course MTH 158
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18:30:07 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 --> Counting Numbers-None Rational Numbers-{1/2, 10.3} Irrational Numbers-{-sqrt(2), pi, sqrt(2), 1/2, 10.3} Real Numbers- {-sqrt(2), pi, sqrt(2), 1/2, 10.3}
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18:30:34 ** 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
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18:31:07 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 --> 2(x)=4(6)
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18:31:25 ** 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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18:34:23 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 --> First work whats in the brakets, starting with whats in the ()s. Next times that by 6. Then multiply 5 times 4. then subtract two from 20 and then substract the 2 remaining numbers. 2-5*4-[6*(-1)] 2-5*4+6 2-20+6 -18+6 -12
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18:34:36 **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 --> Ok
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18:41:34 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 --> I use FOIL. Multiply the first, outter, inner and last x^2-4x-2x+8 (x^2)-6x+8
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18:42:54 ** 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 --> Ok i will not use FOIL
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18:44:55 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 --> Because you don't just split the two and put the numerator over the denominator you have to add the 4+3 and the 2+5 because they're in ()s. then divide 7/7 = 1
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18:45:52 ** 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 --> ok
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18:46:35 Query Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> That the foil was a limited way of doing that type of problem.
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