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# Recent problems solved by 'scott8148'

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 Miscellaneous_Word_Problems/160711: Weights of 75 pounds and 90 pounds sit at the ends of a 15 foot long board. Where should the fulcrum be placed to balance the board? I don't know what formula to use to solve this equation. Any help would be appreciated.1 solutions Answer 118491 by scott8148(6628)   on 2008-10-06 21:25:31 (Show Source): You can put this solution on YOUR website!the weight multiplied by the distance from the fulcrum is a quantity called the "moment" __ at balance, the moments on either side of the fulcrum are equal 75(x)=90(15-x) __ 75x=1350-90x __ 165x=1350 __ x=90/11 the fulcrum should be 90/11 feet from the 75 lb end
 Miscellaneous_Word_Problems/160713: A 40-pound weight is placed 6 feet from the fulcrum on a lever, and a 60-pound weight is placed 8 feet from the fulcrum on the other side. Where should a 30-pound weight be placed to give equilibrium? This is a question on a handout and I can't find the formula to work this problem. Any help would be apprecitated. Thanks so much.1 solutions Answer 118490 by scott8148(6628)   on 2008-10-06 21:15:16 (Show Source): You can put this solution on YOUR website!the weight multiplied by the distance from the fulcrum is a quantity called the "moment" __ at equilibrium, the moments on either side of the fulcrum are equal 40(6)+30(x)=60(8) __ 240+30x=480 __ 30x=240 __ x=8
 Linear_Algebra/160480: f(x)=x^3. g(x)=(sq. root of)x. h(x)=x-4. and j(x)=2x. If k(x)=(sq. root of x^3-4), Express k(x) as a composite of three of the four functions listed. Please explain how you arrived at your solution! I'm begging for help!!!1 solutions Answer 118371 by scott8148(6628)   on 2008-10-05 17:45:56 (Show Source): You can put this solution on YOUR website!start with f(x) __ that's your x^3 h(x) subtracts 4 __ so h(f(x))=x^3-4 last is g(x) __ it takes sqrt __ g(h(f(x)))=sqrt(x^3-4) k(x)=g(h(f(x)))
 Linear_Equations_And_Systems_Word_Problems/160423: This question is from textbook Intermediate Algebra 311 Tickets sold for a total of 385.50. student tickets = .50 and non students cost 1.50. How many of each were sold ? I don't know where to begin1 solutions Answer 118340 by scott8148(6628)   on 2008-10-05 12:35:04 (Show Source): You can put this solution on YOUR website!"311 Tickets sold" __ s+n=311 __ s=311-n "a total of 385.50" __ .50s+1.50n=385.50 __ s+3n=771 substituting __ (311-n)+3n=771 __ 2n=460 __ n+230 substituting __ s+(230)=311 __ s=81
 Polynomials-and-rational-expressions/160399: Can anyone show me how to solve this equation. 1 solutions Answer 118332 by scott8148(6628)   on 2008-10-05 12:11:01 (Show Source): You can put this solution on YOUR website!factoring __ (5x^2-3)(3x^2-5)=0 5x^2-3=0 __ x^2=3/5 __ x=ħsqrt(3/5) 3x^2-5=0 __ x^2=5/3 __ x=ħsqrt(5/3)
 Radicals/160413: Given: square root of (10x+6)(-) square root of (4x+4) = 2 Solution: 1. I isolated sq rt. of (10+6) = 2 +sq.rt.(4x+4) 2. sq. rt. of (10x+6)^2 = {2 + (4x+4)}^2 3. get rid of sq. rt. 10x +6 = 4 + 4sq.rt.of (4x+4) + 4x+4 4. 10x +6 = 4x + 8 + sq.rt.(4x+4)mult.4 5. 6x -2 = sq.rt.(4x+4) mult.4 6. (6x-2)^2 = {sq. rt. (4x +4)mult. 4}^2 7. 36x^2 - 24x +4 = 16 (4x+4) 8. 36x^2 - 24x +4 = 64x + 64 9. 36x^2- 88x - 60= 0 After this I am having difficulty to come up with the solution. Where did I go wrong?1 solutions Answer 118331 by scott8148(6628)   on 2008-10-05 12:03:18 (Show Source): You can put this solution on YOUR website!your work seems fine so far dividing by 4 __ 9x^2-22x-15=0 using quadratic formula __ x=(22ħ32)/18 __ x=(11ħ16)/9 __ x=-5/9 and x=3
 Quadratic_Equations/160400: Could someone please show me how to get the line of symentry, vertex and the min/max of the line. 1 solutions Answer 118329 by scott8148(6628)   on 2008-10-05 11:45:37 (Show Source): You can put this solution on YOUR website!this eqn is in the form y=a(x-h)^2+k (sometimes called the "vertex form") the vertex is (h,k) the axis of symmetry is x=h the min/max is the vertex __ min if a is positive __ max if a is negative
 Linear-systems/160365: -4x - 5y - 8z = 268 -10x + 7y + 6z = -786 -12x + 9y - 2z = -548 I need to solve this using any method, but id like to see the steps and the correct answer. I'm not sure where to start with this one, im just lost. Thank you so much for all your help. I tried to do this on my own, i thought i should multiply the first equation by 3 and add to the 3rd equation,but im not sure what to do next, or if that was even where to start.1 solutions Answer 118312 by scott8148(6628)   on 2008-10-05 01:01:15 (Show Source): You can put this solution on YOUR website!looking at the values of the coefficients (numbers), the numbers for the z terms seem the easiest for eliminating multiply 3rd eqn by 3, add to 2nd eqn __ -46x+34y=-2430 __ -23x+17y=1215 __ multiplying by 41 __ -943x+697y=-49815 __ (A) multiply 3rd eqn by 4, subtract from 1st eqn __ 44x-41y=2460 __ multiplying by 17 __ 748x-697y=41820 __ (B) adding eqns (A) and (B) __ -195x=-7995 __ x=41 substituting __ 44(41)-41y=2460 __ y=-16 substituting __ -4(41)-5(-16)-8z=268 __ z=-44
 Linear-systems/160345: -3x + y + 11z = -410 -4x - 6y + 5z = -214 -2x - 2y + 6z = -244 I need to solve this using any method, but id like to see the steps and the correct answer. I'm not sure where to start with this one, im just lost. Thank you so much for all your help.1 solutions Answer 118308 by scott8148(6628)   on 2008-10-04 21:43:21 (Show Source): You can put this solution on YOUR website!dividing 3rd eqn by -2 gives NEW 3rd eqn __ x+y-3z=122 new 3rd eqn times 3, added to 1st eqn __ 4y+2z=-44 __ 2y+z=-22 new 3rd eqn times 4, added to 2nd eqn __ -2y-7z=274 adding eqns __ -6z=252 __ z=-42 substituting __ 2y+(-42)=-22 __ y=10 substituting __ x+(10)-3(-42)=122 __ x=-14
 Linear-systems/160344: -11x - 3y - 10z = 17 -12x - 5y + 2z = 84 3x - 6y + 3z = 51 I need to solve this system of linear equations using any method. I'd like to see the steps and the correct answer. I'm not sure which method would be the easiest and I'm just stuck. Thank you for all your help.1 solutions Answer 118303 by scott8148(6628)   on 2008-10-04 20:33:40 (Show Source): You can put this solution on YOUR website!reduce (simplify) where you can __ dividing 3rd eqn by 3 gives a NEW 3rd eqn __ x-2y+z=17 new 3rd eqn times 10, added to 1st eqn __ -x-23y=187 __ -23y-187=x new 3rd eqn times -2, added to 2nd eqn __ -14x-y=50 substituting __ -14(-23y-187)-y=50 __ 321y=-2568 __ y=-8 substituting __ -23(-8)-187=x __ -3=x substituting __ (-3)-2(-8)+z=17 __ z=4
 Linear-systems/160343: -11x = 395 + y 14y = -634 - 10x I need to solve this system of linear equations using any method. I'd like to see the steps and the correct answer. I'm not sure which method would be the easiest and I'm just stuck. Thank you for all your help.1 solutions Answer 118300 by scott8148(6628)   on 2008-10-04 20:10:20 (Show Source): You can put this solution on YOUR website!subtracting 395 from 1st eqn __ -11x-395=y substituting into 2nd eqn __ 14(-11x-395)=-634-10x __ -154x-5530=-634-10x -144x=4896 __ x=-34 substituting __ -11(-34)-395=y __ -21=y
 Finance/160036: 1st sum of money at 6% 2nd sum of money is twice the first sum + \$1000 at 10% and the total annual income is \$620.. how much is invested at each rate and how did you get it.. this has to be done in the i=prt form1 solutions Answer 118062 by scott8148(6628)   on 2008-10-02 21:12:20 (Show Source): You can put this solution on YOUR website!s=1st sum, so 2s+1000=2nd sum (6%)(s)+(10%)(2s+1000)=620 __ .06s+.2s+100=620 __ .26s=520 __ s=2000 2s+1000=5000
 Linear_Algebra/160050: x+5y-z=16 3x-3y+2z=12 2x+4y+z=20 Please help me solve this. I have tried and keep getting a decimil point that doesn't fit in. 1 solutions Answer 118061 by scott8148(6628)   on 2008-10-02 21:06:10 (Show Source): You can put this solution on YOUR website!add 1st eqn and 3rd eqn __ 3x+9y=36 __ x+3y=12 __ x=12-3y multiply 1st eqn by 2, then add 2nd eqn __ 5x+7y=44 substituting __ 5(12-3y)+7y=44 __ 60-8y=44 __ y=2 substituting __ x=12-3(2) __ x=6 substituting __ (6)+5(2)-z=16 __ z=0
 Miscellaneous_Word_Problems/160053: This question is from textbook Algebra and Trigonometry Structure and Method book 2 I have been struggling to figure out this word problem and I was wondering if someone could help me? Please and Thank you!! I would deeply appreciate it. Problem solving: using systems Last summer Bret earned \$32 a day and Sandra earned \$36 a day. Together they earned a total of \$3560. How much did each earn, if Bret worked 5 days more than Sandra?1 solutions Answer 118060 by scott8148(6628)   on 2008-10-02 20:55:04 (Show Source): You can put this solution on YOUR website!earnings is days times rate __ let d=Sandra, so d+5=Brett 36(d)+32(d+5)=3560 __ 68d+160=3560 __ 68d=3400 __ d=50 Sandra __ 36 * 50 Brett __ 32 * 55
 Exponents/160064: i seem to have forgotten everything i knew about calculations with numbers expressed as powers of 10. ie: the difference between 6.022x10 to the power of 23 and 6.24 times 10 to the power of 25. help bob 74 yrs old 8 yrs of college curses1 solutions Answer 118056 by scott8148(6628)   on 2008-10-02 20:39:35 (Show Source): You can put this solution on YOUR website!6.24x10^25 is the same as 624x10^23 with the orders of magnitude (exponents of 10) the same, you can just add or subtract (624-6)x10^23
 Probability-and-statistics/159985: 40% of students find a job in there chosen field, in a group of 5 what is the probability that at least 1 find a job in his or her field. I'm trying but my answers are way off. I don't know what i'm doing wrong.1 solutions Answer 118004 by scott8148(6628)   on 2008-10-02 16:04:38 (Show Source): You can put this solution on YOUR website!"40% of students find a job in there chosen field" __ so 60% DON'T "the probability that at least 1 find a job in his or her field" __ is 1 minus the probability that none find a job in their field probability of NONE (out of 5) is .6*.6*.6*.6*.6 or .6^5 or .078 so the probability of at least 1 is 1-.078 or .922
 Graphs/160001: Problem reads as . Find the equation of a relation using the point-slope or slope-intercept equation. 1. m= 3/5, (0,3) ____ 2. m= 1/4, (3,-1/4). Could anyone help with these?1 solutions Answer 117994 by scott8148(6628)   on 2008-10-02 15:53:08 (Show Source): You can put this solution on YOUR website!you are given the slope of the line and a point that the line goes through __ using point-slope 1. y-3=(3/5)(x-0) __ y=(3/5)x+3 2. y-(-1/4)=(1/4)(x-3) __ y=(1/4)x-1
 Graphs/159802: I am trying to find the vertex for the following problem: x^2+3x-4=0 All the help I could get would be appreciated. 1 solutions Answer 117836 by scott8148(6628)   on 2008-10-01 11:27:52 (Show Source): You can put this solution on YOUR website!the vertex is on the axis of symmetry general eqn for axis is x=-b/(2a) x=-3/(2*1) __ x=-3/2 substituting __ y = (-3/2)^2 + 3(-3/2) - 4 __ y = 9/4 - 9/2 -4 __ y = -25/4 vertex is (-3/2,-25/4)
 Complex_Numbers/159623: A food store makes a 9-lb mixture of peanuts, cashews, and raisins. Peanuts cost \$1.50 per pound, cashews cost \$2.00 per pound, and raisins cost \$1.00 per pound. The mixture calls for twice as much peanuts than cashews. The total cost of the mixture is \$13.00. How much of each ingredient did the store use? I am really confused with this problem.1 solutions Answer 117713 by scott8148(6628)   on 2008-09-30 17:00:08 (Show Source): You can put this solution on YOUR website!"a 9-lb mixture of peanuts, cashews, and raisins" __ p+c+r=9 " twice as much peanuts than cashews" __ p=2c "The total cost of the mixture is \$13.00" __ 1.5p+2c+1r=13 substituting __ (2c)+c+r=9 __ 3c+r=9 __ r=9-3c substituting __ 1.5(2c)+2c+9-3c=13 __ 2c=4 __ c=2 substituting __ p=2(2) __ p=4 substituting __ r=9-3(2) __ r=3
 Inequalities/159440: my question is very difficult i cant figure out if your suppose to flip the sign and then do the proble or just do the proble also about the number sign if you make it hollow or what because i dont get when were suppose to make it hollow or shadow question# 24.) 6y<4.21 solutions Answer 117583 by scott8148(6628)   on 2008-09-29 19:26:55 (Show Source): You can put this solution on YOUR website!you flip the sign (arrow) when you multiply or divide by a negative value dividing by 6 __ y<.7 since y is less than .7, but not equal to .7; the circle is open (hollow) if it was less than or equal to (≤) then the circle would be solid (shadow)
 Miscellaneous_Word_Problems/159455: This question is from textbook Algebra and Trigonometry Structure and Method book 2 I have been struggling with this word problem and I was wondering if someone could help me? Please and Thank you!! I would deeply appreciate it. Problem Solving: Using Systems For a recent job, a plumber earned \$28/h, and the plumber's apprentice earned \$15/h. The plumber worked 3 hours more than the apprentice. If together they were paid \$213, how much did each earn? (Hint: First write an expression for the number of hours each worked on the job.)1 solutions Answer 117582 by scott8148(6628)   on 2008-09-29 19:18:50 (Show Source): You can put this solution on YOUR website!"The plumber worked 3 hours more than the apprentice" __ p=a+3 "together they were paid \$213" __ 28p+15a=213 substituting __ 28(a+3)+15a=213 __ 28a+84+15a=213 __ 43a=129 __ a=3 substituting __ p=(3)+3 __ p=6
 Linear_Equations_And_Systems_Word_Problems/159456: I have solved similar linear equations previously, but this one stumps me. The answer is 4L per the book, but I cannot get to that answer. Here is the question: How many liters of a 60% acid solution must be mixed with a 75% acid solution to get 20L of a 72% solution?1 solutions Answer 117581 by scott8148(6628)   on 2008-09-29 19:10:41 (Show Source): You can put this solution on YOUR website!let x="liters of 60%", so 20-x="liters of 75%" (60%)(x)+(75%)(20-x)=(72%)(20) __ .6x+15-.75x=14.4 __ -.15x=-.6 __ x=4
 Functions/159450: This question is from textbook Algera 1 My little sister is currently taking Algebra 1 and is having trouble with a problem so she asked me, but even though I'm really good at Pre-Cal and all I am having trouble remembering how to do the simplest problem. So I could really use your help. y=1/3x Find the Domain Thank you, Cali1 solutions Answer 117580 by scott8148(6628)   on 2008-09-29 19:03:54 (Show Source): You can put this solution on YOUR website!the domain means "allowable" values for x __ values that result in a y value usually the bigest "no-no" in this situation is a value that results in division by zero (which is undefined) in this case, x can be any value EXCEPT zero using interval notation __ (-∞,0)U(0,+∞)
 Linear-systems/159428: Hi. I need help solving this problem for my physics class. I am a bit rusty on solving systems. I need to solve for x and y. 47-x=17y 23y+81=-3x1 solutions Answer 117567 by scott8148(6628)   on 2008-09-29 17:05:33 (Show Source): You can put this solution on YOUR website!from 1st eqn __ -x=17y-47 __ x=47-17y substituting into 2nd eqn __ 23y+81=3(17y-47) __ 23y+81=51y-141 __ 222=28y __ 111/14=y substituting __ x=47-(17(111/14)) __ x=-1229/14
 Geometry_Word_Problems/159421: Please help..(I am the mom :) The length of a rectangle is 3 times the width. The perimenter is 96 cm. Find the width and the length. I know that P= 2(L+W). But I can't figure out the correct equation to get the length and width. Thanks,KS1 solutions Answer 117565 by scott8148(6628)   on 2008-09-29 16:55:48 (Show Source): You can put this solution on YOUR website!"The length of a rectangle is 3 times the width" __ L=3W just substitute into your perimeter equation __ P = 2(3W+W) __ 96 = 8W __ 12=W L=3W __ L=3(12) __ L=36
 Complex_Numbers/159310: Campus Rentals rents 2 and 3 bedroom apartments for \$700 and \$900 per month respectively. Last month they had six vacant apartments and reported \$4600 in lost rent. How many of each type of apartment were vacant? Can someone please explain to me how to make this into equations?1 solutions Answer 117476 by scott8148(6628)   on 2008-09-28 21:29:48 (Show Source): You can put this solution on YOUR website!d="2 brm", t="3 brm" "six vacant apartments" __ d+t=6 "reported \$4600 in lost rent" __ 700d+900t=4600
 Complex_Numbers/159311: The sum of three numbers is 20. The second number is 4 times the first, and the sum of the first and third is 8. Find the numbers, How do you make these equations?1 solutions Answer 117474 by scott8148(6628)   on 2008-09-28 21:25:38 (Show Source): You can put this solution on YOUR website!f="1st number", s="2nd number", and t="3rd number" "The sum of three numbers is 20" __ f+s+t=20 "The second number is 4 times the first" __ s=4f "the sum of the first and third is 8" __ f+t=8
 Complex_Numbers/159314: Jonathon and members of his Spanish Club are going to Costa Rica over spring break. Before his trip, he purchases 10 travelers checks in denominations of \$20, \$50, and \$100, totaling \$370. He has twice as many \$20 checks as \$50 checks. How many of each type of denomination of travelers checks does he have? I do not understand how to make this into 3 algebraic equations. If someone could just ezplain that, i would appreciate that.1 solutions Answer 117471 by scott8148(6628)   on 2008-09-28 21:21:06 (Show Source): You can put this solution on YOUR website!t="\$20 checks", f="\$50 checks", and h="\$100 checks" "he purchases 10 travelers checks" __ t+f+h=10 "totaling \$370" __ 20t+50f+100h=370 "twice as many \$20 checks as \$50 checks" __ t=2f
 Complex_Numbers/159315: Jambalaya is a Cajun dish made from chicken, sausage, and rice. Simone is making a large pot of jambalaya for a party. Chicken costs \$6 per pound, sausage costs \$3 per pound, and rice costs \$1 per pound. She spends \$42 on 13.5 pounds of food. She buys twice as much rice as sausage. How much chicken, sausage, and rice will she use in her dish? Can someone please show me how to make this into 3 algebraic equations. I should be good from there. I would really appreciate it.1 solutions Answer 117468 by scott8148(6628)   on 2008-09-28 21:14:54 (Show Source): You can put this solution on YOUR website!"She spends \$42" __ 6c+3s+1r=42 "on 13.5 pounds of food" __ c+s+r=13.5 "She buys twice as much rice as sausage" __ r=2s
 Graphs/159032: can you please help me solve this 1 solutions Answer 117142 by scott8148(6628)   on 2008-09-25 23:39:55 (Show Source): You can put this solution on YOUR website!adding 2 __ -36>9x __ dividing by 9 __ -4>x