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 'nerdybill'

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 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 4740..4769 , 4770..4799 , 4800..4829 , 4830..4859 , 4860..4889 , 4890..4919 , 4920..4949 , 4950..4979 , 4980..5009 , 5010..5039 , 5040..5069 , 5070..5099 , 5100..5129 , 5130..5159 , 5160..5189 , 5190..5219 , 5220..5249 , 5250..5279 , 5280..5309 , 5310..5339 , 5340..5369 , 5370..5399 , 5400..5429 , 5430..5459 , 5460..5489 , 5490..5519 , 5520..5549 , 5550..5579 , 5580..5609 , 5610..5639 , 5640..5669 , 5670..5699 , 5700..5729 , 5730..5759 , 5760..5789 , 5790..5819 , 5820..5849 , 5850..5879 , 5880..5909 , 5910..5939 , 5940..5969 , 5970..5999 , 6000..6029 , 6030..6059 , 6060..6089 , 6090..6119 , 6120..6149 , 6150..6179 , 6180..6209 , 6210..6239 , 6240..6269 , 6270..6299 , 6300..6329 , 6330..6359 , 6360..6389 , 6390..6419 , 6420..6449 , 6450..6479 , 6480..6509 , 6510..6539 , 6540..6569 , 6570..6599 , 6600..6629 , 6630..6659 , 6660..6689 , 6690..6719 , 6720..6749 , 6750..6779 , 6780..6809 , 6810..6839 , 6840..6869 , 6870..6899 , 6900..6929 , 6930..6959 , 6960..6989, >>Next

 Quadratic-relations-and-conic-sections/752412: find the foci, vertices and length of the two axis of the hyperbola 5x^2-4y^2=801 solutions Answer 457737 by nerdybill(6963)   on 2013-05-25 09:51:13 (Show Source): You can put this solution on YOUR website!form of horizontal hyperbola: (x-h)^2/a^2 - (y-k)^2/b^2 = 1 . a= b= 8 + 20 = c^2 28 = c^2 = c . vertex: (0,0) . foci: (0,+-) . asymptotes: y = +-(b/a)x y = +-x y = +-x
 logarithm/752148: log(2x + 3)=log 71 solutions Answer 457573 by nerdybill(6963)   on 2013-05-24 01:00:04 (Show Source): You can put this solution on YOUR website!log(2x + 3)=log 7 2x + 3 = 7 2x = 4 x = 2
 test/752110: Solve equation: First problem: 4g^2-32g=0 Second problem: 3m^2=-6m1 solutions Answer 457563 by nerdybill(6963)   on 2013-05-23 22:23:02 (Show Source): You can put this solution on YOUR website!First problem: 4g^2-32g=0 factor out common factor of 4g: (4g)(g-8)=0 setting each term to zero: g = {0, 8} . Second problem: 3m^2=-6m 3m^2+6m = 0 factor out common factor of 3m: (3m)(m+2) = 0 setting each term to zero: m = {0, -2}
 Quadratic-relations-and-conic-sections/752059: how do you work out x^2-4y^2-2x-24y-39=01 solutions Answer 457550 by nerdybill(6963)   on 2013-05-23 20:24:46 (Show Source): You can put this solution on YOUR website!x^2-4y^2-2x-24y-39=0 reorder terms: x^2-2x-4y^2-24y = 39 group terms: (x^2-2x)-(4y^2+24y) = 39 (x^2-2x)-4(y^2+6y) = 39 complete squares: (x^2-2x+1)-4(y^2+6y+9) = 39+1-36 (x-1)^2-4(y+3)^2 = 4 (x-1)^2 /4 - (y+3)^2 = 1 . This is a horizontal hyperbola (h,k) is (1,-3) a is 2 b is 1
 test/751858: 3 ( log 5 - log 3 ) - ( log 5 - 2 log 6 ) = 2 - log n , find n. 1 solutions Answer 457457 by nerdybill(6963)   on 2013-05-23 09:40:57 (Show Source): You can put this solution on YOUR website!3 ( log 5 - log 3 ) - ( log 5 - 2 log 6 ) = 2 - log n , find n. . 3 ( log 5 - log 3 ) - ( log 5 - 2 log 6 ) = 2 - log n 3log 5 - 3log 3 - ( log 5 - 2 log 6 ) = 2 - log n log 5^3 - log 3^3 - ( log 5 - 2 log 6 ) = 2 - log n log 125 - log 27 - ( log 5 - 2 log 6 ) = 2 - log n log 125 - log 27 - ( log 5 - log 6^2 ) = 2 - log n log 125 - log 27 - ( log 5 - log 36 ) = 2 - log n log 125 - log 27 - log 5 + log 36 = 2 - log n log 125/27 - log 5 + log 36 = 2 - log n log 125/(27*5) + log 36 = 2 - log n log (125*36)/(27*5) = 2 - log n log (125*36)/(27*5) = 2 - log n log (125*36)/(27*5) - 2 = -log n -[log (125*36)/(27*5) - 2] = log n 10^(-[log (125*36)/(27*5) - 2]) = n 10^(-[log (4500)/(27*5) - 2]) = n 10^(-[log 900/27 - 2]) = n 10^(-[log 100/3 - 2]) = n 10^(-[1.52287874528 - 2]) = n 10^(0.4771212547196624372950) = n 3 = n
 Inverses/751191: If y varies inversely as x, and y=18 when x=3, find y when x = 8. y=____(simplify your answer.) 1 solutions Answer 457039 by nerdybill(6963)   on 2013-05-21 13:14:25 (Show Source): You can put this solution on YOUR website!If y varies inversely as x, and y=18 when x=3, find y when x = 8. y=____(simplify your answer.) . Inverse variation: y = k/x using:y=18 when x=3 we can find k: 18 = k/3 54 = k . our equation: y = 54/x now we can answer:find y when x = 8 y = 54/8 y = 6.75
 logarithm/751129: If log[2](7) = a and log[2](5) = b express in terms of a and b the formulas i) log[2](35) ii) log [2](2.8) n.b. [x] is the log base (Y) is the number after the base number Please help! 1 solutions Answer 457007 by nerdybill(6963)   on 2013-05-21 10:49:48 (Show Source): You can put this solution on YOUR website!If log[2](7) = a and log[2](5) = b express in terms of a and b the formulas i) log[2](35) log[2](7*5) log[2](7) + log[2](5) a + b ii) log [2](2.8) log [2](7 * .4) log [2](7 * 4/10) log [2](7) + log [2](4/10) log [2](7) + log [2](4) - log [2](10) log [2](7) + log [2](2^2) - log [2](5*2) log [2](7) + log [2](2^2) - (log [2](5)+log [2](2)) log [2](7) + log [2](2^2) - (log [2](5)+log [2](2^1)) log [2](7) + log [2](2^2) - (b+1) log [2](7) + log [2](2^2) -b-1 a + 2 -b-1 a-b+1
 Exponential-and-logarithmic-functions/751125: the max population that earth can sustain is 40 billion. if the current population is 4.2 billion, in how many years will the max population be reached? Assume that each year the population is 2% more than the previous year.1 solutions Answer 456998 by nerdybill(6963)   on 2013-05-21 10:11:28 (Show Source): You can put this solution on YOUR website! the max population that earth can sustain is 40 billion. if the current population is 4.2 billion, in how many years will the max population be reached? Assume that each year the population is 2% more than the previous year. . Exponential growth equation: A = Pe^(rt) the problem give us: P is 4.2 A is 40 r is .02 . 40 = 4.2e^(.02t) 40/4.2 = e^(.02t) ln(40/4.2) = .02t ln(40/4.2)/.02 = t 112.69 = t or 113 years = t
 Average/751098: 40% OF A HOUSE NUMBER IS 48 WHAT IS THE NUMBER OF THE HOUSE1 solutions Answer 456997 by nerdybill(6963)   on 2013-05-21 10:07:06 (Show Source): You can put this solution on YOUR website! 40% OF A HOUSE NUMBER IS 48 WHAT IS THE NUMBER OF THE HOUSE . Let x = the house number then .40x = 48 x = 48/.40 x = 120
 Circles/751118: Find the equation of the circle that is tangent to the x-axis and the circle is at (-7,4).1 solutions Answer 456995 by nerdybill(6963)   on 2013-05-21 10:03:37 (Show Source): You can put this solution on YOUR website!Find the equation of the circle that is tangent to the x-axis and the circle is at (-7,4). . Plotting the center on graph, we can see that the distance between the center and the x-axis is 4. Therefore, the radius is 4. . Standard form of a circle is: (x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius . plug in our data: (x-(-7))^2 + (y-4)^2 = 4^2 (x+7)^2 + (y-4)^2 = 16
 logarithm/751123: Log3 (2x+1)=21 solutions Answer 456993 by nerdybill(6963)   on 2013-05-21 09:59:02 (Show Source): You can put this solution on YOUR website!Log3 (2x+1)=2 (2x+1)= 3^2 2x+1 = 9 2x = 8 x = 4
 Polynomials-and-rational-expressions/751121: Hello i have trouble factoring this certain polynomial. Can someone please help me?? the polynomial is -30m^3n^4-5m^4.1 solutions Answer 456991 by nerdybill(6963)   on 2013-05-21 09:57:50 (Show Source): You can put this solution on YOUR website!-30m^3n^4-5m^4 factor out a -5: -5(6m^3n^4+m^4) factor out m^3: -5m^3(6n^4+m)
Coordinate-system/750622: Hi there I need to calculate out how far and high a boy named Jose throws in a ball in a football match, Y stands for the height in meters and X for the diatance in meters from where jose is standing.
How do I calculate Y=-0,04x^2+0,6x+2
1 solutions

Answer 456739 by nerdybill(6963)   on 2013-05-20 03:22:09 (Show Source):
You can put this solution on YOUR website!
Y=-0.04x^2+0.6x+2
.
Maximum is at vertex:
x-value of vertex is "axis of symmetry":
x = -b/(2a)
x = -0.6/(2*(-0.04))
x = -0.6/(-0.08)
x = 0.6/(0.08)
x = 7.5
Max height:
Y=-0.04(7.5)^2+0.6(7.5)+2
Y= 4.25 meters (max height)
.
Max distance, we set Y to zero and solve for x:
0=-0.04x^2+0.6x+2
0=0.04x^2-0.6x-2
0=0.02x^2-0.3x-1
x = {17.81, -2.81}
throw out the negative solution (extraneous) leaving
x = 17.81 meters (max distance)
.
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=0.17 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 17.8077640640442, -2.80776406404415. Here's your graph:

1 solutions

Answer 456723 by nerdybill(6963)   on 2013-05-19 23:41:57 (Show Source):
You can put this solution on YOUR website!
2a^2-46a+254=0
first, divide both sides by 2:
a^2-23a+127=0
a = {13.80, 9.21}
.
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=21 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 13.7912878474779, 9.20871215252208. Here's your graph:

 Polynomials-and-rational-expressions/750602: if y varies directly as x, and y=9 when x=4, find y when x=161 solutions Answer 456722 by nerdybill(6963)   on 2013-05-19 23:38:11 (Show Source): You can put this solution on YOUR website!if y varies directly as x, and y=9 when x=4, find y when x=16 . When you see "direct variation" think: y = kx . To find k, use "y=9 when x=4": y = kx 9 = k(4) 9/4 = k . so, our equation is: y = (9/4)x . now, we can answer: find y when x=16 y = (9/4)x y = (9/4)(16) y = (9)(4) y = 36
 Rate-of-work-word-problems/749732: from pipe a it takes 4 hours to fill the tank.from pipe b it takes 8 hours empty the tank.if the both pipes are opened how many hours to fill the tank?1 solutions Answer 456126 by nerdybill(6963)   on 2013-05-17 01:17:26 (Show Source): You can put this solution on YOUR website!from pipe a it takes 4 hours to fill the tank.from pipe b it takes 8 hours empty the tank.if the both pipes are opened how many hours to fill the tank? . Let x = time (hours) to fill tank w/both pipes open then x(1/4 - 1/8) = 1 x(2/8 - 1/8) = 1 x(1/8) = 1 x/8 = 1 multiply both sides by 8: x = 8 hours
 Exponential-and-logarithmic-functions/749134: Logx-log2=31 solutions Answer 455854 by nerdybill(6963)   on 2013-05-15 19:26:26 (Show Source): You can put this solution on YOUR website!logx-log2=3 log(x/2)=3 x/2 = 10^3 x/2 = 1000 x = 2000
 logarithm/748318: log(x-3) + log(x+2) = log(4x) I need to know what steps to take to get the answer. Thank you!1 solutions Answer 455448 by nerdybill(6963)   on 2013-05-13 18:25:48 (Show Source): You can put this solution on YOUR website!log(x-3) + log(x+2) = log(4x) adding two logs is equivalent to multiplication: log(x-3)(x+2) = log(4x) now, we can eliminate the logs from both sides: (x-3)(x+2) = (4x) x^2-x-6 = 4x x^2-5x-6 = 0 (x+1)(x-6) = 0 x = {-1, 6} we throw out the -1 (extraneous solution) leaving x = 6
 Sequences-and-series/748043: Evaluate each geometric series: -2-6-18-54..., N=7 1 solutions Answer 455312 by nerdybill(6963)   on 2013-05-13 03:45:52 (Show Source): You can put this solution on YOUR website!-2-6-18-54..., N=7 . Nth term of geometric series: an = a1*r^(n–1) . r = 3 n = 7 a1 = -2 . a7 = (-2)*3^(7–1) a7 = (-2)*3^6 a7 = (-2)*729 a7 = -1458 . answer: -1458
 Graphs/748049: Please help. Ive been stuck on this question for a while and can't seem to figure it out. The question is, "Find an equation of the line that passes through (4, 2); perpendicular to 2x-3y=2"1 solutions Answer 455310 by nerdybill(6963)   on 2013-05-13 03:40:46 (Show Source): You can put this solution on YOUR website!Find an equation of the line that passes through (4, 2); perpendicular to 2x-3y=2 . find slope of: 2x-3y=2 2x=3y+2 2x-2=3y (2/3)x-2/3=y slope is 2/3 a line perpendicular must have a slope that is the "negative reciprocal": -3/2 . plug slope (-3/2) and point (4,2) into the "point-slope form" y - y1 = m(x - x1) y - 2 = (-3/2)(x - 4) y - 2 = (-3/2)x - (-3/2)4 y - 2 = (-3/2)x - (-6) y - 2 = (-3/2)x + 6 y = (-3/2)x + 8 (answer)
 Mixture_Word_Problems/748065: 5.) A chemist mixes liquid that's 87% gas. Together with another liquid that's 93% gas, to obtain 6 gallons that has a blend of 88% gas. How much of the 93% did the chemist use? A.) 1 B.) 3 C.) 5 D.) 61 solutions Answer 455309 by nerdybill(6963)   on 2013-05-13 03:35:35 (Show Source): You can put this solution on YOUR website!5.) A chemist mixes liquid that's 87% gas. Together with another liquid that's 93% gas, to obtain 6 gallons that has a blend of 88% gas. How much of the 93% did the chemist use? A.) 1 B.) 3 C.) 5 D.) 6 . Let x = amount (gallons) of 93% gas then 6-x = amount (gallons) of 87% gas . .93x + .87(6-x) = .88(6) .93x + 5.22-.87x = 5.28 .06x + 5.22 = 5.28 .06x = .06 x = 1 . Answer: A
 logarithm/747651: Write as a single log and simplify a) log(base 3)√45 - log(base 3)√5 Can you please help me out? Thanks so much in advance:) Can you also please show the work:)1 solutions Answer 455067 by nerdybill(6963)   on 2013-05-11 21:59:43 (Show Source): You can put this solution on YOUR website!log(base 3)√45 - log(base 3)√5 log(base 3)√45/√5 log(base 3)√(45/5) log(base 3)√9 log(base 3)3 log(base 3)3^1 1 (answer)
 logarithm/747583: Please help me solve this: Express as a logarithm of a single logarithm: Ln(x-1) + ln (x^2-3) - 1/2ln (y+1) 1 solutions Answer 454986 by nerdybill(6963)   on 2013-05-11 14:33:31 (Show Source): You can put this solution on YOUR website!Ln(x-1) + ln (x^2-3) - 1/2ln (y+1) Ln(x-1) + ln (x^2-3) - ln (y+1)^(1/2) ln(x-1)(x^2-3) - ln (y+1)^(1/2) ln(x-1)(x^2-3)/(y+1)^(1/2)
 Circles/747502: Find the center and radius for the circle defined by the equation: x2 + y2 + 5x − y + 2 = 01 solutions Answer 454965 by nerdybill(6963)   on 2013-05-11 10:45:44 (Show Source): You can put this solution on YOUR website!Put in "standard form" of a circle: (x-h)^2 + (y-k)^2 = r^2 . x^2 + y^2 + 5x − y + 2 = 0 x^2 + y^2 + 5x − y = -2 x^2 + 5x + y^2 − y = -2 (x^2 + 5x) + (y^2 − y) = -2 (x^2 + 5x+ 25/4) + (y^2 − y + 1/4) = -2 +25/4+1/4 (x^2 + 5/2)^2 + (y^2 − 1/2)^2 = -8/4 +25/4+1/4 (x^2 + 5/2)^2 + (y^2 − 1/2)^2 = (-8+25+1)/4 (x^2 + 5/2)^2 + (y^2 − 1/2)^2 = 18/4 (x^2 + 5/2)^2 + (y^2 − 1/2)^2 = (3sqrt(2)/2)^2 . center: (-5/2, 1/2) radius: 3sqrt(2)/2
Quadratic_Equations/747342: h = –16t^2 + vt + c
The equation shown above is the vertical motion formula, where h is the ending height, t is the time in seconds, v is the starting velocity in feet per second, and c is the starting height in feet.
If Adam, who is 6 feet tall, threw his baseball 80 feet per second straight up into the air, which of the following answers is the best estimate of how long it took the ball to come back to the ground?
I think this is the equation, h= -16t^2+80t+6
1 solutions

Answer 454846 by nerdybill(6963)   on 2013-05-10 15:46:44 (Show Source):
You can put this solution on YOUR website!
h= -16t^2+80t+6 (is correct)
.
when the ball is on the ground, h is zero. So, set h to zero and solve for t:
0 = -16t^2+80t+6
0 = 16t^2-80t-6
0 = 8t^2-40t-3
solve using the "quadratic formula" yields:
x = {5.07, -0.07}
throw out the negative value (extraneous) leaving
x = 5.07 seconds
.