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# Recent problems solved by 'scott8148'

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 Rectangles/286991: In rectangle ABCD, AB=(x-5y+94), BC= 3x+2y-82), CD= (4x-6y+55), and DA= (5x+4y-164). Find the perimeter of the rectangle. Could you please help me on this problem? 1 solutions Answer 208098 by scott8148(6628)   on 2010-03-30 17:39:36 (Show Source): You can put this solution on YOUR website!the opposite sides of a parallelogram (rectangle) are equal ___ this leaves you with a system of equations in x and y x - 5y + 94 = 4x - 6y + 55 ___ 3x - y = 39 3x + 2y - 82 = 5x + 4y - 164 ___ 2x + 2y = 82 ___ x + y = 41 ___ y = 41 - x substituting ___ 3x - (41 - x) = 39 ___ 4x = 80 ___ x = 20 substituting ___ y = 41 - (20) = 21 plug in the values for x and y to find the perimeter (sum of the sides)
 Vectors/286948: Let vector v=<5,-1,4>. Give a vector w in the opposite direction of v and with magnitude twelve. Give its components to the nearest tenth. I don't understand how to solve the problem and I can't seem to find any similar examples in the text.1 solutions Answer 208093 by scott8148(6628)   on 2010-03-30 17:28:14 (Show Source): You can put this solution on YOUR website!to get the opposite direction, change the signs of the components w = <-5k, 1k, -4k> the "k" is the factor to make the magnitude of w equal 12 the magnitude is the length of the vector ___ found by using the Pythagorean theorem on the components ___ m^2 = x^2 + y^2 + z^2 144 = 25k^2 + k^2 + 16k^2 = 42k^2 k = sqrt(144/42) = 1.852 (approx) plug in the value of k to find the components of w
 Triangles/286961: I have a triangle with given angles 135, and 30. The side opposite the 135 degree angle is 12 units. The questions is: Find the length of the side opposite the 30 degree angle, x.1 solutions Answer 208088 by scott8148(6628)   on 2010-03-30 17:10:27 (Show Source): You can put this solution on YOUR website!by the Law of Sines ___ x / 12 = [sin(30º)] / [sin(135º)] x = 12 [sin(30º)] / [sin(135º)]
 Rate-of-work-word-problems/286967: Working by herself, Mary requires 16 minutes more than Antoine to solve a mathematics problem. Working together, Mary and Antoine can solve a problem in 6 minutes. If this situation is represented by the equation (6/t)+(6/t+16)=1 , where t represents the number of minutes Antoine works alone to solve the problem, how many minutes will it take Antoine to solve the problem if he works by himself? ........................... ................................................... 6 6 Another look at the equation: ___ + _____=1 ............................ ..................... t t+16 thanks for your time.1 solutions Answer 208083 by scott8148(6628)   on 2010-03-30 17:03:32 (Show Source): You can put this solution on YOUR website!(6 / t) + [6 / (t + 16)] = 1 multiplying by t(t + 16) ___ 6t + 96 + 6t = t^2 + 16t 0 = t^2 + 4t - 96 0 = (t + 12) (t - 8) 0 = t + 12 ___ t = -12 is not realistic 0 = t - 8 ___ t = 8
 Equations/286672: 1.Write a rule for the function represented in the table. x 0 1 2 3 y 4 6 8 10 thank you also sorry if this isn't right place..1 solutions Answer 207919 by scott8148(6628)   on 2010-03-29 21:39:18 (Show Source): You can put this solution on YOUR website!the y-value increases by 2 when the x-value increases by 1 ___ this is called the SLOPE of a linear function ___ the slope is usually represented by the letter "m" there is also a "fudge factor" added (or subtracted) to make the values match up ___ this number is is the y-intercept of the linear function ___ it is the point on the y-axis where the line crosses ___ the intercept is usually represented by the letter "b" solving for b ___ y = 2x + b ___ taking a point from the table ___ 8 = 2(2) + b ___ 4 = b a rule for the function (in slope-intercept form) is ___ y = 2x + 4
 Exponents-negative-and-fractional/286583: I was wondering if I could get a step by step example of (1/4)^-3/2 = non-negative number. The awnser that comes with the problem is 8, but no matter how I manipulate this I can not get to that answer. Thank you!1 solutions Answer 207877 by scott8148(6628)   on 2010-03-29 18:30:51 (Show Source): You can put this solution on YOUR website!using laws of exponents ___ a^(-b) = 1 /(a^b) for fractional exponents; think of the numerator (top) as a power, and the denominator (bottom) as a root (1/4)^-3/2 is: the inverse of; the square root of one-quarter, cubed 1 / {[sqrt(1/4)]^3} 1 / [(1/2)^3] 1 / (1/8) = 8
 test/286056: The lift of an airplane wing is 750 lbs. the drag is 300 lbs what is the magnitude and direction of the resulting force. Represent the problem geometrically and find the resultant force algebraically Thank You I Really appreciate it. 1 solutions Answer 207568 by scott8148(6628)   on 2010-03-28 19:32:46 (Show Source): You can put this solution on YOUR website!you can use Pythagoras to find the magnitude of the resultant R^2 = 750^2 + 300^2 the direction of the resultant is between the vertical and the tail of the plane (opposite the direction of motion) the sine of the direction angle is 750/R
 Functions/286203: In 1994 the life expectancy of males in a certain country was 71.8 years. In 1999, it was 73.9 years. Let E represent the life expectancy in year t and let t represent the number of years since 1994. The linear function E(t)that fits the data is: E(t)= ___t+___ (round to the nearest tenth) Use the function to predict the life expectancy of males in 2004. E(10)=____ Again, thank you kindly in advance. I've spent a good 20 minutes trying to figure out how to even SET UP this problem. :( Thank you!! :o/1 solutions Answer 207560 by scott8148(6628)   on 2010-03-28 19:09:02 (Show Source): You can put this solution on YOUR website!in the five years from 1994 to 1999, the life expectancy increased 2.1 yrs (73.9 - 71.8) ___ so the SLOPE of the linear function is 2.1/5 or .42 E(t) = .42 t + 71.8 just plug in 10 for t to find the second answer
 Miscellaneous_Word_Problems/285147: A purse contains a collection of quarters, dimes, nickels, and pennies. The average value of the coins in the purse is 17 cents. If a penny is removed from the purse, the average value of the coins becomes 18 cents. How many nickels are in the purse? (A) 2 (B) 5 (C) 0 (D) 1 (E) 81 solutions Answer 207196 by scott8148(6628)   on 2010-03-26 22:51:16 (Show Source): You can put this solution on YOUR website!25q + 10d + 5n + p = 17c 25q + 10d + 5n + p - 1 = 18(c - 1) 17c - 1 = 18c - 18 ___ 17 = c q + d + n + p = 17 25q + 10d + 5n + p = 289 q ≤ 11 ___ p ≥ 4 ___ this would be 15 coins and 279 cents two nickels makes 17 coins and 289 cents this means NO dimes, which contradicts the opening sentence...
 Quadratic-relations-and-conic-sections/285141: how do you find the center and radius for this equation for a circle x^2+y^2-18x-18y+53=01 solutions Answer 207193 by scott8148(6628)   on 2010-03-26 22:27:20 (Show Source): You can put this solution on YOUR website!complete the squares (x^2 - 18x + 81) + (y^2 - 18y + 81) = -53 + 81 + 81 (x - 9)^2 + (y - 9)^2 = 109 center ___ (9,9) radius ___ sqrt(109)
 Quadratic_Equations/285066: please help me solve this, its a triangle with a hypotenuse of 12, leg a is x and leg b is (x+5)1 solutions Answer 207180 by scott8148(6628)   on 2010-03-26 22:07:58 (Show Source): You can put this solution on YOUR website!x^2 + (x + 5)^2 = 12^2 2x^2 + 10x + 25 = 144 ___ 2x^2 + 10x - 119 = 0 use the quadratic formula to find x ***************** ANSWER BELOW ***************** x = 5.61 (approx)
 Radicals/285431: If the sides of a square are lengthened by 8cm, the area becomes 144cm^2 find the length of a side of the original square. I could use some help with this.1 solutions Answer 207166 by scott8148(6628)   on 2010-03-26 21:02:31 (Show Source): You can put this solution on YOUR website!(x + 8)^2 = 144 x + 8 = 12 x = 4
 Rate-of-work-word-problems/285456: If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?1 solutions Answer 207155 by scott8148(6628)   on 2010-03-26 20:35:11 (Show Source): You can put this solution on YOUR website!in the combined time (x), they each mix a FRACTION of the 20 total drinks Steve mixes ___ x/5 Sue mixes ___ x/10 Jack mixes ___ x/15 the fractions sum to one (the whole) (x / 5) + (x / 10) + (x / 15) = 1 6x + 3x + 2x = 30 ___ x = 30/11 this is a mathematical solution; since each person would most likely mix a whole number of drinks (not 2/3 of a drink), the number is a good approximation to REALITY
 Travel_Word_Problems/284235: Can you please help me with this problem. I am totally confused when it comes to D=RT word problems. A local commuter train leaves downtown at 5 pm. And express commuter train leaves downtown at 5:30 pm. The express train travels twice as fast as the local, so the local has to pull over on a siding to avoid a crash 45 miles from downtown. At what time would the crash occur? How fast is each train going? Thanks for your help! Christine1 solutions Answer 206262 by scott8148(6628)   on 2010-03-22 23:05:34 (Show Source): You can put this solution on YOUR website!the distance for both trains is 45 mi the time for the local train is 1/2 hr longer ___ for the times to be equal, this must be subtracted the speed of the express is twice the speed of the local time equals distance divided by rate 45 / 2r = (45 / r) - (1/2) 45 = 90 - r ___ r = 45 (this is the speed of the local train) 2r = 90 (this is the speed of the express train) the travel time to the "crash" site is 1/2 hr for the express and 1 hr for the local ___ so the crash time is 6:00 pm
 Money_Word_Problems/283806: Hi! Once again, I'm asking help for one of these pesky (for me, at least) money problems. The answer is supposed to be \$2,000, but the answer that I'm always getting ends up to be way off the mark. The question is as follows: A man had \$6,000. He spent part of it to pay for a jeep and invested the remaining amount as follows: 1/3 of it at 6% and 2/3 of it at 4% simple interest for 1 year. The income from the two investments was \$140. What was the cost of the jeep? Thanks for the time and help! :)1 solutions Answer 205950 by scott8148(6628)   on 2010-03-22 02:01:35 (Show Source): You can put this solution on YOUR website![(6000 - j)(1 / 3)(.06)] + [(6000 - j)(2 / 3)(.04)] = 140 (6000 - j)(.14 / 3) = 140 6000 - j = 3000 ___ 3000 = j not 2000 ___ sorry...
 Miscellaneous_Word_Problems/283801: Hi! I'm not entirely convinced that the answer that I got, which is 6, is the right one, so I'd be really grateful if anyone would bother to solve this one. This problem goes like this: A sum of \$800 was divided equally among a certain number of children. If there had been 4 more children, each would have received only 3/5 as much. How many children were there? Once again, thanks very much! :)1 solutions Answer 205949 by scott8148(6628)   on 2010-03-22 01:51:17 (Show Source): You can put this solution on YOUR website!(800 / n)(3 / 5) = 800 / (n + 4) 2400 (n + 4) = 4000n 2400n + 9600 = 4000n 9600 = 1600n ___ 6 = n
 Finance/283728: Im having trouble solving this problem and ones like it. What is the answer and how is it found? If you buy 3 hotdogs and 3 sodas on your first trip to the concession stand and spend \$22.50. You then go back a second time and spend \$24 and buy 5 sodas and 2 hotdogs. How much does each hotdog cost and how much does each soda cost? 1 solutions Answer 205913 by scott8148(6628)   on 2010-03-21 21:42:16 (Show Source): You can put this solution on YOUR website!3h + 3s = 22.50 ___ multiplying by 2 ___ 6h + 6s = 45.00 2h + 5s = 24.00 ___ multiplying by 3 ___ 6h + 15s = 72.00 subtracting ___ 9s = 27.00 ___ s = 3.00 substituting ___ 2h + 5(3.00) = 24.00 ___ 2h = 9.00 ___ h = 4.50
 Linear-systems/283681: The manager of a factory has found the output at the factory can be modeled by the function T(n)=-0.2n squared+8n-24, where n is the number of workers at the factory and T is the output. Find the number of workers,n, needed to maximize the output. Then find the maximum output with with that number of workers.. I have no idea how to solve this one. 1 solutions Answer 205897 by scott8148(6628)   on 2010-03-21 21:18:15 (Show Source): You can put this solution on YOUR website!the max of the function lies on the axis of symmetry of the parabola the general equation is ___ x = -b / (2a) in this case ___ n = (-8) / [2(-.2)] ___ n = 20 the max output uses 20 workers ___ plug n=20 into the function to find the max T
 Linear-systems/283676: The following points fall on a parabola. Write a system of equations that you could use to determine the equation for the parabola(you do not have to solve the system) This is what is in the box x -2 0 1 y 39 5 91 solutions Answer 205889 by scott8148(6628)   on 2010-03-21 21:10:21 (Show Source): You can put this solution on YOUR website!the general equation is ___ y = ax^2 + bx + c three unknowns and three equations Eq 1 ___ 39 = a(-2)^2 + b(-2) + c Eq 2 ___ 5 = a(0)^2 + b(0) + c Eq 3 ___ 9 = a(9)^2 + b(9) + c
 Mixture_Word_Problems/283565: the store sells cashews for 6.00 per pound and peanuts for 3.00 per pound the manager decides to mix 60 pounds with some cashews and sell the mixture for 4.oo per pound how many pounds should be mixed with the cashews to produce the same revenue. I keep getting this wrong. 1 solutions Answer 205881 by scott8148(6628)   on 2010-03-21 20:53:46 (Show Source): You can put this solution on YOUR website!3(x) + 6(60 - x) = 4(60) 3x + 360 - 6x = 240 120 = 3x ___ 40 = x
 Miscellaneous_Word_Problems/282972: A 6.3 gram sample of an isotope of strotium- 90 was formed in a 1962 explosion of an atomic bomb. The half- life of strontium- 90 is 28 years. In what year will only .07 grams remain?1 solutions Answer 205461 by scott8148(6628)   on 2010-03-19 23:05:35 (Show Source): You can put this solution on YOUR website!.07 = 6.3 (1 / 2)^((x - 1962) / 28) log(.07 / 6.3) = ((x - 1962) / 28)[log(1 / 2)] {[log(.07 / 6.3)] / [log(1 / 2)]} * 28 = x - 1962 [{[log(.07 / 6.3)] / [log(1 / 2)]} * 28] + 1962 = x
 Proportions/282987: Suppose that a street light is 20 feet above the ground. How far from the street light is a 5 foot girl standing if she casts a 4 foot shadow?1 solutions Answer 205459 by scott8148(6628)   on 2010-03-19 22:54:12 (Show Source): You can put this solution on YOUR website!20 / 5 = (x + 4) / 4 80 = 5x + 20 x = 12
 Quadratic_Equations/283001: Factor completely. 7x^2 - 56x + 1121 solutions Answer 205458 by scott8148(6628)   on 2010-03-19 22:51:28 (Show Source): You can put this solution on YOUR website!7 (x^2 - 8x + 16) 7 (x - 4) (x - 4)
 Quadratic_Equations/282692: A track runner ran 6 meters per second one way and jogged 2 meters per second the other way. Both ways are equal in length. The total time it took the runner was 160 seconds. How long is the track? This was a test question and i couldn't figure it out!!!1 solutions Answer 205244 by scott8148(6628)   on 2010-03-18 22:21:28 (Show Source): You can put this solution on YOUR website!time equals distance divided by rate (d / 6) + (d / 2) = 160 d + 3d = 960 ___ 4d = 960 ___ d = 240
 Human-and-algebraic-language/281699: i have tried to figure this out and so has a friend and well math isnt our strong suit soo....here it is....thanks! a cyclist traveled at a rate of 32 mph to visit a nearby town. The cyclist averaged 10 mph on the return round trip took 6.3 hrs, find the distance to the nearby town.1 solutions Answer 204701 by scott8148(6628)   on 2010-03-16 21:57:12 (Show Source): You can put this solution on YOUR website!distance is the same each way ___ time equals distance divided by rate (d / 32) + (d / 10) = 6.3 multiplying by 160 (LCD) ___ 5d + 16d = 63 * 16 21d = 63 * 16 ___ d = 3 * 16 = 48
 Travel_Word_Problems/281742: Travel up a hill at 3 miles per hour and down the hill at 6 miles per hour on the same trail, what is the average speed traveled? Teacher says it is not 4.5 mph.1 solutions Answer 204695 by scott8148(6628)   on 2010-03-16 21:48:30 (Show Source): You can put this solution on YOUR website!teacher is right since the size of the hill is not a factor, let's say the hill is 6 miles long it takes 2 hours to go up (6/3), and one hour to come down (6/6) so you spend 3 hours going 12 miles ___ 12 / 3 = 4 mph
 Average/281177: Helping my son, 7th grade. We need help please. Q- average for five quizzes is 86. To have an average of 88 or more for six quizzes, what is the lowest score to get on the sixth quiz? Thanks.1 solutions Answer 204274 by scott8148(6628)   on 2010-03-15 17:35:25 (Show Source): You can put this solution on YOUR website!an average of 88 for 6 quizzes means a total of 528 points (6 times 88) the current point total is 430 (5 times 86) so the needed score on the 6th quiz (for an 88 average) is 98 (528 minus 430)
 Travel_Word_Problems/280875: Sat Tranh took a short hike with his friends up Mt. Wachusett. They hiked uphill at a steady pace of 1.5 mph, and downhill at a rate of 4mph. If the time to climb the mt. took an hour more than the time to hike down, how long was the entire hike? I tried doing d=rt but there is no distance given here. I also tried 4x= 1.5x-1.5 but it yields the incorrect answer. If someone could help me understand how to do this I would greatly appreciate it!1 solutions Answer 204104 by scott8148(6628)   on 2010-03-14 23:36:28 (Show Source): You can put this solution on YOUR website!if x equals time down, then x+1 equals time up ___ total time is 2x+1 distance is the same, up and down 4 (x) = 1.5 (x + 1) ___ 4x = 1.5x + 1.5 not sure why your equation has the constant term negative...
 Miscellaneous_Word_Problems/280699: Mutt and Jeff need to paint a fence. Mutt can do the job alone 4 hours faster than Jeff. If together they work for 13 hours and finish only 1/2 of the job, how long would Jeff need to do the job alone1 solutions Answer 204014 by scott8148(6628)   on 2010-03-14 17:31:11 (Show Source): You can put this solution on YOUR website![13 / (j - 4)] + (13 / j) = 1/2 26j + 26j - 104 = j^2 - 4j ___ 0 = j^2 - 56j + 104 use quadratic formula to find j
 Proportions/280705: how do i find the time it takes a ball dropped from 10ft. to hit the ground?1 solutions Answer 204007 by scott8148(6628)   on 2010-03-14 17:07:16 (Show Source): You can put this solution on YOUR website!gravitational acceleration is 32ft/sec^2 since the ball starts from rest and free falls ___ 10 = (32/2) t^2 5/8 = t^2 t = sqrt(5/8)
 Travel_Word_Problems/280471: On her camping trip Li spent as much time hiking as she did rafting. She traveled 2.5 mph when she was rafting and 3mph when she was hiking. If she went 3 miles more hiking than she did rafting, how far did she hike? Thank you.1 solutions Answer 203852 by scott8148(6628)   on 2010-03-13 20:46:05 (Show Source): You can put this solution on YOUR website!hiking and rafting times are the same time equals distance divided by rate (x - 3) / 2.5 = x / 3 3x - 9 = 2.5x ___ x = 18