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# Recent problems solved by 'Earlsdon'

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 Triangles/93150: This question is from textbook Problem: One leg of a right triangle has a length of 3m. The other sides have lengths that are consecutive integers. Find these lenths. The other leg is ____ m The length of the hypotenuses is ____m I get the consecutive inegers n, n+1 and if I use the formula a^2 + b^2 = c^2 - I don't know what to plug in for c. I've been shown several ways, and now I'm just confused. Thanks!!! 1 solutions Answer 67784 by Earlsdon(6294)   on 2007-08-17 18:36:00 (Show Source): You can put this solution on YOUR website!Well, on this problem you do have to make at least one assumption: The given side of 3 meters is (or is not) the hypotenuse. If you assume that it is the hypotenuse, it is therefore the longest of the three sides of the right triangle. Since the other two sides are consective integers and each is less then 3, they can only be 1 and 2 mters in length. Well, as soon as you apply the Pythagorean theorem, you soon see that this cannot be so, because does not equal . So the 3-meter side is one of the legs, right? Now you have a choice: Is it the shorter leg or the longer leg (not the hypotenuse)? Let's try the shorter leg. So the hypotenuse, being the longest side must be n+1 and the other leg must be n. Applying the Pythagorean theorem: Subtract from both sides. and... So, the hypotenuse is 5 meters,and the other leg is 4 meters. If you were familiar with Pythagorean triplets, you could easily have guessed this result.
 Quadratic_Equations/93122: I need help with these problems Solve by using the quadratic formula: 3x^2=11x+4 and also find the axis of symmetry: y=-x^2+4x+2 Thanks a million1 solutions Answer 67773 by Earlsdon(6294)   on 2007-08-17 15:10:09 (Show Source): You can put this solution on YOUR website!1) Solve using the quadratic formula: First, write the equation in standard form for quadratic equations: Here, you can see that: a = 3, b = -11, and c = -4 Make the appropriate substitutions into the formula and solve for x: Simplify this. or or or 2) Find the axis of symmetry for: The axis of symmetry is given by: Your equation here is already in standard form: so a = -1, b = 4, and c = 2 The axis of symmetry is: This is the equation of axis of symmetry!
 Graphs/93124: Use a graphing utility to approximate (to two decimals) any relative minimum or maximum values of the function. f(x) =2x^3+3x^2-12X1 solutions Answer 67770 by Earlsdon(6294)   on 2007-08-17 14:48:52 (Show Source): You can put this solution on YOUR website!Find the relative maximum/minimum, by graphing, of: From the graph, it looks like you have a relative maximum at x = -2 and a relative minimum at x = 1.
 Quadratic_Equations/92925: I am having problems with this word problem. The demand and supp;y equations for a certain item are given by D=-5p+40 S=-p^2+30-8 find the equilibrium price. Thanks a million1 solutions Answer 67630 by Earlsdon(6294)   on 2007-08-16 11:18:59 (Show Source): You can put this solution on YOUR website!Find the equilibrium price, p, for the Demand and Supply equations: I assume that you had a typo in your post because you had written: The equilibrium occurs when demand, D, equals supply, S. Let's put this into a standard-form quadratic equation: . Solve using the quadratic formula: or The final answer is that there are two equilibrium prices: p = \$33.57 or p = \$1.43
 test/92937: The median of a set of 9 consecutive integers is 42. What is the greatest of these 9 integers?1 solutions Answer 67629 by Earlsdon(6294)   on 2007-08-16 10:53:16 (Show Source): You can put this solution on YOUR website!Since the "median" of a set of numbers is the middle number and the given set cosists of consecutive integers, then you know that 42 is the middle integer of these nine consecutive integers, so the set looks like... 38,39,40, 41,42,43,44,45,46 The greateset integer is 46
 Trigonometry-basics/92930: This question is from textbook Algebra and Trigonometry find the vertical asymptote of the rational function: f(x)=3x-12/4x-21 solutions Answer 67627 by Earlsdon(6294)   on 2007-08-16 10:46:50 (Show Source): You can put this solution on YOUR website!Find the vertical asymptote of: Notice that, in this function, the denominator will be zero when x = 1/2 The graph of this function has a "discontinuity" at x = 1/2, the line, x = 1/2 is a vertical asymptote.
 Linear_Algebra/92935: This question is from textbook f(x) = 3x(2x – 1). f(–1) =1 solutions Answer 67622 by Earlsdon(6294)   on 2007-08-16 10:17:54 (Show Source): You can put this solution on YOUR website!If f(x) = 3x(2x-1), find f(-1) To do this, you just substitute -1 into the given function where ever there is an x. f(-1) = 3(-1)(2(-1)-1) Evaluate the right side. f(-1) = -3(-2-1) f(-1) = -3(-3) f(-1) = 9...and there you have it!
 Equations/92827: FIND AN X AND A Y THAT MAKS TIS EXPRESSION TRUE Y=4X-31 solutions Answer 67553 by Earlsdon(6294)   on 2007-08-15 16:45:20 (Show Source): You can put this solution on YOUR website!You can find any number of x-y combinations that will work: Choose x = 5 That's just one combination: x = 5 and y = 17 Just choose any value for x, plug it into the equation, solve and you will get the corresponding value of y.
 Linear-equations/92823: find the slope of the line passing through the points (-4,0) and (-4,-2).1 solutions Answer 67538 by Earlsdon(6294)   on 2007-08-15 16:00:58 (Show Source): You can put this solution on YOUR website!Recall that the slope (m) can be described as "Rise over Run" or the change in the y-coordinates over the change in the x-coordinates. In algebrese: Of course, the x's and y's are the coordinates of the given points (-4, 0) and (-4, -2) So let's calculate the slope, m, of the line passing through the given points using the formula: Simplifying this we get: ...but, as you know, division by zero is frowned upon in mathematics, so when you see a slope that has zero in the denominator, (a zero run), this is called an "undefined (not a zero) slope". What it really means is that the line is vertical.
 Linear-equations/92817: Adult tickets for a play cost \$20 and child tickets cost \$16. If there were 27 people at a performance and the theater collected \$646 from ticket sales, how many adults and how many children attended the play?1 solutions Answer 67535 by Earlsdon(6294)   on 2007-08-15 15:39:16 (Show Source): You can put this solution on YOUR website!This problem has no solution! Why? Because, if all 27 attendees were adults (at \$20 each), the maximum that could be collected for ticket sales would be 27(\$20) = \$540, but the problem states that \$646 were collected from ticket sales. Where did the extra \$106 (\$646 - \$540) come from?
 Polynomials-and-rational-expressions/92271: ADD 5b^3 - 8b + 2b^2 and 3b^2 - 7b^3 + 5b1 solutions Answer 67132 by Earlsdon(6294)   on 2007-08-11 10:26:22 (Show Source): You can put this solution on YOUR website!Add: and Group the like-terms together. Combine the like-terms.
 Polynomials-and-rational-expressions/92273: Simplify each of the following expressions. Write your ansewers with positive exponents only. (x^2)^-3(x^-2)/ (x^2)^-41 solutions Answer 67130 by Earlsdon(6294)   on 2007-08-11 10:21:37 (Show Source): You can put this solution on YOUR website!Simplify: = = 1
 Quadratic_Equations/92189: This question is from textbook If the parabola y - 2 = a(x-3)^2 goes through the point (2,0), what is the value of a? please HELP!!1 solutions Answer 67024 by Earlsdon(6294)   on 2007-08-10 11:55:41 (Show Source): You can put this solution on YOUR website!Since you have the equation: and a point (2, 0) through which the graph passes, then the given point (2, 0) is said to satisfy the equation . So you just substitute the x- and y-coordinates of the given point into the equation and solve for a. Substitute x = 2 and y = 0 So... Done!
 Rational-functions/92187: This question is from textbook write each fraction as a terminating or repeating decimal 3/8 huh? i really dont get this1 solutions Answer 67022 by Earlsdon(6294)   on 2007-08-10 11:46:22 (Show Source): You can put this solution on YOUR website!Convert 3/8 to its decimal equivalent. Remember, all fractions are division problems...the numerator (top) is divided by the denominator (the bottom) If you have a calculator, just divide 3 by 8...enter the 3, push the divide key then enter the 8 followed by the = key (or the ENTER key on some calculators). The diplay window will show .375 (This is a terminating decimal) Otherwise, you will have to use long division.
 real-numbers/92186: This question is from textbook please help me understand how to write in a common fraction in lowest terms 1.6(the 6 reapeating) 1 solutions Answer 67021 by Earlsdon(6294)   on 2007-08-10 11:40:12 (Show Source): You can put this solution on YOUR website!Write 1.666... as an equivalent fraction in its lowest terms. Well, the good news is that a repeating decimal (such as 1.666...) is a rational number and can, therefore, be expressed as the ratio of two integers (i.e. a fraction)...but, expressing a repeating decimal as a fraction requires a little more work than does converting a terminating decimal. Here's how it goes: First, separate the integer from the decimal so that we can convert just the decimal part (0.666...) to its equaivalent fraction. Let n = 0.666... Multiply both sides by 10 10n = 6.666... Now subtract n from 10n 10n-n = (6.666...) - (0.666...) 9n = 6 Divide both sides by 9 n = 6/9 ...but n = 0.666..., so 0.666... = 6/9 Reduce this to: 0.666... = 2/3 Finally, add the integer back to get: 1.666... = 1 2/3 or, if you need it as a improper fraction, then: 1.666... = 5/3 You can check this with your calculator by dividing 5 by 3 and the calculator will display 1.666...
 Polynomials-and-rational-expressions/92180: Hello I am not sure how to go about this. If the sides of a square are decreased by 3cm, the area is decreased by 81cm^2. What were the dimensions of the original square. I am thinking (x-3)^2=a-81cm^3, but where do I go from here?1 solutions Answer 67019 by Earlsdon(6294)   on 2007-08-10 11:24:08 (Show Source): You can put this solution on YOUR website!Well, your initial idea is right on! Where A = original area and x = the original length of the side of the square. The next step is to recall that , that is; the original area (A) is equal to the original sides squared , so substitute the A with in the first equation then solve for x. Expand the left side. Subtract from both sides. Subtract 9 from both sides. Finally, divide both sides by -6. cm. Check:
 Inequalities/91904: Can you please explain how to do this problem. the abosolute value of x-2 is less than or equal to 9. The answer is x is less than or equal to 11 or x is greater than or equal to -7. How do you get these?1 solutions Answer 66752 by Earlsdon(6294)   on 2007-08-08 13:25:52 (Show Source): You can put this solution on YOUR website!Solve for x: Recall that if: |a| <= b then either a <= b or a >= -b |x-2| <= 9 Remove the absolute-value bars and write two inequalities: or Solve these two inequalities. or
 Polynomials-and-rational-expressions/91861: This question is from textbook this problem was a little confuseing i dont know how to sovle this one!! but i do think think answer is either cancels out to 0 or x+y can some one help? (x-y/x+y)+(x+y/x-y)1 solutions Answer 66725 by Earlsdon(6294)   on 2007-08-08 11:04:01 (Show Source): You can put this solution on YOUR website!Simplify: I hope I have this right! Add the two fractions. The LCD is Do you see how we get this? Now perform the indicated multiplications. Simplify by combining like-terms. Factor the 2 in the numerator. ...and this is as far as we can go!
 Inequalities/91816: Hello, I need help with this: If y varies directly as x and y = 25 when x = 10, find y when x = 4. Thank you1 solutions Answer 66661 by Earlsdon(6294)   on 2007-08-07 21:53:09 (Show Source): You can put this solution on YOUR website!If y varies directly as x, you can write this as: y = kx where k is called the constant of proportionality. To find the value of k, substitute the given values of y (25) and x (10) and solve for k. 25 = 10k Divide both sides by 10. k = 2.5 Now you have: y = 2.5x so you can find the value of y when x = 4. y = 2.5(4) y = 10
 Quadratic_Equations/91744: I am having some problems solving these problems Use the quadratic formula to solve each of the quadratic equations 2x^2-5x=3 and also 3x^2-2x+1=0 Thank you1 solutions Answer 66614 by Earlsdon(6294)   on 2007-08-07 13:03:38 (Show Source): You can put this solution on YOUR website!Solve for x using the quadratic formula: Problem 1. Subtract 3 from both sides to get your equation into standard form: Apply the formula: Now evaluate this. or You can use the above as a guide to solve problem 2.
 Quadratic_Equations/91743: I am having problems with figuring this problem out and need some help Number problem: Find two consecutive positive integers. Such that the sum of thier squares is 85. Thank a million 1 solutions Answer 66602 by Earlsdon(6294)   on 2007-08-07 11:50:39 (Show Source): You can put this solution on YOUR website!Find two positive consecutive integers such that the sum of their squares = 85. Let x be the first integer, then x+1 would be the next consecutive integer, so you can write: Simplify. Subtract 85 from both sides and combine like-terms. Solve this quadratic equation by factoring. Apply the zero products principle. or so... or so... Discard this solution as you are looking for positive values of x. The two integers are: 6 and 7 = 85
 Miscellaneous_Word_Problems/91734: Melissa wants to have concrete driveway in front of her house. The driveway will measure 62 1/3 feet long and 19 feet wide; and will be 2/3 foot thick. How many cubic yards of cement will be needed for the driveway? Round your answer to the nearest cubic yard. [1 cubic yd = 27 cubic feet] I think that you would multiply 62 1/3 by 19 by 2/3 but I am not certain, Please help. I came up with 31 cubic yards.1 solutions Answer 66600 by Earlsdon(6294)   on 2007-08-07 11:38:44 (Show Source): You can put this solution on YOUR website!Well, you have the right idea. You are finding the volume of cement in the driveway and this is done just as you describe. (62 1/3)(19)(2/3) = 789.56 cu.ft. Now divide this by 27 cu.ft. per cu.yd. 789.56/27 = 29.24 cu.yds. or... 29 cu.yds. rounded to the nearest cu. yd.
 Miscellaneous_Word_Problems/91736: Mike invested \$6000 for one year. He invested part of it at 9% and the rest at 11%. At the end of the year he earned \$624 in interest. How much did he invest at each rate?1 solutions Answer 66598 by Earlsdon(6294)   on 2007-08-07 11:28:34 (Show Source): You can put this solution on YOUR website!Let x = the amount invested at 9%. The interest earned on this amount would then be (0.09)x. The remainder (6000-x) is invested at 11%. The interest earned on this amount would be (0.11)(6000-x) The sum (+) of these two amounts is \$624.00 You can now write the equation needed to solve for x, the amount invested at 9%. (0.09)x + (0.11)(6000-x) = \$624.00 Simplify and solve for x. 0.09x+660-0.11x = \$624.00 Combine like-terms. (0.09-0.11)x+660 = \$624.00 Subtract 660 from both sides. -0.02x = -\$36.00 Divide both sides by -0.02 x = \$1800.00 and... \$6000-x = \$6000-\$1800 = \$4200.00 Solution: \$1,800.00 was invested at 9% \$4,200 was invested at 11% Check: (0.09)(\$1,800.00)+(0.11)(\$4,200.00) = \$162.00 + \$462.00 = \$624.00
 Miscellaneous_Word_Problems/91731: Factorise: #1 a2 + 6ab + 9b2 - 1 PLEASE NOTE THAT IN THE QUESTION a AND b ARE NOT MULTIPLYING BY 2, BUT BOTH HAVE SQUARES i.e. (a)square + 6ab + 9(b)square - 11 solutions Answer 66596 by Earlsdon(6294)   on 2007-08-07 11:13:25 (Show Source): You can put this solution on YOUR website!Factorise: Rewrite this as: Factorise the parentheses. which can be written as: Now you have a difference of two squares which can be factored...oops - factorised thus: Applying this to your problem,we get: Check the answer by multiplying the two factors. Simplify this. Combine like-terms. ...your original expression.
 Linear_Equations_And_Systems_Word_Problems/91663: A mother is 30 years older than her daughter. Five years ago she was four times as old as her daughter. How old are they now?1 solutions Answer 66568 by Earlsdon(6294)   on 2007-08-06 13:49:48 (Show Source): You can put this solution on YOUR website!Start by assigning variables to the unknown quantities: Let M = Mother's present age. Let D = Daughter's present age. From the problem description we can write: Mother's age is (M) is (=) 30 years older than her daughter's age, so: M = D+30 Five years ago, Mother's age (M-5) was (=) four times her daughter's age, so M-5 = 4(D-5) Simplify. M-5 = 4D-20 Rewrite this as: (add 5 to both sides) M = 4D-15 now substitute this for the M in the first equation. D+30 = 4D-15 Simplify and solve for D by adding 15 to both sides. D+45 = 4D Now subtract D from both sides. 45 = 3D Finally, divide both sides by 3. 15 = D or D = 15 This is the daughter's present age. M = D+30 M = 15+30 M = 45 This is the mother's present age. Check: M = D+30 M = 15+30 M = 45 Five years ago: M-5 = 4(D-5) 45-5 = 4(15-5) 40 = 4(10) 40 = 40