course Mth 158 That query program will take a little to get used to, such as what appears to be an instant answer function.
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11:11:48 query 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 --> natural = none. There are no numbers such as {1, 2, 3, . . .} integer = none. There are no numbers such as {. . ., -1, 0, 1, 2, . . .} rational = {(1/2), 10.3} these numbers can be expressed as a quotient with integers (in the form (a/b)) irrational = {-sqrt(2), pi + sqrt(2)} these two numbers are non-terminating and non-repetitive when expressed as a decimal. real = all. All of the numbers in this set meet the requirements for being real, in that none are imaginary numbers.
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11:12:58 ** 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 --> That's an easier way to write the answer than my format.
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11:14:27 query 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 --> The phrases ""the product of 2 and x"" and ""the product of 4 and 6"" are the same aas writing ""2 * x"" and ""4 * 6"". The use of the word ""is"" means that the two phrases are equal to each other, so that the equation becomes ""2 * x = 4 * 6"".
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11:14:43 ** 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.
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11:19:23 query R.1.50 (was R.1.42) Explain how you evaluate the expression 2 - 5 * 4 - [ 6 * ( 3 - 4) ]
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RESPONSE --> We must follow the order of operations, which is this: Work from the innermost grouping out, following these directives: Evaluate exponents Multiply and divide from left to right Add and subtract from left to right There are no exponents in the problem. First, we handle ""(3-4)"", because it is the innermost grouping. The answer to it is -1. Then we can multiply ""[6 * -1]"", as per the order of operations. The answer to it is -6. Next we can evaluate ""5 * 4"", which is 20. All that remains is to add and subtract from left to right. ""2 - 20 + 6 = -12.
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11:19:54 **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 --> Once again, a much easier format to understand, unlike mine.
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11:25:26 query 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 --> What we are going to do is the reverse of factoring. We multiply ""x"" in the first group by ""x"" in the second group. Then we multiply ""x"" in the first group by ""-2"" in the second group. This is what we have so far: x^2 - 2x Then we multiply the ""-4"" of the first group by the ""x"" in the second group, followed by multiplying the ""-4"" by ""-2"". This is the total equation so far: x^2 - 2x - 4x + 8 However, it can be simplified by combining like terms, so that the equation becomes: x^2 - 6x + 8 Thus, the parenthesis are gone, and the equation is in its most reduced form without factoring it.
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11:27:38 ** 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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RESPONSE --> If the program is saying that I used FOIL to get my answer, I'm not sure how. Though what I wrote out was much longer (and as such messier) than the answer provided here, it says the same thing as the answer does. If I did use FOIL, can you explain how?
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11:31:57 query 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 --> This is again determined by the order of operations. Because we need to evaluate each grouping first and work from the inside out, and because the division sign acts as parenthesis (in [(4+3) / (2+5)]), we must evaluate (4 + 3) and (2 + 5) separately. This gives us the fraction (7 / 7), which can be reduced to 1. In the other problem, we are adding two fractions together, and in the first we are dealing with one fraction. Also, [4/2 + 3/5] equals (26 / 10), which is not 1.
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11:33:56 ** 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 --> My math for the second problem [(4/2) + (3/5)] was wrong because I forgot to reduce the fraction to a mixed fraction. However, I did explain the need for the order of operations, but perhaps it was not clear enough. Does this program recognize wrong answers?
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11:35:13 Query Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> The seeming ability of it to recognize answers and state whether they were wrong or not. It confused me a little on a couple of questions, like the one where it says to not use the FOIL method and the last question.
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