course MTH 158 The numbers in your questions do not coinside with the numbers in the book, is that normal? §ëx®XͅμšŽƒ…ÞÃKçƒqóÞ¨ˆYyŠ‡¢assignment #001
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15:07:18 R.1.14 (was R.1.6) Of the numbers in the set {-sqrt(2), pi + sqrt(2), 1 / 2 + 10.3} which are counting numbers, which are rational numbers, which are irrational numbers and which are real numbers?
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RESPONSE --> #26 F = {-sqrt(2), pi + sqrt(2), 1/2 + 10.3} a) Natural Numbers: Null Set c) Rational Numbers: {1/2 + 10.3} d) Irrational Numbers: {-sqrt(2), pi + sqrt(2)} e) Real Numbers: {-sqrt(2), pi + sqrt(2), 1/2 + 10.3} confidence assessment: 3
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15:07:55 01-13-2008 15:07:55 ** Counting numbers are the numbers 1, 2, 3, .... . None of the given numbers are counting numbers Rational numbers are numbers which can be expressed as the ratio of two integers. 1/2+10.3 are rational numbers. Irrational numbers are numbers which can be expressed as the ratio of two integers. {-sqrt(2)}, pi+sqrt(2) are irrational numbers.. **
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NOTES -------> ok
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15:08:52 R.1.32 (was R.1.24) Write in symbols: The product of 2 and x is the product of 4 and 6
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RESPONSE --> #44 The product of 2 and x is the product of 4 and 6. 2x = 4 * 6 confidence assessment: 3
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15:09:15 01-13-2008 15:09:15 ** The product of 2 and x is 2 * x and the product of 4 and 6 iw 4 * 6. To say that these are identical is to say that 2*x=4*6. **
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NOTES -------> ok
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15:13:22 R.1.50 (was R.1.42) Explain how you evaluate the expression 2 - 5 * 4 - [ 6 * ( 3 - 4) ]
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RESPONSE --> # 62 2 - 5 * 4 - [6 * (3 - 4)] First: Evaluate the inner most set of parentheses: 2 - 5 * 4 - [6 * -1] Second: Evaluate the parentheses: 2 - 5 * 4 - (-6) Third: Multiply 2 - 20 + 6 Fourth: Add or Subtract from left to right -18 + 6 = -12 confidence assessment: 3
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15:13:43 01-13-2008 15:13:43 **Starting with 2-5*4-[6*(3-4)]. First you evaluate the innermost group to get 2-5*4-[6*-1] . Then multiply inside brackets to get 2-5*4+6. Then do the multiplication to get 2-20+6. Then add and subtract in order, obtaining -12. **
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NOTES -------> ok
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15:19:20 R.1.80 (was R.1.72) Explain how you use the distributive property to remove the parentheses from the express (x-2)(x-4).
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RESPONSE --> # 98 (x - 4)(x - 2) Using the Distributive Property and the method of factoring you can: First: Multiply the first two terms x * x = x^2 Second: Multiply the outside terms x * 2 = 2x Third: Multiply the inside terms 4 * x = 4x Fourth: Multiply the last two terms 4 * 2 = 8 This gives you x^2 - 2x - 4x + 8 Fifth: Simplify any like variables = x^2 - 6x + 8 confidence assessment: 3
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15:42:14 01-13-2008 15:42:14 ** COMMON ERROR: Using FOIL. FOIL is not the Distributive Law. FOIL works for binomial expressions. FOIL follows from the distributive law but is of extremely limited usefulness and the instructor does not recommend relying on FOIL. Starting with (x-2)(x-4) ; one application of the Distributive Property gives you x(x-4) - 2(x-4) . Applying the property to both of the other terms we get x^2 - 4x - (2x -8). Simplifying: x^2 - 4x - 2x + 8 or x^2 - 6x + 8. *
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NOTES -------> I used FOIL, I've always used FOIL, I've never been told not to. So, know FOIL, but don't rely on it. Got it! The problem in the book was (x-4)(x-2), when I reworked the problem your way I still got the correct answer: x^2 - 6x + 8. My question is are all binomial expressions commutative? I know it worked in this instance, but is that just a fluke? In other words does: (a - b)(c-d) = (c-d)(a-b)
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15:46:48 R.1.86 (was R.1.78) Explain why (4+3) / (2+5) is not equal to 4/2 + 3/5.
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RESPONSE --> #102 In the first problem you add both terms in the numeartor and then both terms in the denominator, or 4 + 3 = 7 and 2 + 5 = 7, then simplify the fraction or 7/7 = 1. In the second problem you must first find the LCM of the denominator, in this case 10. Then multiply each term by the number that will make the denominator equal the LCM. In this case 4/2 * 5/5 + 3/5 * 2/2, which gives you 20/10 + 6/10, which equals 26/10 or 13/5. confidence assessment: 3
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15:53:32 01-13-2008 15:53:32 ** Good answer but at an even more fundamental level it comes down to order of operations. (4+3)/(2+5) means 7/7 which is equal to 1. By order of operations, in which multiplications and divisions precede additions and subtractions, 4/2+3/5 means (4/2) + (3/5), which gives us 2+3/5 = 2 3/5 **
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NOTES -------> Even though I did not include order of operaions in my answer, I believe that my answer still states the same point.
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15:54:32 Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> Hello, who would have known not to use FOIL! My 9th grade Algebra teacher even made up a dance for the method - no lie. It was beat into our brains and now I'm told not to rely on it! That's major! confidence assessment: 3
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