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# Recent problems solved by 'stanbon'

stanbon answered: 57314 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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 Graphs/99600: Factoring 2z^2 -7x -41 solutions Answer 72465 by stanbon(57387)   on 2007-09-21 16:27:01 (Show Source): You can put this solution on YOUR website!Factoring 2z^2 -7x -4 = (2z+1)(z-4) =============== Cheers, Stan H.
 Square-cubic-other-roots/99606: the positive square root of the number 5761 solutions Answer 72464 by stanbon(57387)   on 2007-09-21 16:21:38 (Show Source): You can put this solution on YOUR website!sqrt(576) = 24 ============ Cheers, Stan H.
 Graphs/99601: Factoring 6x^2 -28x -481 solutions Answer 72463 by stanbon(57387)   on 2007-09-21 16:20:16 (Show Source): You can put this solution on YOUR website!Factoring 6x^2 -28x -48 = 2(3x^2-14x-24) = 2(x-6)(3x+4) ============= Cheers, Stan H.
 Expressions-with-variables/99603: I need help!! A wholesaler is offering two different package deals of roses and carnations to florists. One package contains 20 dozen roses and 34 dozen carnations for \$504.00. The other package contains 15 dozen roses and 17 dozen carnations for \$327.00. Let x = cost of one dozen roses Let y = cost of one dozen carnations a. Write a system of equations for this problem. b. Which equation can be multiplied by a coefficient to create an opposite coefficient? What is that value? c. Solve this system for the cost of one dozen roses and the cost of one dozen carnations.1 solutions Answer 72462 by stanbon(57387)   on 2007-09-21 16:16:02 (Show Source): You can put this solution on YOUR website!A wholesaler is offering two different package deals of roses and carnations to florists. One package contains 20 dozen roses and 34 dozen carnations for \$504.00. The other package contains 15 dozen roses and 17 dozen carnations for \$327.00. Let x = cost of one dozen roses Let y = cost of one dozen carnations a. Write a system of equations for this problem. 1st; 20x+34y= 504 2nd: 15x+17y=327 b. Which equation can be multiplied by a coefficient to create an opposite coefficient? 2nd is the best choice What is that value? -2 c. Solve this system for the cost of one dozen roses and the cost of one dozen carnations. 1st: 20x+34y=504 3rd: -30x-34y=-654 -------- Add 1st and 3rd to get: -10x = -150 x = 15 (# of dozens of roses) ------------- Substitute into 20x+34y=504 ot solve for y: 20*15+34y = 504 300 + 34y = 504 34y = 204 y = 6 (# of dozens of carnations) =============== Cheers, Stan H.
 Polynomials-and-rational-expressions/99605: y^2-9y+81=1 solutions Answer 72461 by stanbon(57387)   on 2007-09-21 16:07:26 (Show Source): You can put this solution on YOUR website!y^2-9y+81 Factor using the Quadratic Formula: y = [9 +- sqrt(81-4*81)]/2 y = [9 +- sqrt(-243))/2 y = [9 +- 9isqrt(3))/2 y = [4.5 +- 4.5isqrt(3)] Factors: (y-4.5-4.5isqrt(3))(-4.5+4.5isqrt(3)) ======================= Cheers, Stan H.
 Graphs/99512: I have a graf that the domaint is 0,1,2,3 and therange is 0,.5,2,4.5 what is the funtion if (1.5,y) is part of the graf1 solutions Answer 72440 by stanbon(57387)   on 2007-09-21 13:52:29 (Show Source): You can put this solution on YOUR website!I have a graf that the domaint is 0,1,2,3 and therange is 0,.5,2,4.5 what is the funtion if (1.5,y) is part of the graf ----------------- Plot the three points: (0,0,5),(1,2),(2,2),(3,4.5) It looks like a parabola: y=ax^2+bx+c Substitute to find a, b, and c, If x=0 ; 0.5=0+0+c; so c=1/2 The y = ax^2+bx+1/2 If x=1; 2 = a+b+1/2; so a+b = (3/2) If x=2; 9/2 = 4a+2b+(1/2): 1st: a+b = (3/2) 2nd: 2a+b = 2 ---------- Subtract 1st from 2nd to get: a= 1/2 ---------------- Substitute into a+b=(3/2) to get b = 1 ------------- EQUATION: y = (1/2)x^2 + x + (1/2) So, if x=1.5, y = (1/2)(9/4)+(3/2)+(1/2) = 9/8 + 2 = 25/8 = 3 1/8 =================== Cheers, Stan H.
 test/99554: Determine whether the square root of 77 is rational or irrational. Answer: A) Irrational B) Rational I say irrational since there is no square. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Determine if (a square root symbol with a - inside it) is rational or irrational. Answer: A) Irrational B) Rational I say: A) Irrational There is a negative symbol, also there is no number. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Find the altitude of the triangle. the sides (height) are each 13 and the base (bottom) is 10. Answer: ???? This one I can not find a formula in my books for solving this. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Evaluate (the square root symbol with 9 over 16 inside it) if possible. I say not possible since it is not a whole number with a solution. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Evaluate (small 3 next to the square root symbol with 1 over 64 inside it) if possible. I say not possible since it is not a whole number with a solution. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Am I on the right track? This is a large assignment and due tonight. These are the only ones I am doubting myself on and need your help. Thanks! ;-) 1 solutions Answer 72435 by stanbon(57387)   on 2007-09-21 13:20:13 (Show Source): You can put this solution on YOUR website!Determine whether the square root of 77 is rational or irrational. Answer: A) Irrational B) Rational I say irrational since there is no square. Correct: It is irrational because 77 is not a perfect square. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Determine if (a square root symbol with a - inside it) is rational or irrational. Answer: A) Irrational B) Rational I say: A) Irrational There is a negative symbol, also there is no number. It is neither rational nor irrational; it is a complex or imaginary number. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Find the altitude of the triangle. the sides (height) are each 13 and the base (bottom) is 10. Answer: ???? This one I can not find a formula in my books for solving this. Draw an altitude from the vertex to the base (side 10) You get two right triangles: altitude^2 + 5^2 = 13^2 altitude = sqrt(13^2-5^2) = sqrt144 = 12 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Evaluate (the square root symbol with 9 over 16 inside it) if possible. I say not possible since it is not a whole number with a solution. sqrt(9/16) = [sqrt(9)]/[sqrt(16)] = 3/4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Evaluate (small 3 next to the square root symbol with 1 over 64 inside it) if possible. I say not possible since it is not a whole number with a solution. cube root of (1/64) = [cube root of 1]/[cube root of 64] = 1/4 ================================== Cheers, Stan H. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 Word_Problems_With_Coins/99551: Find the mean and the median. –2, 7/4 ,3/4 , 4, 9 Find the mean and the median. –2, 7/4 ,3/4 , 4, 9 1 solutions Answer 72412 by stanbon(57387)   on 2007-09-21 09:44:41 (Show Source): You can put this solution on YOUR website!John has \$9.95 made up of nickles and dimes. The number of nickels is one more than 2 1/2 times the number of dimes. How many of each does he have? --------------- Let number of dimes be "x" ; value of these is 10x cents Number of nickels is (5/2)x+1 ; value of these is 5[(5/2)x+1]= (25/2)x+5 cents ------------------- EQUATION: value + value = 995 cents 10x + (25/2)x + 5 = 995 22.5x = 990 x = 44 ( number of dimes) (5/2)x+1 = 111 ( number of nickels) ============== Cheers, Stan H.
 Mixture_Word_Problems/99518: By volume, one alloy is 70% copper, 20% zinc, and 10% nickel. A second alloy is 60% copper, and 40% nickel. A third alloy is 30% copper, 30% nickel, and 40% zinc. How much of each alloy must be mixed in order to produce 1000mm3 of a final alloy that is 50% copper, 18% zinc, and 32% nickel?1 solutions Answer 72411 by stanbon(57387)   on 2007-09-21 09:36:37 (Show Source): You can put this solution on YOUR website!Set up three equations. Let the three alloys by a, b, c 1st equation: Copper---: 0.7a+.6b+.3c = 0.50(1000)=500 mg 2nd equation: Zinc-----: 0.2a+ 0b+.4c = 0.18(1000)=180 mg 3rd equation: Nickel---:..............= 0.32(1000)=320 mg --------------- This is three equations in three unknows. I used the Matrix method on a TI calculator and found a = 140 mg of the 1st alloy b = 480 mg of the 2nd alloy c = 380 mg of the 3rd alloy ============== cheers, Stan H.
 Linear_Algebra/99537: Find the mean and the median. –2, 7/4 ,3/4 , 4, 9 1 solutions Answer 72403 by stanbon(57387)   on 2007-09-21 08:11:38 (Show Source): You can put this solution on YOUR website!Find the mean and the median. –2, 7/4 ,3/4 , 4, 9 --------------------------- Mean: add the numbers and divide by 5. 11 10/4 = 13 1/2 = 27/2 (27/2)/5 = 27/10 = 2.7 is the mean ----------------- Median: Put the numbers in ascending order and choose the middle number which is 7/4 =================== Cheers, Stan H.
 Polynomials-and-rational-expressions/99547: Tutor, I am so lost on this problem and I am not sure what I am doing wrong could you explain to me how to solve this problem? Simplify: 3/x-5+1 / 1- 4/x-5 I am so confused so any help is appreciated. Thank you for your help. 1 solutions Answer 72402 by stanbon(57387)   on 2007-09-21 08:05:20 (Show Source): You can put this solution on YOUR website!3/x-5+1 / 1- 4/x-5 With no parentheses it is hard to tell where your numerators and denominators begin and where they end. Cheers, Stan H.
 Polynomials-and-rational-expressions/99548: Tutor, I was wondering if you could tell me whether I solved this problem correctly. add and simplify: 3y/y^2 + 5y +4 + 2y/y^2 -1 I got: 5y/(y+1)(y-4) is this correct? Thank you for your help.1 solutions Answer 72401 by stanbon(57387)   on 2007-09-21 08:02:48 (Show Source): You can put this solution on YOUR website!That's correct. ================ Cheers, Stan H.
 Numbers_Word_Problems/99522: The average weight of 3 children is 24 kg. What it there total wieght?1 solutions Answer 72377 by stanbon(57387)   on 2007-09-20 22:33:14 (Show Source): You can put this solution on YOUR website!3*24 = 72 lbs =========== Cheers, Stan H.
 Quadratic_Equations/99511: Write your result in scientific notation. (2x10^5)(4x10^4) This is what I have done so far: (2x2^5*5^5)(4x2^4*5^5). I know the answer is suppose to be 8x10^9, I can not figure out how to show the rest. Thank you1 solutions Answer 72376 by stanbon(57387)   on 2007-09-20 22:32:03 (Show Source): You can put this solution on YOUR website!(2x10^5)(4x10^4) = (2*4)*(10^5*10^4) = (8*10^9) =============== Cheers, Stan H.
 Equations/99514: How would I solve this equation? I just really need the steps. Please give a walk through process. 4x + 7 = 25 - 5x and t + 9 = 3t - 51 solutions Answer 72374 by stanbon(57387)   on 2007-09-20 22:00:37 (Show Source): You can put this solution on YOUR website!4x + 7 = 25 - 5x Add 5x to both sides to get: 9x + 7 = 25 Subtract 7 from both sides to get: 9x = 18 Divide both sides by 9 to get: x = 2 ----------------------------------------- and t + 9 = 3t - 5 Subtract t from both sides to get: 9 = 2t -5 Add 5 to both sides 2t = 14 Divide both sides by 2 to get: t = 7 ================= Cheers, Stan H.
 Rate-of-work-word-problems/99510: 2 pumps- 1 fills a tank in 5 hours 1 fills a tank in 7 hours-- how many hours to fill the tank with both pumps filling it at the same time? how did you come up with the answer? thanks... 1 solutions Answer 72372 by stanbon(57387)   on 2007-09-20 21:52:02 (Show Source): You can put this solution on YOUR website!2 pumps- 1 fills a tank in 5 hours 1 fills a tank in 7 hours-- how many hours to fill the tank with both pumps filling it at the same time? -------------- 1st tank DATA; Time + 5 hr/job ; Rate = 1/5 job/hr ------------------ 2nd tank DATA: time = 7 hr/job ; Rate = 1/7 job/hr -------------------------------- Together DATA: time = x hr/job ; Rate = 1/x job/hr ----------------------- EQUATION: rate + rate = together rate 1/5 + 1/7 = 1/x Multiply thru by 35x to get: 7x + 5x = 35 12x = 35 x = 35/12 = 3 11/12 hr = 3 hr 55 minutes (time to do the job together) ========================== Cheers, Stan H.
 Angles/99507: Help please! :-) measure of angle 1 is (3y+4) degrees, measure of angle 2 is (6x+20) degrees, and measure of angle 3 is (3x+y+3) degrees. Solve for x and y, then find the real measure of angle 2. Hint: angles 1 and 3 are vertical angles.1 solutions Answer 72371 by stanbon(57387)   on 2007-09-20 21:42:12 (Show Source): You can put this solution on YOUR website!measure of angle 1 is (3y+4) degrees, measure of angle 2 is (6x+20) degrees, and measure of angle 3 is (3x+y+3) degrees. Solve for x and y, then find the real measure of angle 2. Hint: angles 1 and 3 are vertical angles. ------------- If angle 1 and 3 are vertical angles, 3y+4 = 3x+y+3 3x-2y=1 --------------- Comment: Without information on another angle or a second equation in x and y the problem cannot be answered. =============== Cheers, Stan H.
 Polynomials-and-rational-expressions/99505: factoring 9x^2 + 18x -161 solutions Answer 72368 by stanbon(57387)   on 2007-09-20 21:31:24 (Show Source): You can put this solution on YOUR website!factoring 9x^2 + 18x -16 = (3x-2)(3x+8) ==================== Cheers, Stan H.
 expressions/99501: 6x^2 -5x +1 factoring1 solutions Answer 72367 by stanbon(57387)   on 2007-09-20 21:21:53 (Show Source): You can put this solution on YOUR website!6x^2 -5x +1 factoring ----------------- (2x-1)(3x-1) ================ Cheers, Stan H.
 Travel_Word_Problems/99497: Help! PLEASE! I can't seem to figure these out! 1. One number is 6 more than another number. The sum of the sumbers is one more than 3 times their difference. What are the numbers? 2. In a small rowboat, it took Alice 6 hours to go 6 miles upstream, but she was able to return to her starting point in only 45 minutes. Assuming her rowing speed was constant, what was the speed of the current?1 solutions Answer 72366 by stanbon(57387)   on 2007-09-20 21:15:52 (Show Source): You can put this solution on YOUR website!1. One number is 6 more than another number. The sum of the sumbers is one more than 3 times their difference. What are the numbers? -------------------------------------------------- Let one of the numbers be "x"; the other number is "x+6" EQUATION: x + x+6 = 3(x+6-x) + 1 2x+6 = 18+1 x = 13/2 x = 6.5 (one of the numbers) x+6 = 12.5 (the other number) =========================================== 2. In a small rowboat, it took Alice 6 hours to go 6 miles upstream, but she was able to return to her starting point in only 45 minutes. Assuming her rowing speed was constant, what was the speed of the current? ------------- Upstream DATA: distance=6 miles ; time = 6 hrs; rate = d/t= 1 mph ------------------- Downstream DATA: distance = 6 miles ; time = (3/4) hr ; rate = d/t = 6/(3/4) = 8 mph --------------------- Let speed in quiet water be "b"; let speed of stream be "s" ------------- EQUATIONS: b+s = 8 mph b-s = 1 mph ---------- Add to get: 2b = 9mph b = 4.5 mph (speed of boat in quiet water) Substitue to solve for "s": 4.5+s = 8 s = 3.5 mph (speed of the stream) ================ Cheers, Stan H.
 Mixture_Word_Problems/99479: A nursery wants to mix two types of seeds, one type sells for 12 dollars per pound and the other sells at 20 per pound. To obtain 100 pounds of a mixture at 14 dollars per pound, how many pounds of each seeds are needed?1 solutions Answer 72364 by stanbon(57387)   on 2007-09-20 21:01:10 (Show Source): You can put this solution on YOUR website!A nursery wants to mix two types of seeds, one type sells for 12 dollars per pound and the other sells at 20 per pound. To obtain 100 pounds of a mixture at 14 dollars per pound, how many pounds of each seeds are needed? ----------------- Let amont of \$12 seed be x lbs; value is 12x dollars ------------------------- Amount of \$20 seed is "100-x" ; value is 20(100-x) = (2000-20x) dollars ------------------------ Amt of mixture = 100 lbs; value = 14*100 = 1400 dollars ----------------------- EQUATION: value + value = value 12x + 2000-20x = 1400 -8x = -600 x = 75 lbs (amount of \$12 see in the mixture) 100-x = 25 lbs (amount of \$20 see in the mixture) =============== Cheers, Stan H.
 Exponents/99488: This question is from textbook intermediate algebra Question #29 says to simplify... (5*10^8)(y*10^9) textbook answer is 35*10^17. I tried FOIL method. Can get 10^17 but not 35 Thanks Paul1 solutions Answer 72359 by stanbon(57387)   on 2007-09-20 20:30:26 (Show Source): You can put this solution on YOUR website!I think your "y" must be a "7". That is the only way you would get a 35 in the answer ------------- Cheers, Stan H.
 Expressions-with-variables/99447: In this expression I know that the first step is to find the common denominator. And that's where I stopped. Yeah. The expression has complex fractions and involves variables. It is . Where do I start? I believe that I multiply 6(x-2) by 6x however there's already a 6 in both denominators so do I just ignore this and multiply by (x-2)? I'm very confused. Can you help me?1 solutions Answer 72342 by stanbon(57387)   on 2007-09-20 17:50:58 (Show Source): You can put this solution on YOUR website!7/6(x-2)-(x-3)/6x ------------ Least common denominator is 6x(x-2) Rewrite each fraction with the lcd as its denominator: ------------------ 7*x/lcd - (x-3)*(x-2)/lcd -------------- Combine the numerators over the lcd to get: [7x-(x^2-5x+6)]/lcd Simplify the numerator: [-x^2+12x-6]/lcd ----------- Final Answer: [-x^2+12x-6]/[6x(x-2)]
 Number-Line/99448: Question: For each whole number, give the next whole number on a number line.1 solutions Answer 72341 by stanbon(57387)   on 2007-09-20 17:43:01 (Show Source): You can put this solution on YOUR website!If a whole number is "x" the next whole number is "x+1". Cheers, Stan H.
 Money_Word_Problems/99389: Here is a money problem that I need help with. Suppose that the cost C, in dollars, of producing x items is given by C = 3 How many items can be produced for \$ 13,000? Thank you very much for your help. 1 solutions Answer 72339 by stanbon(57387)   on 2007-09-20 17:40:50 (Show Source): You can put this solution on YOUR website!Suppose that the cost C, in dollars, of producing x items is given by C = 3 How many items can be produced for \$ 13,000? ------------------------- Each item costs C/x or 3/x dollars. Then # of items that can be produced for \$13000 = \$13000/(\$3/x) = [4333 (1/3)]x items. ----------------------- Cheers, Stan H.
 Exponents/99444: This problem also includes complex fractions. I simply forget one rule about adding exponents. The equation is . So far I have found the common denominator which is 20x^3. My problem is adding the exponents in the numerator and then simplifying the solution. Would you please help me?1 solutions Answer 72338 by stanbon(57387)   on 2007-09-20 17:32:17 (Show Source): You can put this solution on YOUR website!6/4x^2 + 2/5x The least common denominator is 20x^2 Rewrite each fraction with the lcd as its denominator: 6*5/lck + 2*4x/lcd Combine the numerators over the lcd: [30+8x]/lcd Factor: [2(15+4x)]/lcd Final answer: (15+4x)/10x^2 ======================= Cheers, Stan H.
 Rational-functions/99391: This question is from textbook Solve the matrix (I-A)X=D for the given matrices A,D,and X. [0.1 0.1]=A [0.2 0.1] [7 ]=D [14] [x]=X [y] Please enter each number as a decimal Round each answer to two decimals x= y= please help!1 solutions Answer 72336 by stanbon(57387)   on 2007-09-20 17:27:52 (Show Source): You can put this solution on YOUR website!Suppose B is a proper subset of C. if n(c)=8, what is the maximum number of elements in B?----seven What is the least possible number of elements in B?--------zero Cheers, Stan H.
 Matrices-and-determiminant/99425: Solve the matrix (I-A)X=D for the given matrices A,D,and X. [0.1 0.1]=A [0.2 0.1] [7 ]=D [14] [x]=X [y] Please enter each number as a decimal Round each answer to two decimals x= y=1 solutions Answer 72335 by stanbon(57387)   on 2007-09-20 17:25:30 (Show Source): You can put this solution on YOUR website!Solve the matrix (I-A)X=D for the given matrices A,D,and X. [0.1 0.1]=A [0.2 0.1] ------------------ [7 ]=D [14] ------------- [x]=X [y] --------------------- Please enter each number as a decimal Round each answer to two decimals x= 0.1*7+0.1*14 = 2.4 y= 0.2*7+0.1*14 = 2.8 ========================== Cheers, Stan H.
 Quadratic_Equations/99430: solve the quadatric equations by factoring (x-1)^2=71 solutions Answer 72334 by stanbon(57387)   on 2007-09-20 17:20:18 (Show Source): You can put this solution on YOUR website!(x-1)^2=7 -------------- (x-1)^2-7 = 0 (x-1-sqrt(7))(x-1+sqrt(7)) ------ x = 1+sqrt7 or x = 1-sqrt(7) ================= Cheers, Stan H.
 Distributive-associative-commutative-properties/99440: ok.....what is the communtive property?1 solutions Answer 72333 by stanbon(57387)   on 2007-09-20 17:17:14 (Show Source): You can put this solution on YOUR website!what is the commutative property? Most people "commute" to work; they live one place and work another place. The communtative property means "you can change places" when it comes to addition or multiplication: Add: a+b = b+a Mult: a*b = b*a ==================== Cheers, Stan H.