheers, Stan H.

Rational-functions/89026: what are the conditions needed for the graph of a rational functio to have a vertical asymptote? 1 solutions Answer 64715 by stanbon(57246)   on 2007-07-18 22:20:16 (Show Source): You can put this solution on YOUR website! The denominator must have a factor which becomes zero when x equals some Real Number value and the numerator does not have the same factor. For example: f(x) = x/(x-5) has a vertical asymptote at x=5 =============== Cheers, Stan H.

Miscellaneous_Word_Problems/88989: If I want to make the perfect 12 oz. cup of chocolate milk, it requires that the mixture is 42% Syrup. What I have now is 8 oz. of a milk/syrup mixture that I know contains 30% syrup. What must the syrup concentration be in the remaining mixture that I must add in order to achieve perfection? 1 solutions Answer 64689 by stanbon(57246)   on 2007-07-18 18:44:38 (Show Source): You can put this solution on YOUR website! If I want to make the perfect 12 oz. cup of chocolate milk, it requires that the mixture is 42% Syrup. What I have now is 8 oz. of a milk/syrup mixture that I know contains 30% syrup. What must the syrup concentration be in the remaining mixture that I must add in order to achieve perfection? ------------- Final mixture DATA: Amt of mix = 12 oz. ; amt of syrup = 0.42(12) = 5.04 oz --------------------------- Have now DATA: Amt of mix = 8 oz. ; amt of syrup = 0.30(8) = 2.4 oz ------------------------------ Misture to be added DATA: Amt of mix = 12-8 = 4 oz ; amt of syrup = 4x where x is the percent. ------------------- EQUATION: syrup + syrup = syrup 2.4 + 4x = 5.04 4x = 2.64x = .66 --------------- 66% of the added mixture must be syrup ============= Cheers, Stan H.

Polynomials-and-rational-expressions/88995: This question is from textbook algebra and trigonometry please help me understand how to do the following problem it says "Factor the polynomial. Show all work." 2x^2 + x - 1 1 solutions Answer 64688 by stanbon(57246)   on 2007-07-18 18:32:39 (Show Source): You can put this solution on YOUR website! 2x^2 + x - 1 (2x-1)(x+1) ============== Cheers, Stan H.

Polynomials-and-rational-expressions/88994: This question is from textbook algebra and trigonometry please help in factoring this polynomial problem!! x^2 + x - 6 1 solutions Answer 64687 by stanbon(57246)   on 2007-07-18 18:30:47 (Show Source): You can put this solution on YOUR website! x^2 + x - 6 (x+3)(x-2) =============== Cheers, Stan H.

Travel_Word_Problems/88990: To get to the store from his house, Jim biked 5 kilometers due west and then 12 kilometers due north. On the way back he cut across a field, taking the shortest possible route home. How far did Jim bike on the round trip? 1 solutions Answer 64686 by stanbon(57246)   on 2007-07-18 18:29:06 (Show Source): You can put this solution on YOUR website! 5 km + 12 km + sqrt(5^2+12^2) = 5 + 12 + sqrt(169) = 5 + 12 + 13 = 30 km ============ Cheers, Stan H.

Linear-equations/88991: 1. F(x)=3X+1 2. F(x)=-1/3X-2 3. Slope (-3,5), M=-1 4. Slope (3,0), m=4/3 1 solutions Answer 64685 by stanbon(57246)   on 2007-07-18 18:21:00 (Show Source): You can put this solution on YOUR website! What is the question? Cheers, Stan H.

Graphs/88804: Complete the square and write the given equation in the standard form for the equation of a circle. then give the center and radius of the circle and sketch the graph. x^2-6x+y^2+2y=6 1 solutions Answer 64684 by stanbon(57246)   on 2007-07-18 18:19:17 (Show Source): You can put this solution on YOUR website! give the center and radius of the circle and sketch the graph. x^2-6x+y^2+2y=6 ---------------- Complete the square on the x terms and on the y terms: (x^2-6x+9) + (y^2+2y+1) = 6+9+1 Factor as follows: (x-3)^2 + (y+1)^2 = 16 --------------------- Draw the following circle: Center is at (3,-1) ; the radius = 4 =============== Cheers, Stan H.

Quadratic_Equations/88962: Could you please help me solve the following equation by using the square root method? 9x^2-30x+25=-1 Thank you very much for any help you can provide. 1 solutions Answer 64657 by stanbon(57246)   on 2007-07-18 14:33:56 (Show Source): You can put this solution on YOUR website! solve the following equation by using the square root method? 9x^2-30x+25=-1 ---------- (3x-5)^2 = -1 (3x-5)^2+1 = 0 Factor to get: (3x-5-i)(3x-5+i) = 0 3x-5-i = 0 or 3x-5+i = 0 x=(5+i)/3 or x=(5-i)/3 ================ Here's the square root method. (3x-5)^2 = -1 Take the square root of both sides to get: 3x-5 = i or 3x-5 = -i 3x=5+i or 3x = 5-i x = (5+i)/3 or x = (5-i)/3 ==================== Cheers, Stan H.

Expressions-with-variables/88965: A rectangle has sides of 5x-12 and 5x+12. What is the area of the rectangle? In side the rectangle two squares with sides of x and x are to be removed. What is the remaining area of the rectangle? 1 solutions Answer 64656 by stanbon(57246)   on 2007-07-18 14:21:22 (Show Source): You can put this solution on YOUR website! A rectangle has sides of 5x-12 and 5x+12. -------------- What is the area of the rectangle? (5x-12)(5x+12) = 25x^2-144 sq units ------------------------- Inside the rectangle two squares with sides of x and x are to be removed. What is the remaining area of the rectangle? -------------- Area of the two squares = x^2 + x^2 = 2x^2 Remaining area = 25x^2-144 -(2x^2) = 23x^2-144 ================== Cheers, Stan H.

Systems-of-equations/88944: y=log(x) y=x^0.3 please help me solve this system of equations 1 solutions Answer 64644 by stanbon(57246)   on 2007-07-18 10:00:54 (Show Source): You can put this solution on YOUR website! y=log(x) y=x^0.3 -------- Graph the two equations and find the point of intersection: -------- I did it on a TI-83 and found no intersection. Conclusion: No solution ========= Cheers, Stan H.

percentage/88941: I know the answer, but I want to know the process of getting there. I would like to know step-by-step of how to get this answer. Here is the problem: Use the Pie Charts to answer the question. (Since I can't copy and paste the pie charts, I will just list their percentages. Pie Chart 1: Total Expenditures: -Taxes: 17% -Research & Development: 10% -Salaries: 38% -Advertising: 35% Pie Chart 2: Expenditures on Advertising: -Television: 43% -Newspapers: 36% -Fliers: 3% -Radio: 18% The first pie chart represents a company's expenditures, and the second pie chart shows a breakdown of the company's advertising expenditures. What percent of the company's expenditures is spent on radio advertising? a) 6.3% b) 11.7% c) 18.0% d) 35.0% 1 solutions Answer 64642 by stanbon(57246)   on 2007-07-18 09:49:36 (Show Source): You can put this solution on YOUR website! 18% * 35% = 0.18*0.35 = 0.063 = 6.3% --------- Cheers, Stan H.

Age_Word_Problems/88942: Ruffy is 3/4 as old as Orlie.Four years ago,Ruffy was 1year more than 1/2 old as Orlie.How old is each 1 solutions Answer 64641 by stanbon(57246)   on 2007-07-18 09:43:48 (Show Source): You can put this solution on YOUR website! Ruffy is 3/4 as old as Orlie.Four years ago,Ruffy was 1year more than 1/2 old as Orlie.How old is each -------- NOW DATA: Orlie's age = x yrs ; Ruffy's age = (3/4)x yrs ------------ 4 yrs ago DATA: Orlie's age was (x-4) yrs ; Ruffy's age was (3/4)x-4 -------------- EQUATION: (based on 4 yrs ago DATA) Ruffy =(1/2)Orlie +1 (3/4)(x)-4 = (1/2)(x-4) + 1 Multiply thru by 4 to get rid of the denominators: 3x-16 = 2(x-4) + 4 3x-16 = 2x-4 x=12 (Orlie's age NOW) (3/4)x = 9 (Ruffy's age NOW) =========== Cheers, Stan H.

expressions/88936: These are on exponentials with logs; in case stan happens to see this, thanks alot for your help- I had to use my moms' last paycheck (she had to leave work to have surgery done on her anuerysms) to pay $400 for this class to make sure I have this Algebra II credit to graduate this upcoming year. You taking out time to do those 5 little problems were a BIG help and may god bless you. 2^x = 30 5^x - 1 = 3^x 3.5^3x + 1 = 65.4 16^x - 4 = 3^3 - x 7^x - 2 = 5^x 1 solutions Answer 64640 by stanbon(57246)   on 2007-07-18 09:30:18 (Show Source): You can put this solution on YOUR website! 2^x = 30 Take the log of both sides to get: x(log2) = log30 x = [log30]/[log2] x = 4.90689.. --------------------- 5^(x - 1) = 3^x Take the log of both sides (x-1)log5 = xlog3 xlog5 -xlo3 = log5 x(log5 - log3) = log5 x(0.2218487..) = 0.6987000... x = 5.15066... --------------- 3.5^(3x + 1) = 65.4 Take the log of both sides: (3x+1)log3.5 = log65.4 (3log3.5)x = log65.4 x = 0.329266.... ----------- 16^(x - 4) = 3^(3 - x ) Take the log of both sides (x-4)log16 = (3-x)log3 Can you take it from here? -------- 7^(x - 2) = 5^x Take the log of both sides Can you take it from here? ============= Cheers, Stan H.

Polynomials-and-rational-expressions/88928: Would someone please explain to me step by step how to figure out this problem. Thank you. A triangle has sides 2x-5, 3x+1, and 4x+2. Find the polynomial that represents its perimeter. 1 solutions Answer 64638 by stanbon(57246)   on 2007-07-18 09:00:51 (Show Source): You can put this solution on YOUR website! A triangle has sides 2x-5, 3x+1, and 4x+2. Find the polynomial that represents its perimeter. --------- Add the sides to get the perimeter: 2x-5+3x+1+4x+2 =9x-2 ========== Cheers, Stan H.

Quadratic_Equations/88933: Could someone help me with this one please. If you do not mind would you show me step by step how you came upon the answer? Thank you Solve (x-5)^2=6 1 solutions Answer 64637 by stanbon(57246)   on 2007-07-18 08:58:31 (Show Source): You can put this solution on YOUR website! Solve (x-5)^2=6Solve (x-5)^2=6 ---------- Take the square root of both sides to get: x-5 = sqrt6 or x-5 = -sqrt6 Add 5 to both sides to get: x = 5+sqrt6 or x= 5-sqrt6 ============= Cheers, stan H.

Equations/88931: These are exponential equations ( not that I know what the actually are); can someone please solve these before I die of stupidness!!!! 9^2x = 27^x - 1 5^n-1 = 1/ 25 25^x = 5^(x^2 - 15) 2^x * 4^x+5 = 4^2x-1 sqrt(3)^2x+4 = 9^x-2 1 solutions Answer 64636 by stanbon(57246)   on 2007-07-18 08:56:06 (Show Source): You can put this solution on YOUR website! 9^2x = 27^(x - 1) 3^4x = 3^(3(x-1)) 3^4x = 3^(3x-3) Since the bases are the same the exponents must be equal: 4x = 3x-3 x = -3 ------------- 5^n-1 = 1/ 25 5^(n-1) = 5^-2 n-1 = -2 n=-1 ----------- 25^x = 5^(x^2 - 15) 5^2x = 5^(x^2-15) 2x = x^2-15 x^2-2x-15=0 (x-5)(x+3)=0 x=5 or x=-3 -------------- 2^x * 4^x+5 = 4^2x-1 2^x * 2^(2x+10) = 2^(4x-2) 2^(3x+10) = 2^(4x-2) 3x+10 = 4x-2 x = 12 --------------- sqrt(3)^2x+4 = 9^x-2 3^[(1/2)(2x+4)] = 3^(3(x-2)) 3^(x+2) = 3^(3x-6) x+2 = 3x-6 2x=8 x=4 ============ Be patient; it will come. ============== Cheers, Stan H.

Equations/88930: Help me solve this. Everytime I do a check, it does not balance. 5x-8x+10x=28-10x+3x 1 solutions Answer 64635 by stanbon(57246)   on 2007-07-18 08:43:18 (Show Source): You can put this solution on YOUR website! 5x-8x+10x=28-10x+3x 7x = 28-7x 14x = 28 x = 2 ========== Cheers, Stan H.

Age_Word_Problems/88929: seven years ago,mary was 6times as old as cora.in one year,she will be only twice as old as cora.find their present ages 1 solutions Answer 64634 by stanbon(57246)   on 2007-07-18 08:38:06 (Show Source): You can put this solution on YOUR website! seven years ago,mary was 6 times as old as cora.in one year,she will be only twice as old as cora.find their present ages -------------- 7 years ago DATA: Cora's age = x ; Mary's age = 6x ---------------- NOW DATA: Cora's age = x+7 ; Mary's age = 6x+7 ----------------- One year from now DATA: Cora's age = x+8 ; Mary's age = 6x+8 ------------------- EQUATION: (based on one year from now DATA) 6x+8 = 2(x+8) 6x+8 = 2x+16 4x = 8 x = 2 ---------------- x+7 = 9 yrs old (Cora's age NOW) 6x+7 = 19 yrs old (Mary's age NOW) ======== Cheers, Stan H.

Miscellaneous_Word_Problems/88925: Bill sells is vintage 1974 Road Runner for $9500. He uses the money to invest in a 36 month CD that pays 4.12% interest compounded quartely. How much money will he receive when he cashes in his CD at the end of the 36 months? 1 solutions Answer 64633 by stanbon(57246)   on 2007-07-18 08:29:21 (Show Source): You can put this solution on YOUR website! Bill sells is vintage 1974 Road Runner for $9500. He uses the money to invest in a 36 month CD that pays 4.12% interest compounded quartely. How much money will he receive when he cashes in his CD at the end of the 36 months? ----------- A = P(1+r/n)^(nt) Your Problem: A is the future value P is the pricipal or investment r is the yearly interest rate n is the number of compounding periods per year t is the number of years -------------------- A = 9500(1+0.0412/4)^(4*3) A = 9500(1.1308) A = $10743.06 ================== Cheers, Stan H.

Polynomials-and-rational-expressions/88895: Can you please explain in detail for me...Thank You... 2/ - 1/ = 4/ 1 solutions Answer 64592 by stanbon(57246)   on 2007-07-17 23:22:39 (Show Source): You can put this solution on YOUR website! 2/{y^2-7y+12} - 1/{y^2-9} = 4/{y^2-y-12} Factor where you can to get: [2/[(y-3)(y-4)] - 1/[(y-3)(y+3)] = 4/[(y-4)(x+3)] Multiply thru by (y-3)(y-4)(y+3) to get: 2(y+3) - [y-4] = 4(y-3) 2y+6-y+4 = 4y-12 3y=22 y= 22/3 ============== Cheers, Stan H.

Polynomials-and-rational-expressions/88897: Simplify each expression 1. (y^-4y^5)^2 2. Brackets around the whole problem -3x^8x^-3 divided by 6x^-3x^4 then outside the brackets is a ^3 3. x^8nx^3n 4. x^2n divided by x^5n 1 solutions Answer 64590 by stanbon(57246)   on 2007-07-17 23:12:48 (Show Source): You can put this solution on YOUR website! 1. (y^-4y^5)^2 = [y^1]^2 = y^2 ------------------------- 2. Brackets around the whole problem -3x^8x^-3 divided by 6x^-3x^4 then outside the brackets is a ^3 = [(-3x^5)/(6x)]^3 = [-x^4/2]^3 = [-x^12]]/8 = (-1/8)x^12 ---------------- 3. x^8nx^3n = x^11n ------------------ 4. x^2n divided by x^5n = 1/x^3n =============== Cheers, Stan H.

Polynomials-and-rational-expressions/88896: simplify each expression 1. 15(x^4y^3)^4 divided by 21(x^5y)^2 2. 8^0 3. 12 divided by (2x)^0 4. 1 divided by 5^-3 1 solutions Answer 64588 by stanbon(57246)   on 2007-07-17 23:03:38 (Show Source): You can put this solution on YOUR website! simplify each expression 1. 15(x^4y^3)^4 divided by 21(x^5y)^2 = [15x^16y^12]/[21x^10y^2] = (5/7)x^6y^10 ---------------------------------------------------- 2. 8^0 = 1 --------------------- 3. 12 divided by (2x)^0 = 12/1 = 12 -------------------- 4. 1 divided by 5^-3 = 1/5^-3 = 5^3 = 125 =============================== Cheers, Stan H.

percentage/88888: How many liters of an 11% alcohol solution should be mixed with 60 liters of a 5% alcohol solution to obtain a mixture that is 7% alcohol? 1 solutions Answer 64586 by stanbon(57246)   on 2007-07-17 22:57:09 (Show Source): You can put this solution on YOUR website! How many liters of an 11% alcohol solution should be mixed with 60 liters of a 5% alcohol solution to obtain a mixture that is 7% alcohol? --------- Amt of 5% solution = 60 L ; amt of active ingredient = 0.05*60 = 3 L ------- Amt of 11% solution = x L ; amt of active ingredient = 0.11x L --------------- Amt of 7% mixture = (60+x) L ; Amt of active ingre = 0.07(60+x) = 4.2+0.07x L =================== EQUATION: active + active = active 3 + 0.11x = 4.2+0.07x 0.04x = 1.2 x = 30 liters (amt of 11% solution that must be mixed) ========== Cheers, Stan H.

Polynomials-and-rational-expressions/88865: word problem that I need help with Keiven earned $165 interest for 1 year on an investment of $1500. At the same rate what amount of interest would be earned by an investment of $2500.00. Thank a million 1 solutions Answer 64580 by stanbon(57246)   on 2007-07-17 22:03:25 (Show Source): You can put this solution on YOUR website! Keiven earned $165 interest for 1 year on an investment of $1500. At the same rate what amount of interest would be earned by an investment of $2500.00. ----------- Let x be the amt of interest on $2500 x/2500 = 165/1500 x = 2500(165/1500) x = $275 ============= Cheers, Stan H.