course MTH 158 G????{???d???????assignment #001001. `query 1
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16:21:05 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 --> counting numbers: none rational numbers: 1/2 and 10.3 irrational:-sqrt(2), pi, sqrt(2) real numbers: {-sqrt(2), pi + sqrt(2), 1/2 + 10.3} all confidence assessment: 3
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16:21:29 ** 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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RESPONSE --> ok self critique assessment: 3
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16:23:56 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 --> 2*x=4*6 2x=24 confidence assessment: 3
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16:24:07 ** 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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RESPONSE --> ok self critique assessment: 3
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16:26:23 R.1.50 (was R.1.42) Explain how you evaluate the expression 2 - 5 * 4 - [ 6 * ( 3 - 4) ]
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RESPONSE --> Using the order of operations: Parentheses: 2-5*4- [6*-1], 2 - 5 * 4 - 5 Mulitply: 2 - 20 - 5 add/subtract: -18 - 5; -23 confidence assessment: 3
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16:27:15 **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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RESPONSE --> oops, my math was wrong when I mulitplied six and one...... self critique assessment: 2
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16:28:55 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 --> Using the FOIL method First: x^2 Outside: 4x Inside: -2x Last: 8 x^2 + 4x - 2x +8 x^2 +2x + 8 confidence assessment: 3
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16:29:09 09-02-2007 16:29:09 ** 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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16:32:57 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 --> due to order of operations, (4+3)/(2+5) you add the parentheses, coming up with 7/7 also 1. 4/2 + 3/5: you first have to find a common denominator (10) giving you 20/10 + 6/10 equaling 26/10 breaking down to 13/5. confidence assessment: 3
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16:33:27 ** 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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RESPONSE --> right, I put down due to the order of operations. self critique assessment: 3
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16:34:02 Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> Just a review of basic operations. Distributitive property is something I need to review. confidence assessment: 3
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