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# Recent problems solved by 'rapaljer'

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 Linear-equations/88403: Plot the point with coordinates (–3, –3).1 solutions Answer 64217 by rapaljer(4667)   on 2007-07-14 00:54:21 (Show Source): You can put this solution on YOUR website!Put a DOT in the middle of this: R^2
 Linear-equations/88398: Which of the ordered pairs (0, 0), (–2, 10), (–1, –5), (–3, 9) are solutions for the equation y = 5x? 1 solutions Answer 64209 by rapaljer(4667)   on 2007-07-14 00:21:20 (Show Source): You can put this solution on YOUR website!y = 5x (0,0) and (-1.-5) only. y = 5x If x = -2, then y does NOT equal 10. y = 5x If x = -3, then y does NOT equal 9. R^2
 Linear-equations/88405: Write the equation of the line with slope 4 and y-intercept (0, –5). Then graph the line1 solutions Answer 64204 by rapaljer(4667)   on 2007-07-14 00:05:55 (Show Source): You can put this solution on YOUR website!y=mx+b y=4x-5 R^2
 Linear-equations/88409: Graph 2x – y = 4.1 solutions Answer 64203 by rapaljer(4667)   on 2007-07-14 00:04:12 (Show Source): You can put this solution on YOUR website!Solve for y: The y intercept is -4 and the slope is 2/1. See my lesson plan on graphing by slope intercept method: R^2
 test/88396: 2/5 = 6/15 write 7/16 as a percent write 8% as a fraction write the ratio of 4/13 to 6 in simplest form1 solutions Answer 64200 by rapaljer(4667)   on 2007-07-13 23:48:54 (Show Source): You can put this solution on YOUR website!write 7/16 as a percent: The tutor did NOT write this as a percent. The final answer should be write the ratio of 4/13 to 6 in simplest form. Again I disagree with the answer posted by the other tutor!! The ratio of a to b means a/b. Therefore the ratio of 4/13 to 6 means to divide 4/13 by 6. This means to take . I get the answer of . R^2
 Linear-equations/88305: 2x - 3y= 61 solutions Answer 64197 by rapaljer(4667)   on 2007-07-13 23:39:38 (Show Source): You can put this solution on YOUR website!OOPS!! The other tutor missed this one!! It should be R^2
 Polynomials-and-rational-expressions/88310: I need help solving this word problem At a college there are 300 faculty members and 4200 students. Find the student-to-faculty ratio.1 solutions Answer 64141 by rapaljer(4667)   on 2007-07-13 11:26:26 (Show Source): You can put this solution on YOUR website! R^2
 Pythagorean-theorem/88313: Can someone Help me solve this problem? Find the distance from first base to third base on a baseball diamond if the distance between bases is 90 feet.1 solutions Answer 64140 by rapaljer(4667)   on 2007-07-13 11:23:51 (Show Source): You can put this solution on YOUR website!From first base to third base on a baseball diamond is actually the hyptenuse of a right triangle with right angle at second base! Therefore, the legs of the right triangle are each 90 feet, and the hypotenuse is the direct distance (over the pitcher's mound) from first to third base. By the Theorem of Pythagoras, this would be feet feet approximately! R^2
 Polynomials-and-rational-expressions/88315: please help me, show whether or not(5,3) is a solution of the system: 3x+2y=21 x+y=81 solutions Answer 64139 by rapaljer(4667)   on 2007-07-13 11:22:28 (Show Source): You can put this solution on YOUR website!Just substitute the values for x and y: (5,3) means that x=5 and y =3. 3x+2y=21 3(5) + 2(3) = 21 15 + 6= 21 True x+y=8 5+3 = 8 True Yes, it is a solution. R^2
 Linear-systems/88314: I dont understand the following: solve by graphing x+y=7 2x-y=5 The instructions also say if you solve the system and the variables both add out, you need to tell whether the system consists of lines that coincide (infinite solutions) or parallel lines(no solution)1 solutions Answer 64138 by rapaljer(4667)   on 2007-07-13 11:19:40 (Show Source): You can put this solution on YOUR website!Just add the two equations together, and the y terms subtract out: x+y=7 2x-y=5 -------------- 3x=12 x=4 Substitute back into the first equation: x+y=7 4+y=7 y=3 Check by substituting both values in the second equation: 2x-y=5 2*(4)-3=5 It checks. The solution is the point (4,3). R^2
 Linear-systems/88288: Goodmorning, I need help with this Solve the system by graphing, addition and substitution methods. 3x + y = –1 9x + 3y = –3 Thank you1 solutions Answer 64131 by rapaljer(4667)   on 2007-07-13 09:16:08 (Show Source): You can put this solution on YOUR website!3x + y = –1 9x + 3y = –3 Multiply both sides of the first equation by -3 to eliminate the y terms. -3*(3x + y) = (-3)*–1 9x + 3y = –3 -9x -3 y = 3 9x + 3y = –3 When you add the equations together you get 0=0, which is ALWAYS TRUE. Any time you get 0=0, it means that the equations actually represent the SAME LINE. The entire line is the solution. R^2
 Linear-systems/88289: Can someone help me with this one Solve the system by graphing, addition and substitution methods. 5x – 4y = –5 x – 2y = –7 1 solutions Answer 64130 by rapaljer(4667)   on 2007-07-13 09:12:25 (Show Source): You can put this solution on YOUR website!5x – 4y = –5 x – 2y = –7 Multiply the second equation by -2 to eliminate the y terms: 5x – 4y = –5 -2x +4y = 14 Add the equations: 3x=9 x=3 Substitute x=3 into the first equation: 5x – 4y = –5 5(3) -4y =-5 15-4y = -5 15-15-4y = -5-15 -4y = -20 y=5 Check by substituting both numbers into the second equation: x – 2y = –7 3-2(5) = -7 It checks Solution: (3,5) R^2
 Money_Word_Problems/88287: Hello, I have tried to figure this out but with no success can you help. Bob invested \$20,000, part at 14% and part at 13%. If the total interest at the end of the year is \$2,720, how much did he invest at 14%? this is what I have done so far but it is not proofing out. What am I doing wrong 0.14x+0.13(20,000-x)=2,720 0.14x+2,800-.013x=2,720 0.13x=2,720-2,800 .013x=200 X=200/0.13 X=1538.46 invested @ 14% 20,000-923.07 = 19,076.93 invested @ 13% 1 solutions Answer 64129 by rapaljer(4667)   on 2007-07-13 09:06:27 (Show Source): You can put this solution on YOUR website!You seem to have TWO errors in your second step! 0.14x+0.13(20,000-x)=2,720 0.14x+2,800-.013x=2,720 Should be 0.14x+0.13(20,000-x)=2,720 0.14x+2,600-0.13x=2,720 Continuing: 0.01x = 120 x= \$12000 20000-x = \$8000 Check: .14(12000)+.13(8000)=2720 R^2
 Money_Word_Problems/88161: The demand and supply equations for a certain item are given by D=-5p+40 S=-p^2+30p-8 Find the equilibrium price.1 solutions Answer 64128 by rapaljer(4667)   on 2007-07-13 09:00:34 (Show Source): You can put this solution on YOUR website!The equilibrium price is where supply = demand. D=-5p+40 S=-p^2+30p-8 Use either the quadratic formula or a graphing calculator: p=1.43 or p = 33.57 R^2
 Geometry_Word_Problems/88174: if a quadrilateral is inscribed in a circle its opposite angles will be supplementary. find the measure of angle A if the measure of angle C=40 degrees 1 solutions Answer 64125 by rapaljer(4667)   on 2007-07-13 08:48:38 (Show Source): You can put this solution on YOUR website!If angles A and C are supplementary, and angle C is 40 degrees, then angle A is 180-40 = 140 degrees. R^2
 Polynomials-and-rational-expressions/88179: I need help on solving equation using either zero-factor property or sq root property. 45+x2-14x=01 solutions Answer 64124 by rapaljer(4667)   on 2007-07-13 08:45:10 (Show Source): You can put this solution on YOUR website! R^2
 Polynomials-and-rational-expressions/88240: I need help my question reads: solve each equation using either zero-factor or square root property y2-4y+4=0 x2-36=01 solutions Answer 64123 by rapaljer(4667)   on 2007-07-13 08:42:10 (Show Source): You can put this solution on YOUR website! R^2
 Polynomials-and-rational-expressions/88193: Can someone please help me with this problem? Factor out the GCF 6a2-12a3b+36ab1 solutions Answer 64121 by rapaljer(4667)   on 2007-07-13 08:38:41 (Show Source): You can put this solution on YOUR website!The greatest common factor for is 6a. Take out the common factor, and this is left: R^2
 Polynomials-and-rational-expressions/88281: How do I find the x,y intercepts of an equation after completing the square?1 solutions Answer 64119 by rapaljer(4667)   on 2007-07-13 08:31:52 (Show Source): You can put this solution on YOUR website!I may be misunderstanding your question, but when you are solving an EQUATION, you usually have a single variable, like . You can find roots or solutions of the equation (in this case, it would be x=2 or x=-2) by equation solving methods. However, to have x and y intercepts, you must have TWO variables (TWO dimensions!). This would be like . In order to find the x intercepts, you let y = 0, and find x--in this case it would be (0,2) and (0,-2). You can find the y-intercepts by letting x=0, and find y--in this case, it would be (0,-4). I'm not sure how completing the square fits into this question. R^2
 Polynomials-and-rational-expressions/88221: factor each expression can some one please help me on this problem x2-251 solutions Answer 64104 by rapaljer(4667)   on 2007-07-12 22:12:58 (Show Source): You can put this solution on YOUR website! This is a difference of two squares: First times First must give you x^2: (x____)(x____) Last times Last must give you -25. Try -5*+5= -25!! (x-5)(x+5) The middle term is +5x -5x, which subtract out. R^2
 Quadratic_Equations/88265: Is the following trinomial a perfect square? Explain why or why not. x^2 – 18x + 81 1 solutions Answer 64103 by rapaljer(4667)   on 2007-07-12 22:09:03 (Show Source): You can put this solution on YOUR website! Yes! It is a perfect square trinomial essentially because the x^2 coefficient is 1, and if you take HALF of the middle term and SQUARE the result, you get the last term which is 81. In other words, if you take half of -18, you get -9, then if you square the (-9) you get 81, which is the last term of the trinomial. Therefore, it IS a perfect square trinomial!! R^2