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# Recent problems solved by 'lwsshak3'

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 Exponential-and-logarithmic-functions/696959: Solve log(base6) (x^2+7)=log(base6)(1-5x)1 solutions Answer 429523 by lwsshak3(6509)   on 2012-12-26 19:17:48 (Show Source): You can put this solution on YOUR website!Solve log(base6) (x^2+7)=log(base6)(1-5x) x^2+7=1-5x x^2+5x+6=0 (x+3)(x+2)=0 x+3=0 x=-3 or x+2=0 x=-2
 Linear-equations/696957: parallel and perpendicular lines i need to put my answer into slope - intercept form,y= mx+b form find the equation of the parallel line that passes thru the given information Problem m=3/2 thru (2,6) I come up up with y-6=2/3(x-2) But i dont think this is right now i am stumped on these three problems i need help with m = -4 thru (-2,3) and my other problem m=1/3 thru (-1,3) also m=1/4 thru (2,-4) thank you for your help i am so mixed up i try and i get it backwards 1 solutions Answer 429521 by lwsshak3(6509)   on 2012-12-26 19:10:32 (Show Source): You can put this solution on YOUR website!Standard form of equation for a straight line: y=mx+b, m=slope, b=y-intercept m=3/2 thru (2,6) equation: y=3x/2+b solve for b using coordinates of given point 6=3*2/2+b b=6-3=3 equation: y=3x/2+3 use this same method to solve the following 3 problems: .. m = -4 thru (-2,3) m=1/3 thru (-1,3) m=1/4 thru (2,-4)
 Inequalities/696954: -17<3+10x_<33 This is my problem This is what I came up with but I'm not sure how to plot it as an interval notation and I'm not sure if my answer is correct. -17<3+10x_<33 -17-3<3-3+10x_<33-3 -20<10x_<30 -20/10<10x/10_<30/10 -2 5x+3_<-2 or 13-x_<6 5x+3-3_<-2-3 5x_<-5 5x/5_<-5/5 x_<-1 or 13-x_<6 13-13-x_<6-13 -x_<-7 -x/-1_<-7/-1 x_>71 solutions Answer 429514 by lwsshak3(6509)   on 2012-12-26 18:57:57 (Show Source): You can put this solution on YOUR website!-17<3+10x≤33 add (-3) to each term -20<10x≤30 divide each term by 10 -2 < x ≤ 3 number line: <......(-2<==>3]..........> solution: (-2, 3]
 Problems-with-consecutive-odd-even-integers/696828: The speed of the boat in still water is 15km/hr.It can go 30 km upstream and return to down stream in 41/2hrs.find the speed of the stream.1 solutions Answer 429422 by lwsshak3(6509)   on 2012-12-26 01:53:20 (Show Source): You can put this solution on YOUR website!The speed of the boat in still water is 15km/hr.It can go 30 km upstream and return to down stream in 41/2hrs.find the speed of the stream. ** let x=speed of stream (15+x)=speed of boat downstream (15-x)=speed of boat upstream travel time=distance/speed 30/(15+x)+30/(15-x)=9/2 60/(15+x)+60/(15-x)=9 LCD: (15+x)(15-x) 60(15-x)+60(15+x)=9(15+x)(15-x) 60(15-x+15+x)=9(225-x^2) 60(30)=2025-9x2 9x^2=2025-1800 9x2=225 take sqrt of both sides 3x=15 x=5 speed of stream=5 km/hr
 Problems-with-consecutive-odd-even-integers/696790: A fisherman can row a boat 8km downstream and return in 100min. If the speed of the stream is 2km per hour, find the speed of the boat in still water?1 solutions Answer 429420 by lwsshak3(6509)   on 2012-12-26 01:34:06 (Show Source): You can put this solution on YOUR website!A fisherman can row a boat 8km downstream and return in 100min. If the speed of the stream is 2km per hour, find the speed of the boat in still water? ** let x=speed of boat in still water x+2=downstream speed x-2=upstream speed speed=distance/travel time 8/(x+2)+8/(x-2)=100/60 LCD:(x+2)(x-2) 8(x-2)+8(x+2)=(100/60)*(x+2)(x-2) 8(x-2+x+2)=100(x+2)(x-2)/60 240(2x)=100(x^2-4) 480x=100x^2-400 100x^2-480x-400=0 10x^2-48x-40=0 solve by following quadratic formula: a=10, b=-48,c=-40 ans: x≈5.52 speed of boat in still water≈5.52 km/hr
 Age_Word_Problems/696866: THE SUM OF THE AGES OF SON AND FATHER IS 56 YERAS.AFTER 4 YEARS THE AGE OF THE FATHER WILL BE THREE TIMES THAT OF THE SON.FIND THE AGE OF THE FATHER? 1 solutions Answer 429413 by lwsshak3(6509)   on 2012-12-26 00:38:37 (Show Source): You can put this solution on YOUR website!THE SUM OF THE AGES OF SON AND FATHER IS 56 YERAS.AFTER 4 YEARS THE AGE OF THE FATHER WILL BE THREE TIMES THAT OF THE SON.FIND THE AGE OF THE FATHER? ** let x= age of father 56-x=age of son after 4 yrs x+4=age of father (56-x)+4=(60-x) age of son x+4=3(60-x) x+4=180-3x 4x=176 x=44 age of father: 44
 Age_Word_Problems/696869: Five years ago I was thrice as old as my son and ten years later I shall be twice as old as my son. How old are we now?1 solutions Answer 429411 by lwsshak3(6509)   on 2012-12-26 00:29:01 (Show Source): You can put this solution on YOUR website!Five years ago I was thrice as old as my son and ten years later I shall be twice as old as my son. How old are we now? let x=son's age now 5 yrs ago: x-5=son's age 3(x-5)=parent's age 10 yrs later: x+10=son's age 2(x+10)=parent's age parent's age 10 yrs later=parent's age 5 yrs ago plus 15 2(x+10)=15+3(x-5) 2x+20=15+3x-15 x=20 3(x-5)+5=50 son's age now: 20 parent's age now: 50
 Expressions-with-variables/696836: Please help me multiply these and put them in simplest form: 1.) ^2 . ^3 2.) . 1 solutions Answer 429401 by lwsshak3(6509)   on 2012-12-25 21:43:50 (Show Source): You can put this solution on YOUR website! 1.) ((b+4)/(2))^2 . ((3)/(b+4))^3 (b+4)^2/4*27/(b+4)^3 (1/4)*27/b+4 27/4(b+4) 2.) ((b+4)/(b-2)) . ((b^2-4)/(b^2-16)) ((b+4)/(b-2)) . (b+2)(b-2))/(b+4)(b-4) (b+2)/(b-4)
 Quadratic_Equations/696853: Find values of a and k for which each parabola contains the given points y-k = a(x+3)^2 ; (-5,1) (1,7) 1 solutions Answer 429397 by lwsshak3(6509)   on 2012-12-25 21:21:36 (Show Source): You can put this solution on YOUR website!Find values of a and k for which each parabola contains the given points y-k = a(x+3)^2 ; (-5,1) (1,7) ** y-k = a(x+3)^2 y=a(x+3)^2+k set up two equations with coordinates of given points: 1=a(-5+3)^2+k 7=a(1+3)^2+k .. 1=a(-2)^2+k 7=a(4)^2+k .. 1=4a+k 7=16a+k .. 4=16a+4k 7=16a+k .. -3=3k k=-1 .. 1=4a-1 4a=2 a=1/2 check:(using point (1,7) 7-(-1)=1/2(1+3)^2 8=8
 Quadratic-relations-and-conic-sections/696352: What is the radius of the circle given by the equation below? x^2 + 8x = -y^2 - 16y - 161 solutions Answer 428961 by lwsshak3(6509)   on 2012-12-21 01:17:49 (Show Source): You can put this solution on YOUR website!What is the radius of the circle given by the equation below? x^2 + 8x = -y^2 - 16y - 16 ** Standard form of a circle: , (h,k)=(x,y) coordinates of center, r=radius. To find the radius of given circle, convert given equation to standard form. x^2 + 8x = -y^2 - 16y - 16 complete the square: x^2+8x=-y^2-16y-16 x^2+8x+y^2+16y=-16 (x^2+8x+16)+(y^2+16y+64)=-16+16+64 r^2=64 r=8
 Quadratic-relations-and-conic-sections/695436: Hyperbola: 9x^2-16y^2-18x-32y-151=0 Center: Verticies: Foci: Asympototes: Graph: 9(x^2-2x+1)-16(y^2-2y+1)=151+16+9 9(x-1)^2-16(y-1)^2=1761 solutions Answer 428811 by lwsshak3(6509)   on 2012-12-20 03:09:27 (Show Source): You can put this solution on YOUR website!Hyperbola: 9x^2-16y^2-18x-32y-151=0 9x^2-18x-16y^2-32y-151=0 complete the square: (you already did with a small error which I have corrected) This is a hyperbola with horizontal transverse axis: (x-term listed first) Its standard form of equation: , (h,k)=(x,y) coordinates of center. Center:(1,-1) a^2=16 a=√16=4 Vertices: (1±a,-1)=(1±4,-1)=(-3,-1) and (5-1) .. b^2=9 b=√9=3 .. c^2=a^2+b^2=16+9=25 c=√25=5 Foci: (1±c,-1)=(1±5,-1)=(-4,-1) and (6-1) .. Asymptotes:(straight line equations that go thru center, of the form y=mx+b, m=slope, b=y-intercept) For hyperbolas with horizontal transverse axis: slope=±b/a=±3/4 Equation for asymptote with negative slope: y=-3x/4+b solve for b using coordinates of center. -1=-3*1/4+b b=-1/4 equation:y=-3x/4-1/4 .. Equation for asymptote with positive slope: y=3x/4+b solve for b using coordinates of center. -1=3*1/4+b b=-7/4 equation:y=3x/4-5/4 .. Graph: 9(x^2-2x+1)-16(y^2+2y+1)=151-16+9 9(x-1)^2-16(y+1)^2=144 (x-1)^2/16-(y+1)^2/9=1 .. See graph below: y=±((9(x-1)^2/16)-9)^.5-1
 Quadratic-relations-and-conic-sections/695930: Find the foci of the ellipse with the equation: ((x^2)/36))+((y^2)/(64))=11 solutions Answer 428810 by lwsshak3(6509)   on 2012-12-20 02:17:37 (Show Source): You can put this solution on YOUR website!Find the foci of the ellipse with the equation: ((x^2)/36))+((y^2)/(64))=1 This is an ellipse with vertical major axis: (denominator of y-term>denominator of x-term) Its standard form of equation: , a>b, (h,k)=(x,y) coordinates of center. .. For given equation: center: (0,0) a^2=64 b^2=36 c^2=a^2-b^2=64-36=28 c=√28≈5.3 foci: (0,0±c)=(0,0±√28)=(0,0±5.3)=(0,-5.3) and (0,5.3)
 Quadratic-relations-and-conic-sections/696070: How do I change this into H-K form to find the properties of an elipse: x^2+4y^2-6x-16y+21=01 solutions Answer 428808 by lwsshak3(6509)   on 2012-12-20 02:03:16 (Show Source): You can put this solution on YOUR website!How do I change this into H-K form to find the properties of an elipse: x^2+4y^2-6x-16y+21=0 complete the square x^2-6x+4y^2-16y+21=0 (x^2-6x+9)+4(y^2-4y+4)=-21+9+16 (x-3)^2+4(y-2)^2=4 (x-3)^2/4+(y-2)^2/1=1 This is an ellipse with horizontal major axis and center at (3,2) length of horizontal major axis=2a=4 length of minor axis=2b=2
 Quadratic-relations-and-conic-sections/696101: what is the equation for this conic section with An ellipse with vertices (-4, 0) and (4, 0) and a minor axis of length 6. 1 solutions Answer 428806 by lwsshak3(6509)   on 2012-12-20 01:49:06 (Show Source): You can put this solution on YOUR website!what is the equation for this conic section with An ellipse with vertices (-4, 0) and (4, 0) and a minor axis of length 6. ** This is an ellipse with horizontal major axis. (x-coordinate changes but y-coordinates do not)Its standard form of equation: , a>b, (h,k)=(x,y) coordinates of center .. For given ellipse: center: (0,0) length of horizontal major axis=8=2a a=4 a^2=16 length of minor axis=6=2b b=3 b^2=9 Equation of given ellipse:
 Trigonometry-basics/695318: In my class we are graphing tangent functions and I missed the past two days. In the equation... y=1/2tan2(x-5π/6)+1 I know the period= π/2 Horizontal asymptote= y=1 Steepness= 1/2 Phase shift = -5π/6 Now for my asymptote I ended up with ananswer of 13π/12+π/2k,kei. I do not feel my math is correct and wanted to know if that was the true answer.1 solutions Answer 428767 by lwsshak3(6509)   on 2012-12-19 20:13:36 (Show Source): You can put this solution on YOUR website!y=1/2tan2(x-5π/6)+1 Equation for tan function: y=tan(Bx-C), period=π/B, phase shift=C/B Rewrite given equation in this form: y=1/2tan(2x-10π/6)+1 B=2 period=π/B=π/2 1/4 period=π/8=3π/24 phase shift=C/B=(10π/6)/2=5π/6 (to the right) vertical asymptote at x=13π/12+2πk,k=any integer (function undefined at this point) horizontal asymptotes: none
 Rational-functions/695292: For the function: f(x): (5x-3)(x+4)/(-3x-4)(4x-3) What are the x and y intercepts?1 solutions Answer 428651 by lwsshak3(6509)   on 2012-12-19 02:58:53 (Show Source): You can put this solution on YOUR website!For the function: f(x): (5x-3)(x+4)/(-3x-4)(4x-3) What are the x and y intercepts? ** y-intercepts: set x=0 y=(5x-3)(x+4)/(-3x-4)(4x-3) y=(-3)(4)/-4)(-3) =-12/12 =-1 .. x-intercepts set y=0 (5x-3)(x+4)=0 x=3/5,-4
 Rational-functions/695670: what are the vertical, horizontal, and oblique asymptotes of F(x)=10/(x-3)(x^2-49) 1 solutions Answer 428650 by lwsshak3(6509)   on 2012-12-19 02:43:02 (Show Source): You can put this solution on YOUR website!what are the vertical, horizontal, and oblique asymptotes of F(x)=10/(x-3)(x^2-49) F(x)=10/(x-3)(x+7)(x-7) Horizontal Asymptote: y=0 or x-axis (degree of numerator less than degree of denominator) Vertical Asymptotes:x=-7, 3 and 7 (set denominator=0, then solve for x) Oblique asymptotes: none (To exist, numerator must be 1 degree higher than degree of denominator)
 logarithm/695491: Solve 1-log(3x+1)=log(x-2) log base =101 solutions Answer 428506 by lwsshak3(6509)   on 2012-12-18 02:30:16 (Show Source): You can put this solution on YOUR website!Solve 1-log(3x+1)=log(x-2) log base =10 1-log(3x+1)=log(x-2) 1=log(x-2)+log(3x+1) log(10)=log[(x-2)(3x+1)] (x-2)(3x+1)=10 3x^2-5x-2=10 3x^2-5x-12=0 (x-3)(3x+4)=0 x=3 or x=-4/3 (reject, (x-2)>0
 Equations/695450: The expression 2x^3+x^2-7x-6 factorizes into a product of three factors. Given that two of the factors are (x+1) and (x-2), write down its third factor. 1 solutions Answer 428505 by lwsshak3(6509)   on 2012-12-18 02:20:55 (Show Source): You can put this solution on YOUR website!The expression 2x^3+x^2-7x-6 factorizes into a product of three factors. Given that two of the factors are (x+1) and (x-2), write down its third factor. ** use synthetic division: .....2....|...2......1.......-7.....-6....... .......................4........10.....6.... ..............2.......5.........3......0... (x-2)(2x^2+5x+3)=0 (x-2)(x+1)(2x+3)=0 third factor: (2x+3)
 Equations/695472: Factorise x^3+3x^2-4x-12 completely.1 solutions Answer 428504 by lwsshak3(6509)   on 2012-12-18 01:53:16 (Show Source): You can put this solution on YOUR website!Factorise x^3+3x^2-4x-12 completely. x^3+3x^2-4x-12 x^2(x+3)-4(x+3) (x^2-4)(x+3) (x+2)(x-2)(x+3)
 Length-and-distance/695474: Write the equation of a line that passes through the points (4,4) and (-2,1). Your answer should be in slope intercept form (y = mx + b) im so confused i have no clue how to do any of this..1 solutions Answer 428502 by lwsshak3(6509)   on 2012-12-18 01:45:19 (Show Source): You can put this solution on YOUR website!Write the equation of a line that passes through the points (4,4) and (-2,1). Your answer should be in slope intercept form (y = mx + b) ** equation of a line: y=mx+b, m=slope, b=y-intercept slope=∆y/∆x=(4-1)/(4-(-2))=3/6=1/2 equation y=(1/2)x+b solve for b using coordinates of one of the given points(4,4) (either point can be used) 4=(1/2)4+b b=2 equation of given line: y=x/2+2
 Percentage-and-ratio-word-problems/695481: the ratio of two no is 3:5, and their difference is 46. find the larger no?1 solutions Answer 428501 by lwsshak3(6509)   on 2012-12-18 01:36:01 (Show Source): You can put this solution on YOUR website!the ratio of two no is 3:5, and their difference is 46. find the larger no. let x=larger no. y=smaller no. 3/5=y/x x-y=46 y=x-46 3/5=(x-46)/x 3x=5x-230 2x=230 x=115 larger no.=115
 Travel_Word_Problems/695475: A plane leaves the airport and flies East at 200 mph. 2 hours later, another plane leaves and flies West at 150 mph. Write and solve a system of linear equations that can be used to determine when the planes are 750 miles apart.1 solutions Answer 428500 by lwsshak3(6509)   on 2012-12-18 01:26:08 (Show Source): You can put this solution on YOUR website!A plane leaves the airport and flies East at 200 mph. 2 hours later, another plane leaves and flies West at 150 mph. Write and solve a system of linear equations that can be used to determine when the planes are 750 miles apart. ** let x-2=travel time of plane flying East x=travel time of plane flying West(when planes are 750 miles apart) distance=*travel time*speed equation: 150(x-2)+200x=750 150x-300+200x=750 350x=1050 x=3 planes are 750 miles apart after 3 hrs
 Travel_Word_Problems/695477: The speed of a stream is 3 km/h. A boat travels 4 km upstream in the same time it takes to travel 10 km downstream. What is the speed of the boat.1 solutions Answer 428499 by lwsshak3(6509)   on 2012-12-18 00:59:03 (Show Source): You can put this solution on YOUR website!The speed of a stream is 3 km/h. A boat travels 4 km upstream in the same time it takes to travel 10 km downstream. What is the speed of the boat. ** let x=speed of the boat in still water x-3=speed upstream x+3=speed downstream travel time=distance/speed (same for upstream and downstream) 4/(x-3)=10/(x+3) 10x-30=4x+12 6x=42 x=6 speed of the boat in still water=6 km/hr
 Age_Word_Problems/695458: The ratio of the ages of Rajesh to that of Ramesh is 5 : 8. After 10 years the new ratio of their ages will be 7 : 10. What is the age of Ramesh at present?1 solutions Answer 428498 by lwsshak3(6509)   on 2012-12-18 00:48:32 (Show Source): You can put this solution on YOUR website!The ratio of the ages of Rajesh to that of Ramesh is 5 : 8. After 10 years the new ratio of their ages will be 7 : 10. What is the age of Ramesh at present? ** let y=Rajesh's present age let x=Ramesh's present age y/x=5/8 y=5x/8 .. After 10 years: y+10=Rajesh's age x+10=Ramesh's age (y+10)/(x+10)=7/10 7x+70=10y+100 7x+70=10(5x/8)+100 7x+50x/8=30 56x+50x=240 6x=240 x=40 Ramesh's present age=40
 Travel_Word_Problems/695463: A bus leave Sacramento traveling South at 40 mph. A half hour hour later, a car leaves from the same location on the same route at 60 mph. How far from Sacramento will the car overtake the bus?1 solutions Answer 428496 by lwsshak3(6509)   on 2012-12-18 00:14:31 (Show Source): You can put this solution on YOUR website!A bus leave Sacramento traveling South at 40 mph. A half hour hour later, a car leaves from the same location on the same route at 60 mph. How far from Sacramento will the car overtake the bus? ** let x=travel time of car (x+.5)=travel time of bus distance=speed*travel time(the same for car and bus) .. 60x=40(x+.5) 60x=40x+20 20x=20 x=1 distance car overtakes bus=60x=60 miles
 Trigonometry-basics/694532: I don't know how to find the exact value of cos 23pi/12 using the properties of special triangles1 solutions Answer 428052 by lwsshak3(6509)   on 2012-12-15 17:27:47 (Show Source): You can put this solution on YOUR website!find the exact value of cos 23pi/12 using the properties of special triangles Use cos half-angle identity cos(x/2)=±√[(1+cos(x)/2] cos(23π/12)=cos(23π/6)/2)=√[(1+cos(23π/6)/2] For cos(23π/6) use reference angle π/6 in quadrant IV where cos>0 cos(23π/6)=cos(π/6)=√3/2 cos(23π/12) =cos(23π/6)/2) =√[(1+cos(23π/6)/2] =√[(1+√3/2/2] calculator check: cos(23π/12)≈0.9659.. √[(1+√3/2/2]≈0.9659..
 absolute-value/693974: |4x-2 divided by 5| = |6x+3 divided by 2|1 solutions Answer 427963 by lwsshak3(6509)   on 2012-12-15 03:30:57 (Show Source): You can put this solution on YOUR website!|4x-2 divided by 5| = |6x+3 divided by 2| |(4x-2)/5|=|(6x+3)/2| solve for 2 equations (4x-2)/5=(6x+3)/2 5(6x+3)=2(4x-2) 30x+15=8x-4 22x=-19 x=-19/22 check: |(4x-2)/5|=|(6x+3)/2| |(4(-19/22)-2)/5|=|(6(-19/22)+3)/2| |-1.0909|=|-1.0909| 1.0909=1.0909 check ok .. (4x-2)/5=-(6x+3)/2 -5(6x+3)=2(4x-2) -30x-15=8x-4 -38x=11 x=-11/38 check: |(4x-2)/5|=|(6x+3)/2| |(4(-11/38)-2)/5|=|(6(-11/38)+3)/2| |-.6316|=|.6316| .6316=.6316 check ok solution: x=-19/22, -11/38
 absolute-value/694488: |10x+65|=7x+25 1 solutions Answer 427960 by lwsshak3(6509)   on 2012-12-15 03:08:41 (Show Source): You can put this solution on YOUR website!|10x+65|=7x+25 solve for 2 possibilities .. 10x+65=7x+25 3x=-40 x=-40/3 check: (10x+65)=7x+25 |10*-40/3+65|=7*-40/3+25 |10*-40/3+65|=7*-40/3+25 |-68.33|=-68.33 68.33≠-68.33 does not check, no solution .. -(10x+65)=7x+25 -10x-65=7x+25 -17x=90 x=-90/17 check: |10x+65|=7x+25 |10*-90/17+65|=7*-90/17+25 |12.06|=-12.06 12.06≠-12.06 does not check, no solution
 Exponential-and-logarithmic-functions/694003: how do you solve these equations 1) e^-x=5 2) 11^5x=33 3) 4e^2x=171 solutions Answer 427957 by lwsshak3(6509)   on 2012-12-15 02:06:54 (Show Source): You can put this solution on YOUR website!how do you solve these equations 1) e^-x=5 -xlne=ln5 x=-ln5 .. 2) 11^5x=33 5xlog11=log33 5x=log33/log11 x=(log33/log11)/5 x≈0.2916 .. 3) 4e^2x=17 ln4+2xlne=ln17 2x=ln17-ln4 x=(ln17-ln4)/2 x≈.7235
 Quadratic-relations-and-conic-sections/694194: what is the vertex, axis of symmetry, and direction of opening for y=x^2-18x+79?1 solutions Answer 427927 by lwsshak3(6509)   on 2012-12-14 20:30:35 (Show Source): You can put this solution on YOUR website!what is the vertex, axis of symmetry, and direction of opening for y=x^2-18x+79? complete the square y=(x^2-18x+81)+79-81 y=(x-9)^2-3 This is an equation of a parabola that opens upwards. (lead coefficient positive) Its standard form: y=A(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex. For given equation: y=(x-9)^2-3 vertex:(9,-3) Axis of symmetry: x=9