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 Polynomials-and-rational-expressions/461113: is the expression to te right simplifid corectly? explain in complete sentences why or why not? 3a + b/7 + b = 3a/71 solutions Answer 316260 by oberobic(2304)   on 2011-06-14 21:53:06 (Show Source): You can put this solution on YOUR website!Assuming you started with 3a +b/7 + b = 3a/7 Multiply both sides by 7 to get rid of fractions. 21a +b +7b = 3a Subtract 3a from both sides 21a +b +7b -3a = 0 Collect terms 18a +8b =0 Divid by 2 9a +4b = 0
 Mixture_Word_Problems/461079: if you need 50lbs of an alloy that is 50% nickel how many pounds of an alloy with 80% must be mixed with an alloy that is 40% nickel1 solutions Answer 316259 by oberobic(2304)   on 2011-06-14 21:48:03 (Show Source): You can put this solution on YOUR website!With problems like this, you have to keep track of how much "pure" stuff you need. It says you need 50 lb of 50% nickel. 50*.5 = 25 lbs of pure nickel . The total of 50 lb is divided between the amount of 40% nickel and 80% nickel x = the amount of 40% nickel (50-x) = the amount of 80% nickel . .4x + .8(50-x)=25 .4x + 40 - .8x = 25 -.4x = -15 x = 37.5 lb of 40% alloy . 50-x = 12.5 lb of 80% alloy . Check your answer. .4*37.5 = 15 .8*12.5 = 10 15+10 = 25 . Done.
 Word_Problems_With_Coins/461089: Aviva has a total of 57 coins, all of which are either dimes or nickels. The total value of the coins is \$4.65. Find the number of each type of coin.1 solutions Answer 316257 by oberobic(2304)   on 2011-06-14 21:41:37 (Show Source): You can put this solution on YOUR website!With coin problems you have to keep track of the number of coins and of their value. For example, d = number of dimes 10d = value of the dimes in cents n = number of nickels 5n = value of the nickels in cents . Given Aviva has \$4.65, which is 465 cents. Aviva has only nickels and dimes, so we can restate the value. 5n + 10d = 465 Aviva has 57 coins in total. n + d = 57 . So we can treat these as a system of equations. . 5n + 10d = 465 n + d = 57 Multiply the second equation by 5 . 5n + 10d = 465 5n + 5d = 285 . Subtract the second equation from the first equation 5d = 180 Divide both sides by 5 d = 36 . Substitute n + d = 57 n +36 = 57 n = 57-36 n = 21 . Check to see if this is right. . 5n = 5*21 = 105 10d = 10*36 = 365 105+365 = 465 which is the right answer . Of course, you could have solved using substitution. . 5n + 10d = 465 n + d = 57 n = 57-d 5(57-d) +10d = 465 285 -5d + 10d = 465 As you can see, you get to the same answer, just in a different way. . Done.
 Graphs/461084: I need to create an equation of a nonlinear function. I don't know what this is. Can you please give me an example? Thanks so much. 1 solutions Answer 316256 by oberobic(2304)   on 2011-06-14 21:32:35 (Show Source): You can put this solution on YOUR website!A nonlinear equation is one in which x has a power. For example . Note that a nonlinear equation is one that cannot be a straight line. The following is the graph of . The following is the graph of . The following is the graph of . Notice that the number of curves (or changes in direction) is one less than the power of x.
 Linear-equations/460022: graph x+3y=0 1 solutions Answer 315514 by oberobic(2304)   on 2011-06-11 18:12:23 (Show Source): You can put this solution on YOUR website!Get the equation in y=mx+b slope-intercept form. Subtract x from both sides Divide both sides by 3 or . When x=0, y=0: (0,0) When x=3, y=-1: (3,-1) Plot the points and draw the line. .
 Polynomials-and-rational-expressions/460026: How do you find all roots to the equation 3x^2+5x=0?1 solutions Answer 315513 by oberobic(2304)   on 2011-06-11 18:07:59 (Show Source): You can put this solution on YOUR website!3x^2 +5x = 0 The first two factors share an x. x(3x +5)=0 . One root is x=0 The other is found by solving 3x = -5 x = -5/3 . Done
 Graphs/460039: I really dont understand this problem: 1 solutions Answer 315511 by oberobic(2304)   on 2011-06-11 18:02:34 (Show Source): You can put this solution on YOUR website!The question is missing...
 Human-and-algebraic-language/460033: Hello. Referred to me by Minka. The function f(x) = 180x/100-x models the cost, f(x), in millions of dollars, to remove x% of a river's pollutants. If the government commits \$60 million for this project, what percentage of the pollutants can be removed? ___% of the pollutants can be removed. Truly greatful to whom replies. Samantha1 solutions Answer 315509 by oberobic(2304)   on 2011-06-11 17:57:41 (Show Source): You can put this solution on YOUR website!Given: . Substitute what you are given. Multiply both sides by 100. Equals are equal, so you can swap sides. Divide both sides by 180. . So, the \$60 million would result in the removal of 33.33333% of the pollutants. . Done. .
 Quadratic_Equations/460031: Find all roots and check your answer to the equation 3x^2+5x=01 solutions Answer 315507 by oberobic(2304)   on 2011-06-11 17:46:18 (Show Source): You can put this solution on YOUR website!3x^2 + 5x = 0 x(3x+5) = 0 . So, one root is x=0 . 3x+5 = 0 3x = -5 x = -5/3 . That's another root. . .
 Evaluation_Word_Problems/460028: Construction utilizes the Pythagorean Theorem in many instances to insure a “square” structure. In laying out the footers or corners of any building the concept of a 3-4-5 right triangle is applied. (1)Name two more dimensions of a right triangle that will also yield a square corner and justify. 1 solutions Answer 315506 by oberobic(2304)   on 2011-06-11 17:43:08 (Show Source): You can put this solution on YOUR website!You could try: 9, 12, 15. Check to see if they fit the Pythagorean Theorem's requirements. C^2 = A^2 + B^2 A = 9 B = 12 C = 15 . A^2 = 81 B^2 = 144 A^2+B^2 = 81+144 81+144 = 225 sqrt(225) = 15 . That's correct. . Done.
 Linear-equations/460008: write the slope-intercept equation for the line that passes through (14, -2) and is perpendicular to 7x - 10y = 18 please show all of your work1 solutions Answer 315502 by oberobic(2304)   on 2011-06-11 17:14:37 (Show Source): You can put this solution on YOUR website!A line perpendicular to another line with have negative inverse slope. The define original line is 7x - 10y = 18 Subtract 7x from both sides -10y = -7x + 18 Divide both sides by -10 y = 7/10*x -18/10 This equation is in slope-intercept format y = mx +b m = 7/10 So, the perpendicular line will have slope -10/7 . y = -10/7*x + b . You need the line to go through the point (14,-2). That means when x=14, y=-2 Substitute that with what we already know -2 = -10/7*(14) + b We can cancel the 14 with the 7 -2 = -10(2) + b -2 = -20 + b Add 20 to both sides 18 = b . y = -10/7*x + 18 . Always check your answer, so substitute x=14 and see what value of y you get. y = -10/7*14 + 18 y = -20 + 18 y = -2 That's right. . A graph is always helpful. In this case, graph both equations to see if they're perpendicular by visual inspection (of course, you KNOW they're perpendicular because of the slopes)...
 Polynomials-and-rational-expressions/460014: A rectangle that is 90cm and the length and width is unknown, also it is 3cm's longer than twice the width? The perimeter is 90cm's.Need to know the algerbric equasion for this and find the unknowns?1 solutions Answer 315500 by oberobic(2304)   on 2011-06-11 17:00:48 (Show Source): You can put this solution on YOUR website!Always list what you know first. p = perimeter l = length w = width p = 2l + 2w p = 2(l+w) p = 90 . The given relationship has to be turned from English into algebra. . length is 3 cm longer than twice the width l = 2w + 3 . Substitute and solve for l. . p = 2l + 2w p = 2(2w+3) + 2w p = 4w + 6 + 2w 90 = 6w + 6 84 = 6w 6w = 84 w = 84/6 w = 14 cm . Substitute this value to find l. . l = 2*w + 3 l = 2*14 + 3 l = 31 cm . Check the perimeter using l = 31 w = 14 2(31)+2(14) = ?? 62 + 28 = 90 Right. . Done
 test/460016: A jet is flying from phoenix to Houston at a speed r of 600 miles per hour. The distancevd between the two cities is about 1200 miles. Which equation can be used to find the time t it takes to make the trip? 1 solutions Answer 315499 by oberobic(2304)   on 2011-06-11 16:52:33 (Show Source): You can put this solution on YOUR website!The standard distance formula is: d = rt where d = distance r = rate (or speed) t = time . r = 600 d = 1200 . So, d = rt Divide both sides by r d/r = t t = d/r t = 1200/600 t = 2 . Done
 Linear-equations/459139: what's the slope of a line passing through the points (2,4) and (-1,-2)1 solutions Answer 314885 by oberobic(2304)   on 2011-06-08 21:29:50 (Show Source): You can put this solution on YOUR website!The slope is the change in y divided by the change in x, also called "rise over run". . The two points are (2,4) and (-1,-2). . Change in y is: -2 -4 = -6 . Change in x is: -1 -2 = -3 . Slope = -6/-3 = 2 . Done.
 Age_Word_Problems/459136: Three years ago, Jeffrey was twice as old as Michael is now. In nine years, Jeffery will be four times as old as Michael is now. What are Jeffery's and Michael's current age.1 solutions Answer 314880 by oberobic(2304)   on 2011-06-08 21:23:22 (Show Source): You can put this solution on YOUR website!Start by defining what their ages are now. J = Jeffrey M = Michael . Three years ago means -3. Jeffrey was twice as old as Michael is now. J-3 = 2M . In nine year means +9. J+9 = 4M . Set up the linear equations. J -2M = 3 J - 4M = -9 .. Subtract the second from the first. 2M = 12 M = 6 . Substitute. J-3 = 12 J = 15 . Always check your work! In this case, use the second equation. J+9 = 4M J+9 = 15+9 =24 4M = 4*6 = 24 Right. . Answer: Jeffrey is 15, and Michael is 6. . Done.
 Numbers_Word_Problems/459130: With a strong wind behind it, a Delta jet flies 2400 miles from Los Angeles to Orlando in 4 hours and 45 minutes. The return trip takes 6 hours, as the plane flies into the wind. Find the speed of the plane in still air, and find the wind speed to the nearest tenth mile per hour. 1 solutions Answer 314878 by oberobic(2304)   on 2011-06-08 21:04:38 (Show Source): You can put this solution on YOUR website!The basic distance equation is d = rt, where d = distance r = rate t = time . Define s = speed of the plane w = speed of the wind . Flying with a tailwind r = s+w . Flying with a headwind r = s-w . Flying with the tailwind d = 2400 t = 4.75 2400 = 4.75*r r = 2400/4.75 r = 505.263158 r = 505.26 . Flying with the headwind d = 2400 t =6 2400 = 6*r r = 400 . s + w = 505.26 s - w = 400 Add 2s = 905.26 s = 452.63 . Find w. s+w = 505.26 w = 505.26 - 452.63 w = 52.63 . Check to see if the distances work. . 6*(452.63-52.63) = ?? 6*(400) = 2400 Right . 4.75*(452.63+52.63) = ?? 4.75*(505.26) = 2399.985 which is close enough to 2400. . Answer: The speed of the plane in still air is 452.6 mph. . Done.
 Travel_Word_Problems/459117: A plane flies 900 miles with a tail wind in 3 hours.It takes the same plane 2 hours to fly the 300 miles when flying against the wind. What is the plan's speed in still air?1 solutions Answer 314876 by oberobic(2304)   on 2011-06-08 20:28:06 (Show Source): You can put this solution on YOUR website!The basic distance equation is: d = rt . We are told that flying with the tailwind 900 = r*3 r = 300 BUT r = speed of the plane + speed of the tailwind . We are told flying with the headwind 300 = r*2 r = 150 BUT this time, r = speed of the plane - speed of the wind . Assuming the wind is constant...which is important. . We can define: s=speed of the plane w=speed of the wind . Substitute what we know: s+w = 300 s-w = 150 . Add the linear equations. 2s = 450 . Solve for s s = 225 . Substitute to solve for w w = 75 . Check by substituting these value to see if you get the correct distance. . 3(225+75) = ?? 3(300) = 900 Right . 2(225-75) = ?? 2(150) = 300 Right . Re-read the question to see what answer is required. . Answer: The plane's speed in still air is 225 miles/hr. . Done.
 Rectangles/459110: the perimeter of a rectangle is 20 inches. the length of the rectangle is 2inches longer than than the width. write the equation to determine the width of the rectangle1 solutions Answer 314873 by oberobic(2304)   on 2011-06-08 20:15:52 (Show Source): You can put this solution on YOUR website!P = perimeter L = length W = width P = 2(L+W) . P = 20 . L = W+2 . (W+2)*(W) = 20 . W^2 + 2W = 20 . Done.
 Linear-equations/459109: The x- and y-intercepts of the graph of g are 1 and 4, respectively. What is the linear equation satisfying the given condition. 1 solutions Answer 314871 by oberobic(2304)   on 2011-06-08 20:11:26 (Show Source): You can put this solution on YOUR website!y = mx + b . When x=0, y = 4 (given) (0,4) . When y=0, x = 1 (given) (1,0) . Recall that the change in y divided by the change in x = slope. . Change in y = 4-0 = 4 Change in x = 0-1 = -1 Slope = 4/-1 = -4 . The equation is thus: y = -4x +4 . The graph is: . Notice that the y-intercept is (0,4), the x-intercept is (1,0), and the line goes through both points.
 Pythagorean-theorem/459098: how do I find the unknown length in a right triangle 10cm and 13cm1 solutions Answer 314868 by oberobic(2304)   on 2011-06-08 20:05:53 (Show Source): You can put this solution on YOUR website!There is no solution unless you either know the interior angle, or you know it is a right triangle. The Pythagorean Theorem can be used. . Assuming the 13 is the hypotenuse, . . Assuming the hypotenuse is unknown. . . Done.
 Geometry_Word_Problems/458324: The area of a rectangular wall of a barn is 108 square feet. Its length is 6 feet longer than twice its width. Find the length and width of the wall of the barn?1 solutions Answer 314405 by oberobic(2304)   on 2011-06-06 22:06:26 (Show Source): You can put this solution on YOUR website!L * W = 108 sq ft Length is 6 ft greater than twice the width. L = 2W + 6 Substituting (2W+6)*W = 108 2W^2 + 6W = 108 Divide both sides by 2 W^2 + 3W = 54 W^2 + 3W - 54 = 0 Factor (W +9)(W -6) = 0 Roots are W=-9 and W=6. A negative width is impossible, so W=6 L = 2W + 6 L = 2(6) + 6 L = 18 . Always check your answer. L*W = ?? 18 * 6 = 108 Correct. . Done
 Travel_Word_Problems/458273: One car is going East and is going 10 miles per hr more than a car going west. The distance between their starting points is 184 miles. If they meet in 1 hour and 36 minutes, what is the speed of the two cars.1 solutions Answer 314381 by oberobic(2304)   on 2011-06-06 20:43:29 (Show Source): You can put this solution on YOUR website!s = speed of car going west s+10 = speed of the car going east t = 1 hr 36 min t = 1.6 hr d = 184 miles between the two cars . But they do not travel 184 miles each. They meet somewhere in the middle, but not exactly in the middle because they are going different speeds. However, their combined distance traveled = 184. . 1.6s + 1.6*(s+10) = 184 3.2s +16 = 184 3.2s = 168 s = 52.5 is the speed of the car going west s+10 = 62.5 is the speed of the car going east . Always check your work. . In this case we have to check how far they travel to check these values. . 1.6 hr * 62.5 mph = 100 miles 1.6 hr * 52.5 mph = 84 miles . So, the speeds of the two cars are 62.5 and 52.5 mph. . Done.
 Equations/458265: 2x^2+x-3=0 My class assignment is to plot a grapgh using excel, but the main bit is trying to work out the the intersections of . x=-3 and x=3. I need to plot some coordinates.1 solutions Answer 314359 by oberobic(2304)   on 2011-06-06 19:16:35 (Show Source): You can put this solution on YOUR website!factor 2x^2 +x -3 = 0 . (2x + ?)(x - ?) = 0 . Well the factors of 3 are 1 and 3. So, does that work or do we have to use the quadratic equation? . (2x+3)(x-1) = 0 . So the solutions are x=1 or -3/2. . The graph is
 Human-and-algebraic-language/458204: if the sides of a square are lengthned by 7 inches,the area becomes 121 in^2. find the length of a side of the original square1 solutions Answer 314357 by oberobic(2304)   on 2011-06-06 19:11:24 (Show Source): You can put this solution on YOUR website!s = lengths of the sides of the square s^2 = area (s+7)^2 = 121 given (s+7)(s+7) = 121 s^2 +7s +7s + 49 = 121 . s^2 +7s +7s + 49 -121 = 0 s^2 +14s -72 = 0 . factor (s + ?)(s - ?) = 0 . 2*36 = 72, difference = 34, nope. 4*18 = 72, difference = 14, which is it! . (s +18)(s -4) = 0 . s = -18 or 4 a negative length does not make sense, so s = 4 . add 7 and check area to make sure it is 121 . 11*11=121 is true. . The sides of the original square were 4 inches. . Done.
 Money_Word_Problems/458160: Ed bought \$2,000 in stock shares one week before the stock price dropped \$10.00. If he had waited for the price setback, he could have bought 10 more shares for the same amount. How many shares did he buy?1 solutions Answer 314353 by oberobic(2304)   on 2011-06-06 18:58:38 (Show Source): You can put this solution on YOUR website!In week 1, Ed purchased stock: x = number of shares of stock he bought p = purchase price per share xp = 2000 . One week later...the stock tumbled... price is now (p-10) he could have bought 10 more shares: (x+10) for the same purchase price (x+10)(p-10)=2000 . since x*p = 2000 x = 2000/p p = 2000/x . (x+10)(p-10) = 2000 xp -10x +10p -100 = 2000 . substitute for x (2000/p)*p - 10*(2000/p) +10p -100 = 2000 2000 -20000/p +10p -100 = 2000 -20000/p +10p = 100 multiply by p -20000 + 10p^2 = 100p 10p^2 -100p - 20000 = 0 divide by 10 p^2 -10p - 2000 = 0 factor 20*100 = 2000 < 40*50 = 2000 < . (p-50)(p+40) = 0 . p = 50 or -40, but a negative stock price is nonsense. . p = 50 x = 2000/p x = 40 . So, in week 1, Ed purchased 40 shares at \$50 per share. The next week the stock fell by \$10 Now the price is \$40. For \$2000 he could buy 50 shares now. Which is 10 more shares than he bought the first week. . Done.
 Quadratic_Equations/458256: find the x-intercept and y-intercept: f(x)= -x^2 + 5x + 501 solutions Answer 314351 by oberobic(2304)   on 2011-06-06 18:46:19 (Show Source): You can put this solution on YOUR website!y-intercept occurs when x=0, which is the point (0,50) -x^2+5x+50 can be factored (-x+10)(x+5)=-x^2 -5x +10x +50 So, x=10 and x=-5 will be the roots. y=0, so the points will be (-5,0) and (10,0) A graph is always a good idea.
 Functions/457668: Solve. 5/2x+1/4x=11/4+x1 solutions Answer 313990 by oberobic(2304)   on 2011-06-05 13:06:24 (Show Source): You can put this solution on YOUR website!5/2x + 1/4x = 11/4 + x . These fractions are painful. But we can treat them all as quarters. . Recall 5/2 = 10/4 Also, x = 1/1x = 2/2x = 3/3x = 4/4x... . 10/4x + 1/4x = 11/4 + 4/4x . 11/4x = 11/4 + 4/4x . Subtract 4/4x from both sides 7/4x = 11/4 . Multiply both sides by 4 7x = 11 . Divide both sides by 7 x = 11/7 .
 Graphs/457659: use the intercets to graph the equation. x+2y=4 and 4+4y=81 solutions Answer 313988 by oberobic(2304)   on 2011-06-05 12:53:36 (Show Source): You can put this solution on YOUR website!x + 2y = 4 2y = -x +4 y = -x/2 + 4/2 y = -x/2 + 2 . 4 + 4y = 8 4y = 8 -4 4y = 4 y = 1 .
 Probability-and-statistics/457646: suppose that you are taking a multiple choice quiz with 5 questions and 4 possible answers to each. In how many different ways can you get a 60% on the quiz?1 solutions Answer 313987 by oberobic(2304)   on 2011-06-05 12:50:02 (Show Source): You can put this solution on YOUR website!This is a peculiar question because the number of choices does not matter. You either get the answer right or wrong. 60% of 5 = 3/5, so you need to get 3 of the 5 questions right. . You can get them Right or Wrong in several ways, but do you need to know that, too? . RRRWW . Shift left and wrap the one that went of the left end onto the right end RRWWR . Repeat RWWRR . Repeat WRRRW . If you repeat again, you're right back to where you were, so that is not a "new" sequence. . Or you could start with RWRWR and go through those RWRWR WRWRR RWRRW WRRWR RRWRW RWRWR is a repeat sequence . Or you start with: WRWRR, or WWRRR, etc. But that is a lot of work, and error-prone, too. . If you have done anything with permutations and combinations, you may recognize that the question is asking how many ways you can pick 3 specific items from a set of 5 items: C(n,r), where n=5, r=3 Ignoring the "*1" factors That means there are 10 ways you can get 3 questions right out of 5 total questions. . Now if the question were to have asked "at least 60%" then the answer would be different because you would have to consider the case of getting all 5 right as well as 4/5 right. . Done
 test/457640: the expression is equivalent to what?1 solutions Answer 313986 by oberobic(2304)   on 2011-06-05 12:28:33 (Show Source): You can put this solution on YOUR website! . . Adding we get... . Answer: . Done
 Numbers_Word_Problems/457643: I am a number what number am I? this is my homework. this is the question sort of. I am the difference between a third and 25% of £60 What number am I?1 solutions Answer 313985 by oberobic(2304)   on 2011-06-05 12:20:35 (Show Source): You can put this solution on YOUR website!Recognize that, in this case, "of" means multiply: 1/3 * 60 = 20 . Similarly, 25% = 1/4 So, 1/4 * 60 = 15 . The "difference" means to subtract, which is 20 - 15 = 5 . Done.