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# Recent problems solved by 'ewatrrr'

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 Pythagorean-theorem/378256: the hypotnuse of a right triqangle measures 13 centimeters. Find the lengths of the legs if their sum is 17 centimeters.1 solutions Answer 268782 by ewatrrr(10682)   on 2010-11-30 13:24:01 (Show Source): You can put this solution on YOUR website! ``` Hi, lengths of the legs have a sum of 17 centimeters Let x and (17-x) represent the lengths of the legs hypotnuse of this right triqangle measures 13 centimeters Applying the Pythagorean Theorem x^2 + (17-x)^2 = 13cm^2 solving for x x^2 + 17^2 - 34x + x^2 = 13^2 2x^2 -34x +120 = 0 x^2 -17x + 60 = 0 factoring (x-12)(x-5)= 0 (x-12)=0 x = 12 (x-5)= 0 x = 5 the lengths of the legs are 12cm and 5cm CHECKING our Answer 144 + 25 = 169 ```
 Linear-equations/378248: What is the slope of a line that is parallel to the graph of: 2x-3y=6? A. 3/2 B. -2/3 C. 2/3 D. -3/21 solutions Answer 268781 by ewatrrr(10682)   on 2010-11-30 13:16:24 (Show Source): You can put this solution on YOUR website! ``` Hi, Note: the standard slope-intercept form for an equation of a line y = mx + b where m is the slope and b the y-intercept. 2x-3y=6 Solving for y to put into slope-intercept form 2x - 6 = 3y y = (2/3)x - 2 m = (2/3) parallel lines have identical slopes. Answer C would be the correct choice ```
 Age_Word_Problems/378241: The ratio between the ages of the two suspects is 6:5 and the sum of their ages is 55 years. After how many years will the ratio be 8:7.?1 solutions Answer 268780 by ewatrrr(10682)   on 2010-11-30 13:02:29 (Show Source): You can put this solution on YOUR website! ``` Hi, the sum of their ages is 55 years Let x and (55-x) represent their ages now cross multiply to solve for x 6(55-x) = 5x 6*55 -6x = 5x 6*55 = 11x 30 = x Two suspects are 30 and 25 years old now. Let y represent the number of years from now the ratio will be 8:7 (30+y)/(25+y) = 8/7 cross multiplying to solve for y 8(25+y) = 7(30+y) 8*25 + 8y = 7*30 + 7y y = 210 - 200 = 10, the years from now the ratio will be 8:7 ```
 Graphs/378224: Determine the domain and range of the function and graph it? f(x)=sqrt(x) + 11 solutions Answer 268779 by ewatrrr(10682)   on 2010-11-30 12:50:38 (Show Source): You can put this solution on YOUR website! ``` Hi, f(x)=sqrt(x) + 1 Pt(0,1), Pt(4,3), Pt(9,4)on the graph of the function Range (1, ) domain (0,) ```
 Linear-equations/378237: how do i figure out the slop of 3x-6y=12?1 solutions Answer 268778 by ewatrrr(10682)   on 2010-11-30 12:41:31 (Show Source): You can put this solution on YOUR website! ``` Hi, the standard slope-intercept form for an equation of a line y = mx + b where m is the slope and b the y-intercept. 3x-6y=12 Solving for y to put into the slope-intercept form 3x - 12 = 6y y = (3/6)x - 2 Or y = (1/2)x - 2 Pt(0,-2) and (4,0) points on the line m = (1/2) As y increases/decreases by 1, x increases/decreases by 2 ```
 Graphs/378227: Determine the domain and range of the function and graph it? f(x)=(x-6)^2+51 solutions Answer 268774 by ewatrrr(10682)   on 2010-11-30 12:33:51 (Show Source): You can put this solution on YOUR website! ``` Hi, Determine the domain and range of the function and graph it f(x)=(x-6)^2+5 the vertex form of a parabola, where(h,k) is the vertex vertex is Pt(6,5) Range (5, )Domain(, )Or all real numbers. ```
 Trigonometry-basics/378203: Find all the solutions between 0 and 2pi to the equation cos(2x)=sin(x)+11 solutions Answer 268771 by ewatrrr(10682)   on 2010-11-30 12:18:17 (Show Source): You can put this solution on YOUR website! ``` Hi, Find all the solutions between 0 and 2pi to the equation cos(2x)=sin(x)+1 = 1 - 2sin^2 1 - 2sin^2(x) = sin (x) + 1 2sin^2(x) + sin (x) =0 sin(x)[2sin(x) + 1] = 0 sin(x)=0 x = 0, 2sin(x) + 1 = 0 sin(x) = -1/2 x = 7/6 pi, 11/6 pi (cos(x), sin(x)) ```
 Quadratic_Equations/378185: what are the x-intercepts (to the nearest tenth) of the equation f(x)=-2x^2+4x+31 solutions Answer 268740 by ewatrrr(10682)   on 2010-11-30 11:08:09 (Show Source): You can put this solution on YOUR website! ``` Hi x-intercepts (to the nearest tenth) of the equation f(x)=-2x^2+4x+3 0 = -2x^2 + 4x + 3 x = 1 - 1.58 = -.58 = -.6 x = 1 + 1.58 = 2.58 = 2.6 x- Intercepts: Pt(-.6,0) and Pt(2.6,0) ```
 Quadratic_Equations/378183: A right triangle has sides of length such that the hypotenuse is 3 inches less than twice the shorter leg and the longer leg is 3 inches longer the shorter leg. how long is each side of the triangle?1 solutions Answer 268735 by ewatrrr(10682)   on 2010-11-30 10:50:39 (Show Source): You can put this solution on YOUR website! ``` Hi, Let x represent the length of the shorter leg. then the hypotenuse is (2x-3) and the other leg is (x+3) Applying the Pythagorean Theorem*** x^2 + (x+3)^2 = (2x-3)^2 solving for x x^2 + x^2 + 6x + 9 = 4x^2 -12x + 9 2x^2 - 18x = 0 2x(x-9)= 0 x = 0 Extraneious solution x = 9, the length of the shorter leg. Other two sides are 12 & 15 CHECKING our Answer*** 81 + 144 = 225 ```
 test/378169: 1.mrs jones bakes x cakes she gives two of them away how many does she keep. 1 solutions Answer 268728 by ewatrrr(10682)   on 2010-11-30 10:25:28 (Show Source): You can put this solution on YOUR website! ``` Hi, bakes x cakes ... gives two of them away Mrs Jones keeps (x-2) cakes ```
 Triangles/378147: one leg of a right triangle is 12 cm longer than the other, and the area of the right triangle is 110 cm squared. Find the length of the longer leg1 solutions Answer 268724 by ewatrrr(10682)   on 2010-11-30 10:16:55 (Show Source): You can put this solution on YOUR website! ``` Hi one leg of a right triangle is 12 cm longer than the other Let x and (x+12cm) represent the lengths of the legs of this right triangle A = (1/2)b*h 110cm^2 = (1/2)x(x+12cm) 220 = x^2 + 12x 0 = x^2 + 12 - 220 factoring (x+22)(x-10)= 0 Note:SUM of the inner product(22x) and the outer product(-10x) = 12x (x+22) = 0 x = -22 extraneous solution (x-10)= 0 x = 10 10cm and 22cm are the lengths of the two legs Letting c represent the length of the longer lefg & applying the Pythagorean Theorem 10^2 + 22^2 = c^2 584 = c^2 (discarding negative solution for length) 24.17cm = c ```
 Travel_Word_Problems/378167: A plane flies at a speed of 350 miles per hour. How far will it travel in 3 hours? 1 solutions Answer 268717 by ewatrrr(10682)   on 2010-11-30 10:06:43 (Show Source): You can put this solution on YOUR website! ``` Hi D = r*t Units are in a consistent form in the question D = 350mph*3hr = 1050mi, the distance the plane travels in 3 hours ```
 Triangles/378153: if the side of an equilateral triangle measures 10 inches, what is it's height?1 solutions Answer 268707 by ewatrrr(10682)   on 2010-11-30 09:37:52 (Show Source): You can put this solution on YOUR website! ``` Hi side of an equilateral triangle measures 10 inches Let x represent the height. Applying the Pythagorean Theorem 5^2 + x^2 = 10^2 25 + x^2 = 100 x^2 = 75 Note: negative solution is extraneous for length ```
 Travel_Word_Problems/378154: Albert is driving at 80 miles per hour. How far will he go in 45 minutes1 solutions Answer 268704 by ewatrrr(10682)   on 2010-11-30 09:32:33 (Show Source): You can put this solution on YOUR website! ``` Hi D = r*t Note: all units of measure must be consistent. 45min = 3/4 hr D = 80mph*(3/4)hr = 60mi ```
 Parallelograms/378075: Suppose the heights of 18-year-old men are approximately normally distributed, with mean 69 inches and standard deviation 2 inches. (a) What is the probability that an 18-year-old man selected at random is between 68 and 70 inches tall? (b) If a random sample of sixteen 18-year-old men is selected, what is the probability that the mean height x is between 68 and 70 inches?1 solutions Answer 268702 by ewatrrr(10682)   on 2010-11-30 09:30:03 (Show Source): You can put this solution on YOUR website! ``` Hi a)probability that an 18-year-old man selected at random is between 68 and 70 inches tall = .5 NORMSDIST(.5) = .6915 = -.5 NORMSDIST(-.5) = .3085 P(-.5 < z > .5) = .6915 - .3085 = .3829 Or 39.29% b)random sample of sixteen 18-year-old men is selected test statistic = z= 1/(2/4) = 2 NORMSDIST(2) = .6915 = .9773 z = -1/(2/4)= -2 NORMSDIST(-2) = .6915 = .0228 P(-2 < z > 2) = .9973 - .0228 = .9545 Or 95.45% ```
 Travel_Word_Problems/377707: Suppose it takes you 10 minutes to walk from home to school at a rate of 264ft./min. Your friend lives closer to school than you do. Which inequality represents the distance d (in feet) that your friend lives from school? A.)d<264 B.)d>264 C.)d>2640 D.)d<26401 solutions Answer 268399 by ewatrrr(10682)   on 2010-11-29 16:30:01 (Show Source): You can put this solution on YOUR website! ``` Hi D = r*t you take 10 minutes to walk from home to school at a rate of 264ft./min. D = 264ft/min*10min = 2640ft, the distance to school for You Your friend lives closer to school than you do. D. d < 2640ft would be the correct selection for your friend's distance ```
 Inequalities/377703: m-7>-8 - The underscroll if for the sign showing greater than or equal to.1 solutions Answer 268397 by ewatrrr(10682)   on 2010-11-29 16:25:47 (Show Source): You can put this solution on YOUR website! ``` Hi, m-7 ≥ -8 Adding 7 to both sides of the inequality m ≥ -1 ```
 logarithm/377694: please help! i"m trying to solve: log 2 (x-1) - log 2 (x+3) = log 2 (1/x) This is what i tried, but i think it's wrong: used quotient rule like this: log 2 (x-1/x+3) = log 2 (1/x) OK! NOW WHAT???!!! I'm lost! :( 1 solutions Answer 268396 by ewatrrr(10682)   on 2010-11-29 16:23:29 (Show Source): You can put this solution on YOUR website! ``` Hi log 2 (x-1) - log 2 (x+3) = log 2 (1/x) log 2 (x-1) - log 2 (x+3) - log 2 (1/x)=0 =0 2^0 = (x-1)/(x+3)(1/x) 1 = x(x-1)/(x+3) (x+3) = x^2 -x x^2 -2x - 3 = 0 (x-3)(x+1)= 0 (x-3)=0 x = 3 (x+1)= 0 x = -1 reject as a solution Any solution that makes an argument (or base) zero or negative must be rejected. log 2 ((-1)-1) - log 2 ((-1)+3) = log 2 (1/(-1)) ```
 Quadratic-relations-and-conic-sections/377632: Find the center and radius of the circle x^2+y^2-6x+2y+6=01 solutions Answer 268389 by ewatrrr(10682)   on 2010-11-29 16:10:26 (Show Source): You can put this solution on YOUR website! ``` Hi, Find the center and radius of the circle The standard equation of a circle with center C(h,k) and radius r is : x^2+y^2-6x+2y+6=0 (x-3)^2 + (y+1)^2 -9 -1 + 6 = 0 (x-3)^2 + (y+1)^2 = 4 (x-3)^2 + (y+1)^2 = 2^2 Center is Pt(3,-1) r = 2 ```
 Quadratic_Equations/377633: Solve 3x^2=4x-11 solutions Answer 268388 by ewatrrr(10682)   on 2010-11-29 16:06:31 (Show Source): You can put this solution on YOUR website! ``` Hi, Solving 3x^2=4x-1 3x^2 - 4x + 1 = 0 factoring (3x -1)(x -1)=0 Note:SUM of the inner product(-1*x) and the outer product(-3x) = -4x (3x -1)=0 x = 1/3 (x -1)=0 x = 1 ```
 Miscellaneous_Word_Problems/377686: The First and Fourth terms of a geometric sequence are 5 and 135. Use the geometric sequence formula to find the value of r. (R=Rate or Ratio) Any Help will be appreciated.1 solutions Answer 268386 by ewatrrr(10682)   on 2010-11-29 16:02:56 (Show Source): You can put this solution on YOUR website! ``` Hi, The First and Fourth terms of a geometric sequence are 5 and 135 Note: for a geometric series: 135 = 5*r^3 27 = r^3 3 = r ```
 Word_Problems_With_Coins/377645: Eighty-six coins made up of dimes and quarters amount to \$14.60. How many of each of these coins is there?1 solutions Answer 268384 by ewatrrr(10682)   on 2010-11-29 15:58:32 (Show Source): You can put this solution on YOUR website! ``` Hi, Let x represent the number of quarters, then (86-x) would be the number of dimes Question states 25x + 10(86-x) = 1460 cents solving for x 25x + 860 - 10x = 1460 15x = 600 x = 40, the number of quarters. 46 dimes (86-40) CHECKING our Answer 25*40 + 10*46 = 1000 + 460 = 1460 cents or \$14.60 ```
 Numbers_Word_Problems/377641: Find three consecutive integers such that four times the sum of all three is 2 times the product of the larger two. 1 solutions Answer 268380 by ewatrrr(10682)   on 2010-11-29 15:52:40 (Show Source): You can put this solution on YOUR website! ``` Hi, Let x, (x+1) and (x+2) represent the three consecutive integers Write as we Read*** 4[x + (x+1) + (x+2)]=2(x+1)(x+2) solving for s 4x + 4x + 4 + 4x + 8 = 2[x^2 + 3x + 2] 12x + 12 = 2x^2 + 6x + 4 2x^2 -6x - 8 = 0 x^2 - 3x -4 = 0 (x-4)(x+1) = 0 (x-4)=0 x = 4 three consecutive integers are 4,5,6 (x+1)=0 x = -1 three consecutive integers are -1,0,1 CHECKING our Answers*** 4 * 15 = 2*30 = 60 4 * 0 = 2 * 0*1 = 0 ```
 Square-cubic-other-roots/377673: a 10 foot ladder is leaning against a house. The bottom of the ladder is 5 feet from the building. how high is the top of the ladder? round to the nearest hundredth.1 solutions Answer 268368 by ewatrrr(10682)   on 2010-11-29 15:39:12 (Show Source): You can put this solution on YOUR website! ``` Hi, Let x represent how high is the top of the ladder Applying the Pythagorean Theorem 5^2 + x^2 = 10^2 25 + x^2 = 100 x^2 = 75 (positive solution only appropriate here) x = 11.18 ft, how high the top of the ladder is ```
 Numbers_Word_Problems/377670: product of a number increased by 10 and 4 equals 221 solutions Answer 268360 by ewatrrr(10682)   on 2010-11-29 15:32:38 (Show Source): You can put this solution on YOUR website! ``` Hi, Let x represent the number Write as we Read*** (x + 10)*4 = 22 solving for x 4x + 40 = 22 4x = -18 x = -18/4 Or -9/2 CHECKING our Answer*** ```
 Polynomials-and-rational-expressions/377655: Graph the parabolas. Show the vertex, axis of symmetry, x intercepts, y intercepts and write the domain and range in interval notation. f(x)=x^2-4x+3 f(x) = (x+1)^2-41 solutions Answer 268357 by ewatrrr(10682)   on 2010-11-29 15:28:55 (Show Source): You can put this solution on YOUR website! ``` Hi Note: the vertex form of a parabola, where(h,k) is the vertex f(x)=x^2-4x+3 Or f(x)= (x-2)^2 -1 in vertex form: x-intercepts (3,0)&(1,0) vertex Pt(2,-1), axis of symmetry x = 2, (0,3) the y-intercept f(x) = (x+1)^2-4 x-intercepts (1,0)&(-3,0) vertex Pt(-1,-4), axis of symmetry x = -1, (0,-3) the y-intercept ```
 Rate-of-work-word-problems/377656: a tank can be filled in 45 minutes and by another pipe in 55 minutes. how long will it take both to fill it?1 solutions Answer 268347 by ewatrrr(10682)   on 2010-11-29 15:07:13 (Show Source): You can put this solution on YOUR website! ``` Hi Let x represent time in minutes it takes to fill the tank together Per minute is the Equalizer 1/45 + 1/55 = 1/x Mulitplying each term by 45*55x so as all denominators = 1 55x + 45x = 45*55 100x = 45*55 x = 45*55/100 x = 27.75 min, time in minutes it takes to fill the tank together ```
 Probability-and-statistics/377638: There are 3 trails on the north face of Cowles Mountain and 2 trails on the south face. How many routes are there going up the north face and down the south face?1 solutions Answer 268329 by ewatrrr(10682)   on 2010-11-29 14:41:50 (Show Source): You can put this solution on YOUR website! ``` Hi Each of the 3 north face trails has two options on the south face going down 3*2 = 6 6 is the total number of different routes possible going up the north face and down the south face ```
 Probability-and-statistics/377628: The mean concentration of carbon dioxide is 365 parts per million with a standard deviation of 100 parts per million. Take a sample from 25 cities. Describe the sampling distribution of the sample mean. Find the probability that the sample mean concentration will be above 385 parts per million. So far, I am able to figure (385-365)/(100/(sqrt 25)) = 0.0527 At this point, checking the Z table I get the value of 0.06031. I'm not sure where I go from here in finishing this problem. Any help would be greatly appreciated.1 solutions Answer 268324 by ewatrrr(10682)   on 2010-11-29 14:36:53 (Show Source): You can put this solution on YOUR website! ``` Hi (385-365)/(100/(sqrt 25)) = 20/20 = 1 Note: Z table or NORMSDIST(1)= .8413 1 - .8413 = .1587 Or 15.87% is the probability that the sample mean concentration will be above 385 parts per million. ```
 Rate-of-work-word-problems/377620: I have a problem on my homework that has very little detail in the textbook. I need to know a formula for the following: Two pipes working together can fill a tank in 12hrs. Working alone, the larger one can fill the tank in 18hrs less than the smaller one. How long does it take for the smaller tank working alone? Thank you so much!1 solutions Answer 268310 by ewatrrr(10682)   on 2010-11-29 14:24:02 (Show Source): You can put this solution on YOUR website!Hi the larger one can fill the tank in 18hrs less than the smaller one. Let x represent the time for the smaller alone, then (x-18hr)would be the time for the larger alone Per hour is the Equalizer 1/x + 1/(x-18) = 1/12 Mulitiplying each term by 12x(x-18)so all denominators = 1 12(x-18) + 12x = x(x-18) solving for x 12x - 12*18 +12x = x^2 - 18x 24x - 12*18 = x^2 - 18x x^2 - 42x + 216 = 0 x = 6 Cannot use x = 36hr, the time for the smaller alone. 18hr for the larger alone (36-18) CHECKING our Anwer 1/36 + 1/18 = 2/72 + 4/72 = 6/72 = 1/12
 Linear-systems/377618: I am needing help with this verbal problem please read entire thing to the bottom as is a little long and Thank you for you help. a. when x=75 c=2x+20 =2(75)+20 =150+20 =170 we have the ordered pair(75,170) b.when x=300 c=2x+20 =2(300)+20 =600+20 =620 we have the ordered pair(300,620) c. when x=1000 c=2x+20 =2(1000)+20 =2000+20 =2020 WE HAVE THE ORDERED PAIR (1,000,2020) In the example, find the number of units produced when the total cost is (a)\$430, (b)\$700 and (c)\$1,400. write the answers as ordered pairs. I am really confused as to how to do this and the steps to take to do this. I would really appreciate some help on this. 1 solutions Answer 268303 by ewatrrr(10682)   on 2010-11-29 14:02:31 (Show Source): You can put this solution on YOUR website! ``` Hi c=2x+20 Can only assume that x is the number of units and c is the cost of producing them. (a)\$430 \$430 = 2x + 20 \$410 = 2x 205 = x, the number of units costing \$430 (205,430) (b)\$700 c = \$700 \$700 = 2x + 20 \$680 = 2x 340 = x, the number of units costing \$700 (340,700) (c)\$1,400 c =\$1400 \$1400 = 2x + 20 \$1380 = 2x 690 = x the number of units costing \$1400 (690,1400) ```