Algebra ->  Tutoring on algebra.com -> See tutors' answers!      Log On

 Tutoring Home For Students Tools for Tutors Our Tutors Register Recently Solved
 By Tutor
| By Problem Number |

Tutor:

# Recent problems solved by 'RAY100'

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, >>Next

 logarithm/199745: if n is a natural number such that n=p1 power a1 *p2 power a2*p3 power a3..............*pk power ak and pk are distinct primes , then show that log n>=k log21 solutions Answer 150190 by RAY100(1637)   on 2009-06-11 19:43:08 (Show Source): You can put this solution on YOUR website!n= p(1)^a(1) + p(2)^a(2) + p(3)^a(3) + .........+ p(k)^a(k) . n is a natural number,,,this leads to n=1 or larger integer. ,,,, AND it limits each term of the sequence to a positive number. That is, the p"s cannot be + or -, as this would restrict the terms to an even number, to make n positive, which was not stated. . Likewise, the "a" values cannot be negative, leading to a fraction, or a fraction, which would lead to not whole numbers. . The given that p(k) is a distinct prime, leads to the min value of p(k) being the min prime, or 2 .,,,or larger,,, (1 is a special number, not prime) . n = something positive * a number 2 or larger raised to a positive number( making it >2) . n>2^ k . and taking log of both sides . log n > log 2^k or log n > k log 2
 Linear_Equations_And_Systems_Word_Problems/199742: Explain in your own words, using the definition of probability why: a) the probability of an event that cannot occur is 0; b) the probability of an event that must occur is 1. 1 solutions Answer 150188 by RAY100(1637)   on 2009-06-11 19:19:26 (Show Source): You can put this solution on YOUR website!Probability is the ratio of the number going the desired way, to the total possible numbers' . something that will not happen has 0 chances / total possible chances., or P=0 . If something is certain, we know all of the chances will be in numerator / same number = 1 . And the P = 1,
 Expressions-with-variables/199722: Can someone please help me with this: The Acme Class Ring Company designs and sells two types fo rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. Its takes 3 man-hours to make one VIP ring versus 2 man-hours to make one SST ring. How many of each type of ring should be made daily to maximize the companys profit, if the profit on a VIP ring is \$40 and an SST ring is \$35? a. 14 VIP AND 10 SST b. 16 VIP AND 8 SST c. 12 VIP AND 12 SST1 solutions Answer 150174 by RAY100(1637)   on 2009-06-11 18:30:05 (Show Source): You can put this solution on YOUR website!Let v = # VIP Rings ,,,,and s = # SST Rings , (1) 3 v + 2 s = 60 hrs . (2) v + s = 24,,,,,or v = 24 -s . subst in (1),,,, 3(24-s) +2 s = 60 . 72 -3s +2s =60 . 12 = s . v = 24-s=24-12=12,,,,which is answer (C) . Profit from 12 each is 12(40) + 12 (35) = \$ 900, made within guidelines . Checking the other options . A) 14(40) +10(35) =\$ 910 BUT checking hrs, 14(3) + 10(2) = 62 hrs,,,,over limit of 60 . B) 12(40) + 8(35) = \$ 760,,,,, low with hrs of 12(3) +8(2) = 52,,, also low
 Human-and-algebraic-language/199746: area of a sale. The area of in square meters for a triangular sale is given by A(x)=x^2+5x+6 Find A(5), if the hignt of the sail is x+3 meters, then what is the lenght of the sail? 1 solutions Answer 150171 by RAY100(1637)   on 2009-06-11 17:17:52 (Show Source): You can put this solution on YOUR website!A(x) = x^2 +5x +6 . a(5) = (5)^2 + 5(5) +6 = 56 . A(x) = x^2 +5x +6 = 1/2 ( h) (l) = (1/2) (x+3) h,,,,,,,area of triangle = 1/2 base * height . { (x+3)(x+2) } / (1/2) ( x+3) = 2(x+2) = h . check . A(5) = 56, (x+3)= 8,, A = 1/2 * 8 * h = 56,,,,,h= 112/8 = 14 . h=2(x+2) = 2 (5+2) =14,,,,,,ok
 Linear-equations/199790: What is the y-intercept of 3x - 2y = 0 1 solutions Answer 150169 by RAY100(1637)   on 2009-06-11 17:07:17 (Show Source): You can put this solution on YOUR website!3x -2y =0 . to find y intercept ,,,let x =0 ( and vice versa ) . at x=0, y=0,,,y intercept is y=0
 Polynomials-and-rational-expressions/199786: Please help me solve this problem 2x^2-14x+3x-211 solutions Answer 150157 by RAY100(1637)   on 2009-06-11 16:04:58 (Show Source): You can put this solution on YOUR website!when there are four terms, try factoring by grouping . 2x^3 -14x +3x -21 . 2x (x-7) +3(x-7},,,,,,like ab +cb= (a+c)b ,,,but b=(x-7) . (2x+3) (x-7) . check by subst x=1 in original and answer, ok
 Linear-equations/199769: A circular path around a lake has a diameter of 1,500 feet (ft). Pranotti jogs around the path 3 times for her morning run. How far does she run? Use 3.14 for and round your answer to the nearest foot.1 solutions Answer 150127 by RAY100(1637)   on 2009-06-11 12:57:04 (Show Source): You can put this solution on YOUR website!for 3 times around, let Distance = 3 * Circumference . d = 3 * 2 *pi * radius, radius = 1500 / 2 = 750 . d = 3 * 2 * 3.14 * 750 = 14,130 ft
 percentage/199770: The following pie chart shows the budget for a local company. The total budget is \$520,000. Find the actual amount budgeted in the category of Taxes. Research 10% Production 40% operating expense 25% Taxes 15% Miscellaneous 10%1 solutions Answer 150126 by RAY100(1637)   on 2009-06-11 12:51:59 (Show Source): You can put this solution on YOUR website!If total budget is \$ 520,000, and taxes are 15 % . .15 * \$520, 000 = \$ 78,000 . check,,,,78 /520 =.15 ,,,,ok .
 Polynomials-and-rational-expressions/199766: Factor the polynomial below completely, given that the binomial following it is a factor of the polynomial. x^3-4x^2+x+6, x+1 A) (x+1)(x^2-5x+6) B) (x+1)(x-3)(x-2) C) (x+1)(x-3)(x+2) D) (x+1)(x+3)(x-2)1 solutions Answer 150125 by RAY100(1637)   on 2009-06-11 12:47:57 (Show Source): You can put this solution on YOUR website!to factor ,,,x^3 -4x^2 +x +6,,,,knowing (x+1) is a factor,,,,use poly division or synthetic division . ,,,,,,-1,,,,1,,,,-4,,,,,+1,,,,6 ,,,,,,,,,,,,,,,,,,,-1,,,,,+5,,,-6 ,,,,,,,,,,,,,,,__________________ ,,,,,,,,,,,,,,1,,,,-5,,,,+6,,,,,0 . (x+1)(x^2 -5x +6),,,,,,,now just factor 2nd term . (x+1) ( x-3) (x-2),,,,,or answer B . to check, multiply factors to reach original,,,,ok
 Polynomials-and-rational-expressions/199767: Translate the verbal expression into an algebraic expression: The difference of n and the square of k A) (n-k)^2 B) n^2 - k C) n-k^2 D) -n*k^21 solutions Answer 150124 by RAY100(1637)   on 2009-06-11 12:34:53 (Show Source): You can put this solution on YOUR website!difference is subtraction . ( n ) - ( k^2 ) . therefore c) n-k^2 .
 Circles/199723: Two chords of a circle are perpendicular and congruent, does one of them have a diameter?1 solutions Answer 150111 by RAY100(1637)   on 2009-06-11 09:22:55 (Show Source): You can put this solution on YOUR website!Please see answer to problem # 199732 thanks
 Circles/199724: Two chords of a circle are perpendicular and congruent, does one of them have a diameter?1 solutions Answer 150109 by RAY100(1637)   on 2009-06-11 09:21:19 (Show Source): You can put this solution on YOUR website!Please see answer to problem # 199732 thanks
 Circles/199725: Two chords of a circle are perpendicular and congruent, does one of them have a diameter?1 solutions Answer 150108 by RAY100(1637)   on 2009-06-11 09:19:48 (Show Source): You can put this solution on YOUR website!Please see answer to problem # 199732 thanks
 Circles/199726: Two chords of a circle are perpendicular and congruent, does one of them have a diameter?1 solutions Answer 150107 by RAY100(1637)   on 2009-06-11 09:18:14 (Show Source): You can put this solution on YOUR website!Please see answer to problem # 199732 thanks
 Circles/199727: Two chords of a circle are perpendicular and congruent, does one of them have a diameter?1 solutions Answer 150106 by RAY100(1637)   on 2009-06-11 09:17:01 (Show Source): You can put this solution on YOUR website!Please see answer to problem # 199732 thanks
 Circles/199728: Two chords of a circle are perpendicular and congruent, does one of them have a diameter?1 solutions Answer 150105 by RAY100(1637)   on 2009-06-11 09:13:44 (Show Source): You can put this solution on YOUR website!please see solution to problem # 199732 thanks
 Geometry_proofs/199731: Given: TR ≅ TY Prove: ΔTRY is isosceles. Choose the corresponding reason for each statement. 1. TR ≅ TY 2. TR=TY 3. ΔTRY is isosceles.1 solutions Answer 150103 by RAY100(1637)   on 2009-06-11 09:09:01 (Show Source): You can put this solution on YOUR website!1. given . 2 definition of congruence (sides of equal length) . 3 definition of an isosceles triangle ( 2 sides equal)
 Equations/199735: solve each equation, is whats in my book. 4x+5x-10=35 and 9x +6x-12x= -7x+2x-12+5x1 solutions Answer 150102 by RAY100(1637)   on 2009-06-11 09:02:40 (Show Source): You can put this solution on YOUR website!(1) 4x +5x -10 = 35 9x -10 =35,,,,,combining like terms 9x =45,,,,,,,,adding 10 to both sides x=5,,,,,,,,,,,,,dividing by 9 . (2) 9x+6x-12x = -7x +2x -12 +5x 3x = -12,,,,,,,,,combining like terms x= -4,,,,,,,,dividing by 3 .
 Circles/199732: Two chords of a circle are perpendicular and congruent, does one of them have a diameter?1 solutions Answer 150100 by RAY100(1637)   on 2009-06-11 08:52:44 (Show Source): You can put this solution on YOUR website!Very interesting question Let's start with a rough sketch of a circle, now one chord, now another perpendicular chord that goes thru center. This is the situation that answers your question, yes it can happen but it does not have to. . The principle that puts the second chord thru the center is,,,, it must be a perpendicular bisector. ALL perp bisectors go thru center, hence could be diameters. . It is easy to take your sketch, and just slide the second chord to one side or the other. It does not go thru center, and is not a diameter. Your problem did not specify bisection. . Another interesting construction, again draw a rough circle and one chord. Draw a second chord, perpendicular to first but located at an end of the first chord. NOW, if we connect the other ends of the chord, we have a triangle. But, a very special triangle, it is a right inscribed triangle, that divides the circle into two semicircles, and has the hypotenuse as the diameter. Good luck with class
 logarithm/199294: Prove that 7^(n+2)-35(7^n-1)/44(7^n+2) is equal to 1/491 solutions Answer 149806 by RAY100(1637)   on 2009-06-08 14:24:08 (Show Source): You can put this solution on YOUR website![ 7^(n+2) -35*7^9n-1)] / [ 44(7^(n+2) ) ] = 1/49 . [ 1-35*7^-3] / 44 = 1/49 . [ 1 - 35 / (49*7) ] / 44 = 1/49 . [ 1-5/49] / 44 = 1/49 . [49/49 -5/49 ] / 44 = 1/49 . [ 44 / 49 ] / 44 = 1/49 . (44/49) * (1/44) = 1/49 = 1/49,,,,,,ok
 Polynomials-and-rational-expressions/199341: 1.) (r^-4) ( -6r^2t^2) 2.) w^3 / -6w^-6 3.) (k^6) (k^3)^5 4.) t^-9 / g^-91 solutions Answer 149804 by RAY100(1637)   on 2009-06-08 14:07:01 (Show Source): You can put this solution on YOUR website!Remember negative exponent is reciprocal,,,,a^-2 = 1/a^2 . AND , to divide common bases,,,substract exponents,,,,a^4/a^2=a^(4-2) = a^2 . (1) (r^-4)(-6r^2t^2) = -6 r^-2t^2= -6t^2 / r^2 . (2) w^3 / (-6w^-6) = w^9/-6 = (-1/6) w^9 . (3) k^6 / (k^3)^5 = k^6/k^15 =k^-9 = 1/k^9 . (4) t^-9 / q^-9 = q^9/t^9 = (q/t)^9 . check by assigning numbers to variables and checking original and answer,,,all ok
 expressions/199349: 4(P-9)=641 solutions Answer 149803 by RAY100(1637)   on 2009-06-08 13:50:49 (Show Source): You can put this solution on YOUR website!4(p-9) =64 . p-9 = 64/4 = 16 . p =16 +9 =25 . check . 4(25-9) =64 . 4(16) =64,,,,,ok
 Rational-functions/199343: Give the equations of any vertical,horizontal, or oblique asymptotes. 1.f(x)= 1/x-2 2.f(x)= x+2/x-2 3.f(x)= x^2+x-2/x-21 solutions Answer 149802 by RAY100(1637)   on 2009-06-08 13:47:38 (Show Source): You can put this solution on YOUR website!please see problem 199342
 expressions/199345: if y times 1 minus x=z than what is x?1 solutions Answer 149801 by RAY100(1637)   on 2009-06-08 13:42:34 (Show Source): You can put this solution on YOUR website!y * (1-x) = z . y-xy =z . -xy = z -y . x = (z-y) / ( -y) = -z/y +1 =1-z/y . check by letting x=4, y=2, then z=-6,,,,ok for both original and answer
 expressions/199346: -6r + s - rs r=5 s=71 solutions Answer 149799 by RAY100(1637)   on 2009-06-08 13:33:47 (Show Source): You can put this solution on YOUR website!-6r +s -rs . r(-6-s) +s . 5(-6-7) +7 . 5(-13) +7 . -65 +7 . -58 . check using direct subst into initial eqn . -6(5)+(7) -(5)(7) = -30 +7 -35 = -65 +7 =-58,,,,ok
 Rational-functions/199342: Give the equations of any vertical,horizontal, or oblique asymptotes. 1.f(x)= 1/x-2 2.f(x)= x+2/x-2 3.f(x)= x^2+x-2/x-2 1 solutions Answer 149796 by RAY100(1637)   on 2009-06-08 13:13:42 (Show Source): You can put this solution on YOUR website!Remember,,, form y= a(n)x^n +..... / b(m) x^m +...... . for VERTICAL ASYMPTOTES,,,,,,find zero"s of denominator . in all 3 cases above,,, (x-2) =0,,,or x=2 is a vertical asymptote . For HORIZONTAL ASYMPTOTES,,,, . if n less than m,,,,,,y=0 . if n=m,,,,,y = a(n)/b(m) . n>m,,,,,,, no horizontal asymptote . In the 1st case,,, n=0,m=1,,,or n is less than m,,,,,y=0 is hor asymptote . in the 2nd case,,,n=1,m=1,,or n=m,,,,y = a(n)/b(m) = 1/1 =1,,,, y=1 is hor asymptote . in the 3rd case, n=2,m=1 ,,or n>m,,,,,therefore no hor asymptote . for OBLIQUE ASYMPTOTES (SLANT) . if n=(m+1),,,divide numerator by denominator ,,,,and set answer (without remainder) =y . in the 3rd case above ,,,n=2,m=1,,or n=(m+1),,,,therefore there is a SLANT asymptote . ( x^2 +x -2) / (x-2) = x+3 +4/(x-2) . setting y = x+3,,,,,,for slant asymptote . .We might also look for x intercepts,,,,which are zero's of numerator. . case 2 ,,,has one at x=-2 . case 3,,,has one at x=-2,,and another at x=+1 .
 Functions/199338: Hello! Find a function whose graph is a parabola with vertex (5, -7) and that passes through the point (4, 1). thanks for your help!1 solutions Answer 149795 by RAY100(1637)   on 2009-06-08 12:39:10 (Show Source): You can put this solution on YOUR website!There are actually two parabolas that meet this criteria, a "y" parabola, and an "x" parabola . the standard form for a "y" parabola is ,,,, ( y-k) = a (x-h)^2, where (h,k) is the vertex . substituting our data,,,, vertex at (5, -7) and (4,1),,,,, ( y-(-7) ) = a (x-5)^2 . @ ( 4,1),,,, (1) +7 =a ( 4-5)^2,,,,8=a(1),,,, a=8 . "y" parabola is y+7 = 8(x-5)^2,,,or y= 8(x-5)^2 -7 . to check substitute in both given points,,,ok . The standard form for an "x" parabola is,,,,,(x-h) =a ( y-k)^2 . or (x-5) = a (y+7)^2,,,,,and @ (4,1),,,,, (4-5) = a (1+7)^2,,,,a= -1/64 . or (x-5) = -1/64 (y+7)^2,,,,,or x= -1/64 (y+7) ^2 +5 . to check substitute in both sets of points,,,,,,ok
 Travel_Word_Problems/199340: Fred paddled for 5 hours with a 6km/hr current to reach a campsite. The return trip against the same current took 10 hours. Find the speed of Fred's canoe in still water.1 solutions Answer 149793 by RAY100(1637)   on 2009-06-08 11:59:50 (Show Source): You can put this solution on YOUR website!Let x = velocity in still water . Distance = Velocity * Time . D1 = (x+6) 5 = 5x +30 . D2 = (x-6) 10 = 10x -60 . but D1 = D2 . 5x +30 = 10x -60 . 90 = 5x . 18 = x . checking . (18 +6) * 5 = (18-6) 10 . 120 =120,,,,ok
 Points-lines-and-rays/199329: I need your assistant again I miss this one on my quiz and I need to know the correct way to do this. Find the volume of a refrigerator that is a rectangular solid and is 2 meter tall and has a base that is 1.2 meters square. thank you so much!!!!!!!!!!!!!!!!!!!!1 solutions Answer 149792 by RAY100(1637)   on 2009-06-08 11:49:59 (Show Source): You can put this solution on YOUR website!Remember that the volume of a rectangular solid, or prism ,,,,Vol = B * h,,,, where B is the Area of the base,,,,and h is the height . vol = ( 1.2 *1.2 ) * 2 = 2.88 sq meters ,
 expressions/199332: 8x+2=7(x-4)+61 solutions Answer 149784 by RAY100(1637)   on 2009-06-08 11:03:15 (Show Source): You can put this solution on YOUR website!Remember order of operations . 8x +2 = 7(x-4) +6 . 8x +2 = 7x -28 +6 . 8x -7x = -2 -28 +6 . x= -24 . check . 8( -24) +2 = 7( ( -24) -4 ) +6 . -192 +2 = -196 +6 . -190 = -190,,,,,,ok .
 Points-lines-and-rays/199331: I'm having a really hard time figuring this problem out please help What is the area in feet of circular tablecloth that has a diameter of 42 inches?1 solutions Answer 149781 by RAY100(1637)   on 2009-06-08 10:05:49 (Show Source): You can put this solution on YOUR website!Remember that Area = pi * rad^2 . we are given diameter = 42, or radius = 21 ,,,,(42/2) . Area = pi * r^2 = pi * 21^2 = pi * 441 = 1385.44 inches ^2 . . an obscure Area formula is A = pi d^2 /4 = pi 42^2 /4 = 1385.44 also .