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# Recent problems solved by 'rapaljer'

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 Graphs/84559: Graph f(x) = –3x – 2.1 solutions Answer 60905 by rapaljer(4667)   on 2007-06-05 21:58:57 (Show Source): You can put this solution on YOUR website!f(x) = –3x – 2 is a straight line graph, with y intercept of -2, and slope of -3. It should look like this: R^2 at SCC
 Equations/84482: Solve. (x + 3)^2 = 3 I came up with 5+-SQRT3 Did I just maybe get it right?1 solutions Answer 60903 by rapaljer(4667)   on 2007-06-05 21:43:48 (Show Source): You can put this solution on YOUR website!This problem would have been a LOT easier to solve if, instead of using the quadratic formula as Checkley suggested you do, you just take the square root of each side: Now, just subtract 3 from each side: You were ALMOST correct!! Never mind Checkley's chiding!! R^2 at SCC
 Equations/84483: Determine whether SQRT25/68 is rational or irrational. I came up with Irrational. Did I just maybe get it right?1 solutions Answer 60902 by rapaljer(4667)   on 2007-06-05 21:39:53 (Show Source): You can put this solution on YOUR website!The answer you were given to this problem by Checkley is WRONG! YOU WERE CORRECT in saying that this is an irrational number. An irrational number is a REAL NUMBER, but it is one that is NOT rational. That is, it CANNOT be expressed as a quotient of two integers. Irrational numbers include radical expressions that do not come out even, such as , , etc. If the square root happens to be of a perfect square, such as , then it is considered to be rational. Your answer involves the square root of a number, 68, that is not a perfect square. Therefore it is an irrational number. is a REAL but yet an IRRATIONAL NUMBER. R^2 at SCC
 Graphs/84219: This question is from textbook College Algebra Given the above grapg, identify the graph of the function (line, parabola, hyperbola, or exponential) and given the domain and range as shown in the graph1 solutions Answer 60745 by rapaljer(4667)   on 2007-06-04 06:38:58 (Show Source): You can put this solution on YOUR website!You have to give us a problem. We don't have your book. See my Lesson Plans on Domain and Range in algebra.com or see my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com, look for "MATH IN LIVING COLOR", "College Algebra", "Chapter 2". R^2 at SCC
 Functions/84090: I would like to get a clear deffinition of a function. Why do we use functions. What are we trying to solve1 solutions Answer 60744 by rapaljer(4667)   on 2007-06-04 06:35:03 (Show Source): You can put this solution on YOUR website!A function is a set of points in which no two points have the same x coordinate. It is like a set of points that has a special uniqueness relationship. For example, is you have x=y^2, this is NOT a function because if you let x = a given number, like 4, and you solve for y, you will get TWO values of y (that is, y = 2 or y=-2), so there is NOT a unique value of y. On the other hand, if you have y=x^2, then this IS a function, since for any value of x, there is ONLY one value of y, so it does have this uniqueness property. For more on Functions, Domain, and Range, see my Lesson Plan in algebra.com, or go to my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com, then look for "MATH IN LIVING COLOR", "College Alegebra", "Chapter 2", "Functions, Domain, and Range". R^2 at SCC
 Polynomials-and-rational-expressions/84267: Factor by using the zero product theorem and factoring.. 5a2 - 33a = 141 solutions Answer 60742 by rapaljer(4667)   on 2007-06-04 06:24:26 (Show Source): You can put this solution on YOUR website! The hard part of this is the factoring of the trinomial since the coefficient of the a*2 is NOT 1. I call this "Advanced Trinomial Factoring", and I have a Lesson PLan for this topic in algebra.com, or go to my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Then look for "MATH IN LIVING COLOR", "Basic Algebra", "Chapter 2", "Advanced Trinomial Factoring." or or or R^2 at SCC
 Distributive-associative-commutative-properties/84328: (4-t)(-7)=1 solutions Answer 60739 by rapaljer(4667)   on 2007-06-04 06:11:41 (Show Source): You can put this solution on YOUR website!(4-t)(-7)= -7(4-t) -28 + 7t R^2 at SCC
 Rectangles/84326: In general why is it important to square both sides of an equation?1 solutions Answer 60730 by rapaljer(4667)   on 2007-06-03 23:31:20 (Show Source): You can put this solution on YOUR website!When an equation has one or more square roots involving a variable, it is necessary to square both sides of the equation one or more times in order to remove the square roots and enable you to solve the equation. The trick however, is that when you square both sides of an equation, you do NOT guarantee that the answers that you get at the end of the problem will solve the original equation. These are called EXTRANEOUS ROOTS and must be rejected!! Therefore, any time you square both sides of an equation, you MUST check the answers! They are NOT guaranteed!! R^2 at SCC
 Equations/84327: multiply 7(t-5)=1 solutions Answer 60729 by rapaljer(4667)   on 2007-06-03 23:28:20 (Show Source): You can put this solution on YOUR website!This is the distributive property: 7(t-5) = 7t -35 R^2 at SCC
 Polynomials-and-rational-expressions/84323: This question is from textbook College Algebra Hello! My name is Salem and I am a concurrently enrolled student at Carl Albert State College. I have just started College Algebra and I asked my high school math teacher to help me with this question and neither of us can get it right. Can you please help me? It is due tomorrow! Here is the question: In words, it is: (x over x squared minus one), minus (x plus three over x squared minus x) equals (negative three over x squared plus x). 1 solutions Answer 60728 by rapaljer(4667)   on 2007-06-03 23:27:05 (Show Source): You can put this solution on YOUR website! First factor each denominator in order to find the LCD: The LCD = x(x-1)(x+1), so multiply both sides of the equation by the LCD, makin note that x cannot equal 0, 1, or -1: When ALL these denominators divide out, this is all that is left: The answer does NOT make any denominators zero, so it should check okay! It does, but it's hairy! R^2 at SCC PS. Get your math teacher to check out my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Take a look at, among other pages, my "MATH IN LIVING COLOR PAGES!"
 Numeric_Fractions/84324: This question is from textbook Coll. Alg. Graphing Approach 1 over(x+h)^2 minus 1 over x^2 all this over h. I have the solutions manual but I don't now how they got x^2-(x+h)^2 for the numerator after mult. by LCD. What happened to the 1's in the original numerator? Thank you! Jackie1 solutions Answer 60727 by rapaljer(4667)   on 2007-06-03 23:07:51 (Show Source): You can put this solution on YOUR website! It may help to write this in a different format: DIVIDED BY Now, you have to get the common denominator before you can subtract the first two fractions: It's hairy, but this is why your numerator is , over the common denominator (times h, of course). R^2 at SCC
 Functions/84299: Using k as the constant of proportionality, write an equation that expresses: 2 varies jointly as a and b. I don't really get where to start with this, I'd like to see the steps and the answer please, thank you for your time!1 solutions Answer 60726 by rapaljer(4667)   on 2007-06-03 22:51:39 (Show Source): You can put this solution on YOUR website!This is much easier than it looks. Joint variation means that the variable varies as the PRODUCT of two or more variables. By the way, was this supposed to be "Z varies jointly as a and b"??? Using k as the constant of proportionality, write an equation that expresses: Z varies jointly as a and b. Z=k*(ab) Z=kab R^2 at SCC
 Circles/84318: This question is from textbook I am confused as to how to find the radius and center of a circle by using an equation. Here's the equation: x^-4x+y^+2y=-11 solutions Answer 60725 by rapaljer(4667)   on 2007-06-03 22:47:38 (Show Source): You can put this solution on YOUR website!You must complete the square on the x and y terms respectively: You must "complete the square" by taking HALF of the x coefficient, and SQUARE the result, adding this amount to each side of the equation. Repeat by taking HALF of the Y coefficient, SQUARE, and add to each side of the equation. It should look like this: The center is at x=2 and y=-1, and r^2 = 4. Therefore, the center is (2,-1) and r=2. R^2 at SCC
 Inverses/84322: 3 ____ + ___1 x + 3 x 1 solutions Answer 60724 by rapaljer(4667)   on 2007-06-03 22:40:07 (Show Source): You can put this solution on YOUR website!Assuming that you mean , the first step is to find the LCD, which must contain both factors of x and x+3. This LCD= x(x+3). The second step is to build each fraction so it's denominator is x(x+3): The fraction does not reduce. R^2 at SCC
 Linear-equations/84273: Graph f(x) = –3x + 2.1 solutions Answer 60723 by rapaljer(4667)   on 2007-06-03 22:35:24 (Show Source): You can put this solution on YOUR website!f(x) = -3x + 2 The graph is a straight line, with a y-intercept at 2, and the slope is -3. This means to start with the first point by going UP 2 units on the y-axis. Then, from this point move DOWN 3, RIGHT 1 unit, and put the second point. Connect the two points with a straight line, and it should look like this: R^2 at SCC
 Probability-and-statistics/84169: A school sent 5 students to a Spelling Bee. The team was made up of 4 people. How many combinations of 4 students could make up team?1 solutions Answer 60616 by rapaljer(4667)   on 2007-06-02 13:14:48 (Show Source): You can put this solution on YOUR website!Since there are 5 students to choose from, and a "team" consists of 4 players, you are taking a combination of "5 students taken 4 at at time". One way to write this is C(5,4). To find the value of this: =. An easier way to do this is to realize that CHOOSING 4 out of 5 to be on the team is EXACTLY the same as choosing 1 out of 5 to NOT be on the team. There are obviously 5 ways to choose 1 person NOT to be on the team, so the answer is 5. R^2 at SCC
 expressions/84173: Evaluate 4^-51 solutions Answer 60615 by rapaljer(4667)   on 2007-06-02 13:09:05 (Show Source): You can put this solution on YOUR website!Do you need help with negative exponents? If so, I have several Lesson Plans in algebra.com, or you can check out my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Then look for "MATH IN LIVING COLOR", and look in "Basic Algebra" in Chapter 2. R^2 at SCC
 expressions/84178: Find the GCF of 90m2np3 and 150mn3p2. 1 solutions Answer 60614 by rapaljer(4667)   on 2007-06-02 13:03:57 (Show Source): You can put this solution on YOUR website!The Greatest Common Factor (GCF) is the largest possible number/variable expression that divides evenly into both of the given quantities. and The numbers that divide evenly into BOTH 90 and 150 would be 1, 2, 3, 5, 6, 10, 15, and 30. The largest such number is 30. You also have common factors of m, n, and p. Since m divides evenly into m^2 but NOT viceversa, m is a common factor. Actually, it turns out that when variables raised to different powers are involved, you can just choose the LOWEST POWER each factor. By this way of thinking, you can determine that n is a common factor (when compared to n^3), and also p^2 is a common factor (when compared to p^3). Therefore, putting it all together, the GCF = . R^2 at SCC
 Polynomials-and-rational-expressions/84174: Factor each product.. (p-3)(p+5)1 solutions Answer 60613 by rapaljer(4667)   on 2007-06-02 12:54:44 (Show Source): You can put this solution on YOUR website!Do you mean to "expand" or "multiply"? If you have a product of two binomials, usually you are asked to multiply the product. This would be what we sometimes call "F OI L". In this case: (p-3)(p+5) FIRST times FIRST = OUTER times OUTER = INNER times INNER = LAST times LAST = Add these terms together and combine like terms: Now, if you were given this trinomial, you would be asked to "factor it", which is to change this trinomial to a product of two binomials that you started out with. For more help with this topic, see my Lesson Plans in algebra.com, or my website under "Basic Algebra", "Samples from Basic Algebra: One Step at a Time", "Chapter 2", "Section 2.01." R^2 at SCC
 Divisibility_and_Prime_Numbers/84158: The Prime numbers between successive gaps of ten numbers are: 2, 3, 5, and 7. 11, 13, 17, and 19. 23 and 29. 31 and 37. 41, 43, 47, and (not 49 - square of 7) 53 and 59. 61 and 67. 71, 73, and 79 and (not 77) 83 and 89. 91 and 97. Can you see a pattern forming? Despite of this I was not able to formulate a simple and general expression so that I could tell whether or not a number is prime by simply looking at the number and applying the above sequence. Can you help? Please! I am very excited about this project. It is my own thought and has not been assigned to me as a homework. Thankyou.1 solutions Answer 60607 by rapaljer(4667)   on 2007-06-02 11:59:41 (Show Source): You can put this solution on YOUR website!I think you are looking for something that doesn't exist!! Although the great mathematicians have been looking for one for centuries, there is NO pattern of prime numbers, and there is no way to recognize a prime number by looking at the sequence of primes around it. The only way to identify whether is number is prime is by the Sieve of Eratosthenes--that is, to test for divisibility by every prime number up to and including the square root of the number. R^2 at SCC