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# Recent problems solved by 'longjonsilver'

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 Inequalities/49750: Please check for correctness...thanks!! x – (-4)^3 * x + 1 > 12 x + 64x + 1 >12 65x > 11 x > 11/65 AND 4 - 3x < 6 - x -3x + x < 6 - 4 -2x < 2 x < -1 Thank you!! Andrea1 solutions Answer 33006 by longjonsilver(2297)   on 2006-08-24 08:43:56 (Show Source): You can put this solution on YOUR website!all correct except for last line: -2x < 2 x > 2/(-2) x > -1 jon
 real-numbers/49752: This question is from textbook 1.Integer(Z) What does (z)means? 2.Rational(Q)What does (Q)maens? 1 solutions Answer 33005 by longjonsilver(2297)   on 2006-08-24 08:41:51 (Show Source): You can put this solution on YOUR website!instead of writing the word "integer" we use the symbol Z instead of writing the word "rational" we use the symbol Q Jon
 expressions/49533: Okay guys I think I got this but want to check with someone of "authority". Simplify the following equations as much as possible: 10 + sqrt(16 - 9) / (4 / 2)^3 = (10 + √7) / 8 = 12.65 / 8 = 1.58 Thanks!! Andrea 1 solutions Answer 32887 by longjonsilver(2297)   on 2006-08-22 04:19:09 (Show Source): You can put this solution on YOUR website!you don't have brackets around 10 + sqrt(16 - 9) so i do not know if the denominator of 8 is under everything, as you wrote or just the radical part... that is for you to clarify to yourself. If it is everything, then is correct. Do not evaluate it...the question asks you to simplify NOT evaluate. Your answer is incorrect in that it is a rounded up version of a never ending decimal. That is why we write radicals... they are the EXACT number. What we could do is: but this is questionably NOT simpler than ... so leave it alone as as your answer. jon.
 Linear-equations/49535: 7. Find the equation for the following line Parallel to 6x - 4y + 12 = 0, and passing through the line x = 3. 6x – 4y + 12 = 0 -4y = -6x – 12 y = 6/4x + 3 Now what? I don't understand where to go from here. Andrea 1 solutions Answer 32886 by longjonsilver(2297)   on 2006-08-22 04:12:20 (Show Source): You can put this solution on YOUR website!you now know that the gradient of the quoted equation is 6/4... or more simply 3/2. As the line you are asked to find is parallel to this, we now know that its gradient is also 3/2. Put that into the standard equation of a straight line (y=mx+c) as the value of m. We then need the value of c. To find that, you need to know x and y at a point, any point, which we DONT!: we are told that the line passes through the line x=3 which gives us the x-value but not the y-value. So this question is worded badly if not incorrectly... there is no "equation" there are "equations"... in infinite number of them that are parallel to the quoted line and cross the line x=3 Please check the wording of the question. If it is as you wrote, then go back to your teacher and ask them what they are looking for, because the question has bad maths language. Jon.
 Equations/49534: I'm stuck...help. (x/3) - (x/12) = -4 4x - x = -48 3x = -48 x = -16 As I type it now I think I may be correct. Am I? Andrea1 solutions Answer 32885 by longjonsilver(2297)   on 2006-08-22 04:02:50 (Show Source): You can put this solution on YOUR website!your method is correct. To get rid of the fractions in this question we will multiply every term by 12 and then divide the fractions: (x/3) - (x/12) = -4 12*(x/3) - 12*(x/12) = -4*12 4x - x = -48 3x = -48 x = -48/3 x = -16 CHECK: (-16/3) - (-16/12) (-16/3) - (-4/3) (-16/3) + (4/3) (-16+4)/3 (-12)/3 -4 --> which is the correct answer, so we KNOW we are correct. jon.
 Linear-systems/49536: I honestly don't even know where to start. Any advice would be awesome!! Solve any way you can: 3x - y - 2z = 11 x – 2y + 3z = 12 x + y - 2z = 5 I look forward to your thoughts!! Andrea1 solutions Answer 32884 by longjonsilver(2297)   on 2006-08-22 03:56:58 (Show Source): You can put this solution on YOUR website!it depends upon your level of maths knowledge. You do not state your level. Look at the lessons on this website for Cramer's rule and possibly Gaussian Elimination, if you have come across matrices before. Jon.
 Graphs/49276: Write the equation of the line that passes through point (1,-8) with a slope of 0.1 solutions Answer 32681 by longjonsilver(2297)   on 2006-08-18 06:40:57 (Show Source): You can put this solution on YOUR website!any straight line is of the form y=mx+c. If gradient is zero then that means m=0. We also know that x=1 when y=-8. So, we get -8=(0)(1)+c --> c=-8 So, the equation is, starting from y=mx+c: y=-8 jon
 Linear_Equations_And_Systems_Word_Problems/49261: For 1980 through 1994, the population, P (in 1000's), of Hawaii can be modeled by P = 15.5(t+62), where t=0 represents 1980. a)What was the population in 1993? b)What wa the population increase from 1980 to 1993? I don't understand this one at all!!!!!!!!!!!!1 solutions Answer 32671 by longjonsilver(2297)   on 2006-08-18 04:40:03 (Show Source): You can put this solution on YOUR website!P = 15.5(t+62) is the formula where P is in thousands and t=0 is 1980. So, 1981 ==> t=1 1982 ==> t=2 1983 ==> t=3 1984 ==> t=4 ... 1993 ==> t=13 So in 1993, we will have P = 15.5(t+62) P = 15.5(13+62) P = 15.5(75) P = 1162.5 So the population is 1162.5 thousands --> 1162.5*1000 --> 1,162,500 Back to 1980: t=0 here so P = 15.5(t+62) P = 15.5(0+62) P = 15.5(62) P = 961 --> population is 961,000 in 1980 So the population increase from 1980 to 1993 is (1162500-961000) 201,500 jon.
 Geometric_formulas/49269: find a quadratic equation with roots (4+i)and (4-i)1 solutions Answer 32670 by longjonsilver(2297)   on 2006-08-18 04:32:07 (Show Source): You can put this solution on YOUR website!if the roots are (4+i)and (4-i), then we can say that: x=(4+i) or x=(4-i) hence x-(4+i) = 0 or x-(4-i)=0 Working backwards we then say [x-(4+i)][x-(4-i)] = 0 (x-4-i)(x-4+i) = 0 there you go. jon.
 Expressions-with-variables/49200: This question is from textbook beginning algebra i do not understand 9-(-2)(-7)1 solutions Answer 32630 by longjonsilver(2297)   on 2006-08-17 05:06:49 (Show Source): You can put this solution on YOUR website!as it is written, 9-(-2)(-7) means: 9 minus (the product of -2 and -7) (-2)*(-7) is +14 9-(-2)(-7) 9-14 -5 jon.
 Money_Word_Problems/49207: I am stuck on this one, please help me. Business and finance: The demand equation for certain type of printer is given by D = -200p + 35,000 The supply equation is predicted to be S = -p^2 +400p -20,000 Find the price equilibrium price. 1 solutions Answer 32629 by longjonsilver(2297)   on 2006-08-17 03:43:26 (Show Source): You can put this solution on YOUR website!i am assuming the equilibrium price is when supply=demand? If so, then use that...the 2 equations have to be equal: So, factorise or use the quadratic formula to solve to get your answer(s). jon.
 logarithm/49208: Solve for x: log(4x^2)-log(16x)=1 1 solutions Answer 32628 by longjonsilver(2297)   on 2006-08-17 03:37:13 (Show Source): You can put this solution on YOUR website! Assuming the log is base 10, then to remove the log we next to raise both sides to the base 10: this is where the algebraic method and logs seem to me to be at odds to each other. Looking at the above line, we could do one of 2 approaches. Either divide the lefthand side first or move the 16x up to the righthand side. Approach1: Approach2: so either x=0 or x-40=0 --> x=0 or x=40 This second approach seems to give us 2 answers whereas the first gave us just 1. However, putting x=0 into the original will give you an error, so the only solution is x=40... you must remember to check by substituting your answers back into the question, just to check. jon.
 Exponents/49154: can i get the answere to this algebraic properties 3(2-5)+14=1 solutions Answer 32569 by longjonsilver(2297)   on 2006-08-16 09:54:53 (Show Source): You can put this solution on YOUR website!3(2-5)+14 3(-3)+14 -9+14 5 jon
 Quadratic_Equations/49156: solve 2x²-3x-2÷10+x-3x² I can not figure this problem out.. I have tried about 12 times.. this is my last resort. 1 solutions Answer 32568 by longjonsilver(2297)   on 2006-08-16 09:52:07 (Show Source): You can put this solution on YOUR website!you cannot solve it...it isn't an equation...no equals sign. All you can do is simplify which will involve you factorising the numerator and denominator and then cancelling terms (if possible). --> removed the negative sign to make the squared term positive, so it is easier in my head to factorise. jon.
 Functions/49103: This question is from textbook Algebra 1 How do you figure out functions?1 solutions Answer 32564 by longjonsilver(2297)   on 2006-08-16 04:36:38 (Show Source): You can put this solution on YOUR website!look at the lesson i wrote on functions. It should help you. Jon
 Functions/49121: This question is from textbook Beginning Algebra if f(x) =5x-1 find f(a-2) Please help1 solutions Answer 32563 by longjonsilver(2297)   on 2006-08-16 03:59:46 (Show Source): You can put this solution on YOUR website!functions are VERY VERY simple things to use. They just look frightening because they are a more "professional" way of writing maths and to be honest a fair few maths teachers are rubbish at teaching too. Anyway... All that f(x) =5x-1 means is that given the value "x", as quoted in f(x), then we have to multiply it by 5 and then subtract 1 from that. eg f(2) means multiply it by 5 and then subtract 1. --> f(x) =5x-1 --> f(2) = 5(2)-1 --> f(2) = 10-1 --> f(2) = 9 eg f(-6) means multiply it by 5 and then subtract 1. --> f(x) =5x-1 --> f(-6) = 5(-6)-1 --> f(-6) = -30-1 --> f(-6) = -31 and so f(x) =5x-1 find f(a) --> f(x) =5x-1 --> f(a) =5a-1 DONE and finally --> f(x) =5x-1 --> f(a-2) =5(a-2)-1 --> f(a-2) =5a-10-1 --> f(a-2) =5a-11 DONE When asked to do questions like this, the above is ALL you do. I hope you see how easy it is now. Hope this helps. jon.
 Numeric_Fractions/49134: This question is from textbook I need help multiplying fractions by negative whole numbers, 2/3(-3)1 solutions Answer 32562 by longjonsilver(2297)   on 2006-08-16 03:51:27 (Show Source): You can put this solution on YOUR website!Just do 2 things in your head when you do maths: 1. "see" everything 2. take things in stages OK... point 1 means that is, fully written, + Point 2 means we are multiplying + by -. Then (as fractions do) we multiply the numerators and then also the denominators. + and - multiply to give - 2 and 3 (the numerators) multiply to give 6 3 and 1 (the denominators) multiply to give 3 So the answer is which simplifies to -2. The aim is to just look at and do all this in your head and write and then -2. ==================================================== Now, before you ever multiply fractional terms together, what you should get into the habit of doing is doing any division first, to simplify terms. Since multiplication and division are opposites of each other, it does not matter which order you do these in, for example: (5*3)/12 --> 15/12 --> 5/4 or 5*(3/12) --> 5*(1/4) --> 5/4 It is always PREFERABLE to divide first, so we keep the numbers as simple as we can when we finally multiply. In the above example we did 5*3 but in the second version we only had to do 5*1. So, back to the question: + we can divide the two 3's, giving: + which gives -2, following the same processes in point 2 before. Hope this helps. jon