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# Recent problems solved by 'rapaljer'

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 Coordinate-system/9430: i only have one qustion why in algebra you have to use variables they are letters that take the place of numbers. how can i get my algebra credit or be proficent in algebrs1 solutions Answer 5156 by rapaljer(4667)   on 2005-09-03 00:08:14 (Show Source): You can put this solution on YOUR website!In the English language we use "pronouns" to take the place of a noun. In the same way, a variable is like a "pro-number", in that we use it to take the place of a number. A real life problem does not come with an equation, does it. For example, suppose you are trying to find the length and width of a particular rectangle that has a certain perimeter and some additional characteristics. You don't know what the width and length of the rectangle are, so you assign variables like x or w or l to these unknown quantities until you can find out what they are. Then you can write an equation in terms of these variables, you can solve the equation and find out what numbers those variables represented. That is the whole process of algebra dating back to the Greeks in days of B.C. As to your question of how can you get your algebra credit or be proficient in algebra, I tell you, I LOVE that question. You have to get a good teacher, plan to spend a LOT of time doing homework and PRACTICING, like a musician or an athlete must do to become proficient, and get LOTS of HELP from TUTORS, especially the TUTORS on algebra.com!!! I could write a BOOK on this topic!! R^2 at SCC
 Numeric_Fractions/9421: Hi- I have a second question that I'm having trouble understanding. If you could please let me know what I'm doing wrong I would appreciate it. Problem: - 5/8 - (-11/12) I found the lcd which is 24 so I made the problem: -15/24 - (-22/24) = - 37/24 The book says the answer should be 7/24 Why is that if your subtracting 2 negatives. Please let me know.1 solutions Answer 5155 by rapaljer(4667)   on 2005-09-02 23:56:34 (Show Source): You can put this solution on YOUR website!Just to finish up your problem here, remember that the negative of a negative is a positive: -15/24 - (-22/24) -15/24 + 22/24 7/24
 percentage/9410: a maths exam contained two problems. Problem A was solved by 70% of the students. Problem B was solved by 60%. Every students solved at least one of the problems. Nine students solved both problems. how many students sat the exam?1 solutions Answer 5135 by rapaljer(4667)   on 2005-09-02 18:44:59 (Show Source): You can put this solution on YOUR website!Let x = number of students who took the exam. .7 x = number of students who solved Problem A. .6 x = number of students who solved Problem B. 9 = number of students who solved both problems correctly. Since everyone got at least one problem correct, adding the two categories of students (.7x + .6x) together would include ALL the students who took the exam, but the 9 students who got both problems correct will be counted twice. So when writing the equation, you add these two categories and subtract the overlap, in order to get the total number of students who took the exam This gives the following equation: .7x + .6x - 9 = x 1.3 x - 9 = x Subtract x from each side 1.3x - x - 9 = x - x .3x - 9 = 0 .3x = 9 Divide by .3 x = = = 30 Check: 70% of 30 = 21 60% of 30 = 18 The total of these is 39, which means that 9 got both problems correct. R^2 at SCC
 Linear_Algebra/9407: 22,985 IS WHAT PERCENTAGE OF \$34,505 11,520 IS WHAT PERCENTAGE OF \$34,5051 solutions Answer 5134 by rapaljer(4667)   on 2005-09-02 18:29:50 (Show Source): You can put this solution on YOUR website!Let x = "WHAT" you are trying to find. 22,985 IS WHAT PERCENTAGE OF \$34,505 Divide both sides by 34505 (I hope you are allowed to use a calculator on this one!) Dividing it gives you a decimal, which is approximately .666135 and change to a percent by moving the decimal two places to the right: 66.61% (approximately) Likewise for the second problem: 11,520 IS WHAT PERCENTAGE OF \$34,505 x = = .333864 or 33.39% Now (NO EXTRA CHARGE!), notice that if you add these two percents together, you get 100%. Also notice that if you add the numbers 22,985 and 11,520 you just happen to get the TOTAL which just happens to be the other number in this problem \$34,505. R^2 at SCC
 Distributive-associative-commutative-properties/9401: -3(10)1 solutions Answer 5133 by rapaljer(4667)   on 2005-09-02 18:11:43 (Show Source): You can put this solution on YOUR website!-30 See Lesson Plans on "Signed Numbers" by either me or Longjonsilver. R^2 at SCC
 Average/9237: (-7)x(+3)=(the possibilites are..........-4, -21, -10, or 4)1 solutions Answer 5132 by rapaljer(4667)   on 2005-09-02 18:09:22 (Show Source): You can put this solution on YOUR website!-21 See Lesson Plans on "Signed Numbers" by either me or Longjonsilver. R^2 at SCC
Complex_Numbers/9278: g(x)=-x^2+x-5
1 solutions

Answer 5131 by rapaljer(4667)   on 2005-09-02 18:06:41 (Show Source):
You can put this solution on YOUR website!
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . The discriminant -19 is less than zero. That means that there are no solutions among real numbers. If you are a student of advanced school algebra and are aware about imaginary numbers, read on. In the field of imaginary numbers, the square root of -19 is + or - . The solution is Here's your graph:

 Numeric_Fractions/9289: Hi I am not sure if I am in the right section or not but this is my problem: The directions say to find the LCD and do not combine fractions. 12/5a^2, 9/a^3 I have tried and tried to figure this out and one of the answers I got was 108/59 and then I read the whole problem and figured out I couldn't put the 2 frractions together. Help!!!! Thank you..1 solutions Answer 5130 by rapaljer(4667)   on 2005-09-02 18:03:15 (Show Source): You can put this solution on YOUR website!The problem says "do NOT combine fractions." Just find the LCD. and The LCD must have all the factors of all the denominators. Also, you have to know that a^2 is a factor of a^3, so if you have a factor of a^3, that takes care of the a^2 also. See my Lesson Plan called "Least Common Denominators" for more explanation and examples, and also my own website for free sections of explanation under Basic Algebra. Anyway, for this problem, the LCD must have . This might be the final answer for this problem. However, I'll go to the next step just in case! In the first fraction, your denominator has a 5 factor and an a^2 factor, but it needs another factor of "a" to bring it up to the LCD. So multiply the first fraction, numerator and denominator, by "a": = For the second fraction, you have the a^3 factor, but you are missing the factor of 5. So multiply the numerator and denominator of the second fraction by 5: = According to the instructions in this problem, you are not supposed to put the fractions together. So that should do it, right? R^2 at SCC
 Polynomials-and-rational-expressions/9293: Hi I need a little help with this problem. The directions are to find the LCD and do not combine fractions. 13/x^2-16, 7/x-4 If you could show how you did the problem it would be a big help.. Thank you.1 solutions Answer 5129 by rapaljer(4667)   on 2005-09-02 17:48:42 (Show Source): You can put this solution on YOUR website! and Notice that the denominator of the first fraction factors so you really have: and The objective is to get the denominators to be the same. You are allowed to multiply the numerator and denominator of any given fraction by the same quantity. Can you see that the Least Common Denominator (LCD) is (x-4)(x+4)? The first denominator HAS the LCD, but the second denominator is missing a factor. The second denominator is missing a factor of (x+4). So you must multiply the numerator and denominator of the second fraction by (x+4): and or and R^2 at SCC
 Functions/9296: tell if the interval is open,closed,or neither 9>s>-71 solutions Answer 5128 by rapaljer(4667)   on 2005-09-02 17:40:18 (Show Source): You can put this solution on YOUR website!It's an open interval since the endpoints are NOT included. R^2 at SCC
 Functions/9396: I WANT TO KNOW IF YOU HAVE PRACTICE QUIZZES FOR MATH 1000 ON LINE AND PRACTICE EXAMS ONLINE THAT WILL HELP ME FOR MY EXAM AND A COMPREHENSIVE ONE OF ALL THE EXAMS LIKE A CUMALITIVE FINAL AND MIDTERM 1 solutions Answer 5127 by rapaljer(4667)   on 2005-09-02 17:37:36 (Show Source): You can put this solution on YOUR website!I sure do!! Check for "Basic Algebra Practice Finals" under the "Tests" topic for Lesson Plans. Also, you can check my own website by clicking on my tutor name "rapaljer" at the top of this solution, and go to "Basic Algebra" then look for "Samples from Basic Algebra: One Step at a Time". There are Practice Tests at the end of each chapter. ALL FREE . . . R^2 at SCC
 logarithm/9403: Im not sure how to write the expression as the logarithm of a single quantity... 3(lnx-2ln(x^3-1))+4ln5......I got 3lnx-6lnx^3-6ln+4ln5 I also need help expanding the expression as the sum, difference and/or multiple of logarithms.... log 5y^3/x^21 solutions Answer 5126 by rapaljer(4667)   on 2005-09-02 17:30:34 (Show Source): You can put this solution on YOUR website!This is what I got: log 5y^3/x^2 log 5y^3 - log x^2 log 5 + log y^3 - log x^2 log 5 + 3 log y - 2 log x R^2 at SCC
 percentage/9368: equal fractions have equal....numerators, cross products, none of these or demonitors?1 solutions Answer 5114 by rapaljer(4667)   on 2005-09-02 14:15:57 (Show Source): You can put this solution on YOUR website! Equal fractions have equal cross products! By the way, what is a demonitor?? R^2 at SCC
 Unit_Conversion_Word_Problems/9198: You are riding home from a party and the has been drinking. The car is traveling at 60. mi per hour. Suddenly a child steps into the road ahead. Because the driver has been drinking his reaction time has been slowed by 1.0 second. How many feet toward the impending accident will the car travel before the driver begins to stop?1 solutions Answer 5113 by rapaljer(4667)   on 2005-09-02 14:14:25 (Show Source): You can put this solution on YOUR website!60 miles per hour = = Therefore the car will move 88 ft in the 1 second that the driver is recovering from the alcohol!! PLUS other side effects of the alcohol that cause delays in thinking and poor judgment! DON'T DRINK (even a little bit!) and DRIVE!!! R^2 at SCC
 real-numbers/9388: q prob # 15 out of the elementry algebra math 100a book ////show that each of the following numbers is a rational number by expressing it as a fraction with an integer numerator and a nonzero integer denominator 6,-9,-7/8,3 1/2,-03,2.831 solutions Answer 5111 by rapaljer(4667)   on 2005-09-02 13:59:30 (Show Source): You can put this solution on YOUR website! = R^2 at SCC
 Percentage-and-ratio-word-problems/9385: Two numbers are in the ratio of 5:9 and their sum is 98. Find the numbers.1 solutions Answer 5110 by rapaljer(4667)   on 2005-09-02 13:51:30 (Show Source): You can put this solution on YOUR website! so x+y = 98 Multiply both sides of the equation by 9 14y = 882 y= 63 Check: Sum = 63+35 = 98 R^ at SCC
 Linear-equations/9390: using substitution method is x+y=4 x-y=5 independent,dependent,or inconsistent?1 solutions Answer 5109 by rapaljer(4667)   on 2005-09-02 13:43:56 (Show Source): You can put this solution on YOUR website!Solve for y: x+y=4 y=4-x Substitute into the second equation: x-y=5 x-(4-x) = 5 x-4 +x = 5 2x - 4 = 5 2x = 9 x=9/2 or 4.5 y = 4-x y = 4 - 4.5 y = -.5 or -1/2 Independent, since there is a unique solution. R^2 at SCC
 Quadratic-relations-and-conic-sections/9377: My friend and I think that the answer to this problem is wrong and we would like a second opinion. There are actually two problems, but I will post it on another seperate page. Its and elipse problem. It reads - Graph the ellipse and find the foci. Here is the equation - (9x^2)+(4y^2)= 9 Our disagreement is over the coordinates in which the foci are located? Could you please help us? 1 solutions Answer 5101 by rapaljer(4667)   on 2005-09-02 11:31:37 (Show Source): You can put this solution on YOUR website! Divide both sides by 9: Rewrite this as: The center of the ellipse is at (0,0), and the radius in the x direction is 1, the radius in the y direction is . Therefore the major axis is in the Y-direction, and the foci will be on the y-axis at (0, c) and (0, -c), where Solve for c: or Therefore, I have the foci at ( 0, ) and ( 0,). R^2 at SCC
 Quadratic-relations-and-conic-sections/9378: Here is the second problem that I was talking about in another submitted question. A friend of mine thinks that the answer that we found to this question is wrong, but if it is than I don't know how to solve it. Could you help us. It is also a elipse problem that reads- Graph the equation and find the coordinates of the foci. (25x^2)-(144Y^2)= 3600 I think that there might be a mistake in this problem, but what do I know? That's why I'm asking you.1 solutions Answer 5100 by rapaljer(4667)   on 2005-09-02 11:05:47 (Show Source): You can put this solution on YOUR website!The mistake is that the equation has a DIFFERENCE of squares, which makes this equation a HYPERBOLA that opens right and left. If it is indeed an ELLIPSE, then it must be a SUM of . We would need to know which one is correct to continue. R^2 at SCC
 Miscellaneous_Word_Problems/9380: a new truck can be paid for by 48 monthly payments of x dollars each plus a down payment of 2.5 times the amount of the monthly payment. This implies that the total amount paid for the truck is 2.5x + 48x. a. Use the distributive property to rewrite the expression. b. What is the total amount paid for a truck that has a monthly payment of \$435? 1 solutions Answer 5099 by rapaljer(4667)   on 2005-09-02 10:59:42 (Show Source): You can put this solution on YOUR website!2.5x + 48x x(2.5 + 48) x(50.5) 50.5x (50.5)*(435) = \$21967.50 Check: Down Payment = 2.5*435 = \$1087.50 Payments = 48* 435 = \$20880 Total = \$21967.50 R^2 at SCC
 Quadratic_Equations/9381: how you say solution of a quadratic funtion is a parabola1 solutions Answer 5098 by rapaljer(4667)   on 2005-09-02 10:51:55 (Show Source): You can put this solution on YOUR website!If the equation for a graph is in the form , then it is a quadratic function, and it is a parabola. If a>0, then the parabola opens upward, and if a<0, then it opens downward. The larger the value of a, the steeper (more narrow!) the graph. If the value of a becomes smaller, like a fraction less than 1, then the graph becomes broader. R^2 at SCC
 Proportions/9233: equal fractions have equal.....denomitors,numerators,cross products,or none of these?1 solutions Answer 5070 by rapaljer(4667)   on 2005-09-01 23:38:17 (Show Source): You can put this solution on YOUR website!cross products means the same as , where ad and bc are sometimes called "cross products." R^2 at SCC
 percentage/9346: I posted this earlier but the SOLID LINE above the number did not print out correctly when my question was posted. The question is: what does a solid line above the number .45 mean? I am supposed to rewrite the number ( .45 with a solid line above it) as a fraction. Would it be different than the normal 45/100 ? Thanks so much.1 solutions Answer 5069 by rapaljer(4667)   on 2005-09-01 23:33:24 (Show Source): You can put this solution on YOUR website!.45 with a line over the top of it actually means the repeating decimal: .4545454545454545. . . To find the fraction that it represents, let x = .4545454545 . . . Multiply both sides of this equation by 10 for each digit that repeats. If a single digit repeats, multiply by 10, if two digits repeat (as in this case), multiply both sides by 100, if three digits repeat, multiply by 1000. 100x = 45.45454545 . . . Now subtract the x= .45454545 . . . from each side: 100x = 45.45454545 . . . - x = - .45454545 . . . The result is 99x = 45 so x = R^2 at SCC
 Equations/9291: 28/ (5-1) x 3 = please show your work1 solutions Answer 5066 by rapaljer(4667)   on 2005-09-01 22:02:21 (Show Source): You can put this solution on YOUR website!I'm going to have to disagree with the previous solution to this one!! According to order of operations, you must do multiplications and divisions from LEFT TO RIGHT! Do Parentheses first: 28/ (5-1) x 3 Do multiplications and divisions from LEFT to RIGHT (in this case, the division comes first!): 28/4 x 3 7*3 FINAL ANSWER = 21 R^2 at SCC
 Signed-numbers/9299: classify each number in as many ways as possible. 13/17 3.12112111211112 801.35 1 solutions Answer 5064 by rapaljer(4667)   on 2005-09-01 21:47:27 (Show Source): You can put this solution on YOUR website!13/17 Rational number, Real number 3.12112111211112 Irrational number (there is a pattern, but it does NOT repeat), Real number 801.35 Rational number, Real number R^2 at SCC
 Linear-systems/9302: Please help me solve this equation:2x=-x+91 solutions Answer 5063 by rapaljer(4667)   on 2005-09-01 21:45:21 (Show Source): You can put this solution on YOUR website!2x = -x + 9 Add +x to each side of the equation: 2x + x = -x + x + 9 3x = 9 x = 3 R^2 at SCC
 Distributive-associative-commutative-properties/9345: 8y-(2y-3)=91 solutions Answer 5062 by rapaljer(4667)   on 2005-09-01 21:43:02 (Show Source): You can put this solution on YOUR website!8y - (2y-3) = 9 It might help to re-write this as 8y -1(2y-3) = 9 8y - 2y + 3 = 9 6y + 3 = 9 6y +3 - 3 = 9 - 3 6y = 6 y = 1 R^2 at SCC
 Polynomials-and-rational-expressions/9343: Sorry but I typed an error in the formula before. I am not sure this matters or not. I previously posted it as follows: x^2 + 3x - 10 + 0. It should be = 0 not + 0 So here it is again. Choose the correct solutions for the quadratic equation x^2 + 3x - 10 = 0. I believe the answer to this one is (-5, 2) Thank You1 solutions Answer 5060 by rapaljer(4667)   on 2005-09-01 21:39:33 (Show Source): You can put this solution on YOUR website!I think my solution must have been posted at exactly the same time that you re-posted this problem. I think I corrected that error for you. By the way, I also emphasized that the parentheses notation (-5,2) is NOT appropriate for this type of an answer. There are different notations that (-5,2) could refer to, but THIS is NOT one of them. R^2 at SCC
 Average/9305: 4(x+1)1 solutions Answer 5057 by rapaljer(4667)   on 2005-09-01 21:35:48 (Show Source): You can put this solution on YOUR website!Are you serious?? This is just the distributive property! 4(x+1 ) = 4x + 4 R^2 at SCC
 Expressions-with-variables/9309: solve each system using subtition .Write no solution or infinitely many solutions where appropriate the problem is y=x y=-x+2 1 solutions Answer 5056 by rapaljer(4667)   on 2005-09-01 21:33:53 (Show Source): You can put this solution on YOUR website!Since y=x and y = x+2, substitute the x in the first equation for the y in the second equation: y = x+2 x = x + 2 Add -x to each side: x-x = x-x + 2 0 = 2 And when does 0 = 2? Not in this lifetime!!! So there is NO SOLUTION for this problem. There is no solution because the lines are PARALLEL!! R^2 at SCC
 Functions/9310: I don't understand these problems. How do you solve this? f(x)=10x+11 solutions Answer 5054 by rapaljer(4667)   on 2005-09-01 21:30:07 (Show Source): You can put this solution on YOUR website!This is like the last Solution that I posted. But YOU are supposed to tell ME what value of x to substitute. I'll make up a problem for you. Suppose you wanted to find f(-3). f(x) = 10x + 1 f(-3) = ______ First, this is a special notation that does NOT mean f times x. It is a special notation that is read "f of x", and it means that you are to substitute a value of x into this formula and simplify the result to find the value of the answer. It is MUCH easier than everyone can possibly imagine. Given f(x) = 10x + 1 f(-3) means that you sustitute the value of -3 in place of the x value(s). f(-3) = 10(-3) + 1 f(-3) = -30 +1 = -29 R^2 at SCC