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, >>Next

 Quadratic_Equations/198522: Solve by Factoring 12x(Squared) +19x-18= 0 1 solutions Answer 149047 by nerdybill(6959)   on 2009-06-01 00:49:17 (Show Source): You can put this solution on YOUR website!12x(Squared) +19x-18= 0 (3x-2)(4x+9) = 0 . Setting each to zero: (3x-2)= 0 3x = 2 x = 2/3 and (4x+9) = 0 4x = -9 x = -9/4 . x = {-9/4, 2/3}
Geometry_Word_Problems/198520: A rectangular flower bed 30 yards long by 20 yards wide has a walk of uniform width around it. If the area of the path is 1/4 that of the flower bed, find the width of the path.
1 solutions

Answer 149044 by nerdybill(6959)   on 2009-06-01 00:27:53 (Show Source):
You can put this solution on YOUR website!
A rectangular flower bed 30 yards long by 20 yards wide has a walk of uniform width around it. If the area of the path is 1/4 that of the flower bed, find the width of the path.
.
Let w = width of path
then
Area of flower bed = (30)(20) = 600 sq yards
.
Area of flower bed and walk = (30+2w)(20+2w)
.
Area of path = "area of flower bed and walk" - "area of flower bed"
Area of path = (30+2w)(20+2w) - 600
.
(1/4)600 = (30+2w)(20+2w) - 600
150 = (30+2w)(20+2w) - 600
750 = (30+2w)(20+2w)
750 = 600+60w+40w+4w^2
750 = 4w^2+100w+600
0 = 4w^2+100w-150
0 = 2w^2+50w-75
Using the quadratic equation we get:
w = {1.42, -26.42}
Throw out the negative solution leaves us with:
w = 1.42 yards
.
 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=3100 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 1.41941090707505, -26.4194109070751. Here's your graph:

 Geometry_Word_Problems/198521: The altitude of a triangle is 3/4 the length of its base. If the altitude were increased by 3 feet and the base decreased by 3 feet, the area would be unchanged. Find the length of the base and altitude.1 solutions Answer 149043 by nerdybill(6959)   on 2009-06-01 00:12:44 (Show Source): You can put this solution on YOUR website! The altitude of a triangle is 3/4 the length of its base. If the altitude were increased by 3 feet and the base decreased by 3 feet, the area would be unchanged. Find the length of the base and altitude. . Original triangle: Let b = length of base then (3/4)b = altitude Area = (1/2)b(3/4)b = (3/8)b^2 . Changed triangle: b-3 = length of base (3/4)b+3 = altitude Area = (1/2)(b-3)(3/4)b+3 = (3/8)(b-3)b+3 . Set area equal to each other: (3/8)b^2 = (3/8)(b-3)b+3 b^2 = (b-3)b+3 b^2 = b^2-3b+3 0 = -3b+3 -3 = -3b 1 feet = b (base of triangle) . Altitude: (3/4)b = (3/4)1 = 3/4 feet (altitude)
 Equations/198493: how do you solve this system of equation x+y=8 51x+8y=1931 solutions Answer 149020 by nerdybill(6959)   on 2009-05-31 19:33:14 (Show Source): You can put this solution on YOUR website!You can solve by one of three methods: Substitution, addition or matrix. . I'll apply the "addition method": x+ y= 8 51x+8y=193 . Multiply first equation by -8 to get: -8x-8y=-64 51x+8y=193 . Add the two equations together: -8x-8y=-64 51x+8y=193 ----------- 43x = 129 x = 129/43 x = 3 . To find y, substitute the above into: x+ y= 8 3+ y= 8 y = 5 . Our solution: x = 3 y = 5
 Percentage-and-ratio-word-problems/198495: A blue whale weighs approximately 100 tons, while a house cat weighs 5 pounds. About how many cats would it take to equal the weight of one blue whale?1 solutions Answer 149019 by nerdybill(6959)   on 2009-05-31 19:28:41 (Show Source): You can put this solution on YOUR website!A blue whale weighs approximately 100 tons, while a house cat weighs 5 pounds. About how many cats would it take to equal the weight of one blue whale? . A "ton" is equivalent to 2000 pounds. Therefore, 100 tons is: 100*2000 = 200,000 pounds . 200000/5 = 40,000 cats
 Linear-equations/198444: Find the equation of the line that is parallel to y = 6x – 15 and passes through the origin.1 solutions Answer 148948 by nerdybill(6959)   on 2009-05-31 11:43:54 (Show Source): You can put this solution on YOUR website!y = 6x – 15 is in the "slope-intercept" form y = mx + b where m is slope b is the y-intercept . To be parallel, slopes are identical. So, our new line has m = 6 and crosses (0,0) . Plug the above into the "point-slope" form y - y1 = m(x-x1) y - 0 = 6(x-0) y = 6x (this is what they're looking for)
 Expressions-with-variables/198442: A bike shop rents mountain bikes for a \$8.50 insurance charge plus \$3.50 for each hour. For how many hours can a person rent a bike with \$32.50. Can some one please show me the steps to set this up using an equation editor1 solutions Answer 148946 by nerdybill(6959)   on 2009-05-31 11:22:10 (Show Source): You can put this solution on YOUR website!A bike shop rents mountain bikes for a \$8.50 insurance charge plus \$3.50 for each hour. For how many hours can a person rent a bike with \$32.50. . Let h = number of hours rented then "rental cost" = "insurance" + "hourly charge" 32.50 = 8.50 + 3.50h 24 = 3.50h 6.86 hours = h .
 Graphs/198414: The graphs of the equations 4x-y=6 and x+y=4 intersect at the point whose coordinates are 1.(2,-2) 2.(5,-1) 3.(1,3) 4.(2,2)1 solutions Answer 148936 by nerdybill(6959)   on 2009-05-31 06:11:13 (Show Source): You can put this solution on YOUR website!Solve the system of equations. Do this by the addition method -- add both equations together: 4x-y=6 x+y=4 ------- 5x =10 x = 2 . Substitute the above into: x+y=4 2+y=4 y=2 . Therefore, the graphs cross at: (x,y) = (2,2)
 Polynomials-and-rational-expressions/198432: This question is from textbook Beginning Algebra simplify 8x-12/2x^3-3x^21 solutions Answer 148935 by nerdybill(6959)   on 2009-05-31 06:05:26 (Show Source): You can put this solution on YOUR website! . Factoring numerator and denominator: . Canceling like-terms:
 Triangles/198418: If one of the legs of a right triangle is 3 and the other leg is 5, then the length of the hypotenuse is 1.square root of 34 2.34 3.square root of 8 4.81 solutions Answer 148931 by nerdybill(6959)   on 2009-05-31 00:57:14 (Show Source): You can put this solution on YOUR website!Apply Pythagorean theorem: Let h = hypotenuse then h^2 = 3^2 + 5^2 h^2 = 9 + 25 h^2 = 34 h =
 Proportions/198425: A man mixes peanuts selling at 40 cents a pound with cashew nuts selling at 70 cents a pound to make a 50-pound mixture which he sells at 52 cents a pound. How many pounds of each kind of nuts must he mix?(Only an algebraic solution will be accepted.) 1 solutions Answer 148928 by nerdybill(6959)   on 2009-05-31 00:28:44 (Show Source): You can put this solution on YOUR website!A man mixes peanuts selling at 40 cents a pound with cashew nuts selling at 70 cents a pound to make a 50-pound mixture which he sells at 52 cents a pound. How many pounds of each kind of nuts must he mix? . Let x = pounds of peanuts then 50-x = pounds of cashews . .40x + .70(50-x) = .52(50) .40x + 35 -.70x = 26 35 -.30x = 26 35 = 26 + .30x 9 = .30x 30 pounds = x (peanuts) . Cashews: 50-x = 50-30 = 20 pounds (cashews)
 Square-cubic-other-roots/198429: 3X2+11X=41 solutions Answer 148927 by nerdybill(6959)   on 2009-05-31 00:15:16 (Show Source): You can put this solution on YOUR website! . Setting each term to zero: (3x-1)=0 3x = 1 x = 1/3 . (x+4)=0 x = -4 . Therefore, x = {-4, 1/3}
 Travel_Word_Problems/198427: Tiger Woods hits a golf ball into the air. The equation that describs the path of the ball is h=55t-5t^2. There are three questions. (A How high is it the ball after 2 seconds?) (B When will it first reach 140 meters?) (C When will it hit the ground?)1 solutions Answer 148926 by nerdybill(6959)   on 2009-05-31 00:12:28 (Show Source): You can put this solution on YOUR website!Tiger Woods hits a golf ball into the air. The equation that describs the path of the ball is h=55t-5t^2. There are three questions. (A How high is it the ball after 2 seconds?) h=55t-5t^2 Simply substitute 't' with 2 and solve: h=55(2)-5(2)^2 h=110-5(4) h=110-20 h=90 meters . (B When will it first reach 140 meters?) h=55t-5t^2 Subsitute 'h' with 140 meters and solve: 140=55t-5t^2 0=55t-5t^2-140 0=-5t^2+55t-140 0=-t^2+11t-28 0=t^2-11t+28 0=(t-4)(t-7) t = {4,7} Ball reaches height at 4 and 7 seconds . (C When will it hit the ground?) h=55t-5t^2 Subsitute 'h' with 0 meters and solve: 0=55t-5t^2 0=11t-t^2 0=-t^2+11t 0=t^2-11t 0=t(t-11) t = {0,11} Ball is at 0 meters at 0 seconds and 11 seconds
 Exponential-and-logarithmic-functions/198273: solve LN(x+3)+LNx=LN41 solutions Answer 148823 by nerdybill(6959)   on 2009-05-30 10:04:30 (Show Source): You can put this solution on YOUR website!LN(x+3)+LNx=LN4 LNx(x+3)=LN4 x(x+3)=4 x^2 + 3x = 4 x^2 + 3x - 4 = 0 (x-4)(x+1) = 0 x = {-1, 4} We can toss out the negative solution (ln of a negative does not make sense), leaving us with: x = 4
3. The length of a rectangle is 16cm greater than its width. The area is 35m^2. Find the dimensions of the rectangle, to the nearest hundredth of a metre.
Thanks
1 solutions

Answer 148821 by nerdybill(6959)   on 2009-05-30 10:00:16 (Show Source):
You can put this solution on YOUR website!
3. The length of a rectangle is 16cm greater than its width. The area is 35m^2. Find the dimensions of the rectangle, to the nearest hundredth of a metre.
.
Let w = width
then
w+16 = length
.
w(w+16) = 35
w^2+16w = 35
w^2+16w-35 = 0
Using the quadratic equation, we get:
x = {1.95, -17.95}
We can toss out the negative solution leaving:
x = 1.95 m
.
 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=396 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 1.9498743710662, -17.9498743710662. Here's your graph:

 Miscellaneous_Word_Problems/198087: A 50 m by 120 m park consists of a rectangular lawn surrounded by a path of uniform width. Find the dimensions of the lawn if its area is the same as the area of the path. (Hint: Let x = the width of path)1 solutions Answer 148555 by nerdybill(6959)   on 2009-05-28 00:24:15 (Show Source): You can put this solution on YOUR website! A 50 m by 120 m park consists of a rectangular lawn surrounded by a path of uniform width. Find the dimensions of the lawn if its area is the same as the area of the path. (Hint: Let x = the width of path) . Draw a diagram of the problem -- it'll help you see the problem. . Area of lawn: (50-2x)(120-2x) = 2(25-x)2(60-x) = 4(25-x)(60-x) = 4(150-85x+x^2) = 4x^2 - 340x + 6000 . Area of path: (50)(120) - (50-2x)(120-2x) = 6000 - (4x^2 - 340x + 6000) = -4x^2 + 340x . Since: "Area of lawn" = "Area of path" we have 4x^2 - 340x + 6000 = -4x^2 + 340x 8x^2 - 340x + 6000 = 340x 8x^2 - 680x + 6000 = 0 x^2 - 85x + 750 = 0 (x-75)(x-10) = 0 x = {10, 75} . We can toss out the 75 leaving: x = 10 meters (width of path) . dimensions of lawn: width = 50 -2x = 50 - 20 = 30 meters length = 120 -2x = 120 - 20 = 100 meters Therefore, the lawn is 100 x 20 meters
 Polynomials-and-rational-expressions/197939: find the lowest common denominatior x/x+2 + 3/2=9/21 solutions Answer 148426 by nerdybill(6959)   on 2009-05-27 09:53:52 (Show Source): You can put this solution on YOUR website!The LCD: 2(x+2)
 Numbers_Word_Problems/197936: The sum of two numbers is 29. If the smaller is doubled and the larger is increased by 7, the resulting numbers will be equal. Find both numbers. I need a complete solution. *sobs* I am really sleepy now, still i don't know how to get the answer. *sobs*1 solutions Answer 148425 by nerdybill(6959)   on 2009-05-27 09:23:03 (Show Source): You can put this solution on YOUR website!The sum of two numbers is 29. If the smaller is doubled and the larger is increased by 7, the resulting numbers will be equal. Find both numbers. . Let x = smaller number and y = larger number . Since we have two unknowns, we need two equations: From:"The sum of two numbers is 29" we get equation 1: x + y = 29 . From:"If the smaller is doubled and the larger is increased by 7, the resulting numbers will be equal." we get equation 2: 2x = y + 7 . Using the "substitution method", solve equation 1 for y: x + y = 29 y = 29 - x . Substitute the above into equation 2 and solve for x: 2x = y + 7 2x = 29 - x + 7 3x = 29 + 7 3x = 36 x = 12 (smaller number) . To find the larger number, substitute the above into equation 1 and solve for y: x + y = 29 12 + y = 29 y = 29 - 12 y = 17 (larger number)
 Graphs/197727: Calculate temperature in Fahrenheit if the temperature in celsius is -60C F=(9/5)C+32. I tried to solve the problem using .55 instead of 5/9 but my answer came out wrong.1 solutions Answer 148411 by nerdybill(6959)   on 2009-05-27 04:06:28 (Show Source): You can put this solution on YOUR website!Calculate temperature in Fahrenheit if the temperature in celsius is -60C F=(9/5)C+32. . Simply plug and solve: F=(9/5)C+32 F=(9/5)(-60)+32 F=(9)(-12)+32 F=-108+32 F=-76 (degrees Fahrenheit)
 Linear-equations/197868: Please help me find the slop of : y=-5x-11 solutions Answer 148410 by nerdybill(6959)   on 2009-05-27 04:02:39 (Show Source): You can put this solution on YOUR website!y=-5x-1 . The given equation is already in the "slope-intercept" form of a line: y = mx + b where m is the slope b is the y-intercept . Therefore, the slope is: m = -5
 Travel_Word_Problems/197923: There are 220 barrels of cement in one shed and 510 barrels in another. How many barrels must be transferred from the second to the first shed will contain two thirds as much as the second? I need help setting up the equation...plez. thank you1 solutions Answer 148408 by nerdybill(6959)   on 2009-05-27 00:31:58 (Show Source): You can put this solution on YOUR website!There are 220 barrels of cement in one shed and 510 barrels in another. How many barrels must be transferred from the second to the first shed will contain two thirds as much as the second? . Let x = number of barrels transferred then 220 + x = (2/3)(510-x) . Now, solve for x: 220 + x = (2/3)(510-x) Multiply both sides by 3: 660 + 3x = (2)(510-x) 660 + 3x = 1020 - 2x 660 + 5x = 1020 5x = 360 x = 72 barrels
 Travel_Word_Problems/197786: This word problem is from a handout. I am a math tutor, but am so terrible at solving word problems. Can you give me any helpful advice or direction on how to get better at these??? Here is one from a student's handout sheet. I hope that I got it right, but not at all sure: A PASSENGER PLANE FLEW TO MOSCON AND BACK. IT TOOK THREE HOURS LONGER TO GO THERE THAN IT DID TO COME BACK. THE AVERAGE SPEED ON THE TRIP THERE WAS 196 kn/h. THE AVERAGE SPEED ON THE WAY BACK WAS 280 km/h. HOW MANY HOURS DID THE TRIP THERE TAKE? I solved it as follows: 196x = 280(x-3) x = 10 trip to = 10 hours trip back = 7 hours total trip took 17 hours?????? Thank you in advance for your help.1 solutions Answer 148291 by nerdybill(6959)   on 2009-05-26 11:17:53 (Show Source): You can put this solution on YOUR website!Looks just fine to me. You should identify what 'x' is though: I.E. Let x = time it took to fly to Moscow