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# Recent problems solved by 'richard1234'

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 Miscellaneous_Word_Problems/563517: Using this model, find the percentage of participation that can be expected if \$5 million is spent on this recycling project? Set up an equation and solve algebraically1 solutions Answer 364910 by richard1234(5390)   on 2012-01-26 23:48:38 (Show Source): You can put this solution on YOUR website!What model?
 Graphs/563115: Graph the following equation; calculate the slope, x-intercept, and y-intercept, and label the intercepts on the graph. y = x + 3 1 solutions Answer 364909 by richard1234(5390)   on 2012-01-26 23:48:12 (Show Source): You can put this solution on YOUR website!Slope = 1 x-intercept occurs when y = 0, i.e. 0 = x+3, x = -3. x-intercept: (-3,0) y-intercept occurs when x = 0, y = 0+3 = 3. y-intercept: (0,3) Graph of the function: http://www.wolframalpha.com/input/?i=y%3Dx%2B3
 Rectangles/562968: If the area of a rectangle can be expressed as x2+x-56 cm2, what is the smallest possible value of x? Explain.1 solutions Answer 364908 by richard1234(5390)   on 2012-01-26 23:45:45 (Show Source): You can put this solution on YOUR website!x^2 + x - 56 = 0 when x = 7 or x = -8 (you can check by factoring). It can be shown that x^2 + x - 56 is positive when x > 7 or x < -8. Hence there is no smallest possible value of x (since x can go to negative infinity and the area is still positive). Note that the dimensions themselves do not necessarily have to be polynomials.
 Points-lines-and-rays/563238: Pre Algebra Chapter 6 Resource Book. McDougal Littell Lesson 6.5 Practice A for use with pages 293-297 How to find the specified side length...Given ABC - JKL, find JL Thank you.1 solutions Answer 364907 by richard1234(5390)   on 2012-01-26 23:42:04 (Show Source): You can put this solution on YOUR website!Surely you don't expect tutors on algebra.com to own the exact same textbook that you are using. You should explain the problem more in depth.
 Rational-functions/563052: is f(x)=x(x-1) a polynomial function explain1 solutions Answer 364906 by richard1234(5390)   on 2012-01-26 23:39:30 (Show Source): You can put this solution on YOUR website!Yes; if you were to expand, you obtain f(x) = x^2 - x. Alternatively, you could claim that the product of two polynomials is a polynomial.
 test/563151: Let A, B, C, be integers such that is an integer. Prove that , , are integers.1 solutions Answer 364904 by richard1234(5390)   on 2012-01-26 23:37:41 (Show Source): You can put this solution on YOUR website!You can let where k is an integer, then . Cubing both sides, Here, we can take this equation "modulo 1" by eliminating all the integer expressions (b,c,k^3,3ka). Factor LHS Note that you can replace with . Modulo 1, this is equivalent to -sqrt(a). Here, we show that i.e. it is an integer. I'll let you finish the proof that sqrt{a}, sqrt[3]{b}, and sqrt[3]{c} have to be integers. Pretty daunting problem...unfortunately we cannot assume the converse of the statement is true (i.e. if ... are integers then ... is an integer).
 Quadratic-relations-and-conic-sections/563407: how do you find the (h,k) of the equation x^2+y^2+16x-4y+59=01 solutions Answer 364902 by richard1234(5390)   on 2012-01-26 23:30:31 (Show Source): You can put this solution on YOUR website!Assuming (h,k) is the center of the circle, complete the square: The coordinates of the center are (-8,2).
 Geometry_proofs/563454: a) Prove the diagonals of a cyclic quadrilateral bisect each other b) prove if the diagonals of a quadrilateral bisect each other then the quadrilateral is cyclic. I know the opposite sides of the quadrilateral are equal and the SAS theorem proves the triangles made by the diagonals are equal I just dont know how to write the proofs1 solutions Answer 364901 by richard1234(5390)   on 2012-01-26 23:26:58 (Show Source): You can put this solution on YOUR website!Statements a) and b) cannot be true, since it is possible to find counterexamples for each one. Note that a cyclic quadrilateral is a quadrilateral whose four vertices all lie on a circle. For statement a), a "kite" shape formed by taking a right triangle and reflecting it about the hypotenuse is a counterexample, since such a quadrilateral is cyclic and not every kite shape will have diagonals that bisect each other. For statement b), a parallelogram (other than a rectangle) is a counterexample, because its diagonals bisect each other, but parallelograms (other than rectangles) *cannot* be cyclic (since opposite angles must add to 180).
 Angles/563441: The ratio of the measures of two complimentary angles is 11:5. Find the measures of the angles.1 solutions Answer 364881 by richard1234(5390)   on 2012-01-26 22:10:09 (Show Source): You can put this solution on YOUR website!"Complementary," not "complimentary." Let 11x and 5x be the angles. Since they're complementary, their sum is 90, so 11x+5x = 90. Solve for x, then find 11x and 5x.
 Distributive-associative-commutative-properties/563308: What property is used in 2-2?1 solutions Answer 364880 by richard1234(5390)   on 2012-01-26 22:06:47 (Show Source): You can put this solution on YOUR website!2-2 = 0, not much of an arithmetic property. However, the number -2 functions as the "inverse element" of 2. Generally speaking, if e is an identity element, * is a binary operation, and x is some number (2 in this case) then there exists a y such that x*y = e for all x.
 Probability-and-statistics/563426: What is the variance and the standard deviation of the scores 51,55,61,62,68,71,71,73,81,82,87,89,92,94,95,100? Can someone please help and show all work? Thanks 1 solutions Answer 364879 by richard1234(5390)   on 2012-01-26 22:01:25 (Show Source): You can put this solution on YOUR website!Note that and that variance is equal to the square of the standard deviation. The best method is simply to use a calculator to input the data values, and you should obtain
 logarithm/563456: I need help solving for x in this logrithm: Log(11x + 9) = 3 + log(x + 3) First I moved both logs to the same side: Log(11x + 9) - log(x + 3) = 3 Then I divided the logs in order to condense the equation: Log (11x + 9)/(x + 3) = 3 Next I switched the equation from log form to expodential form: 10^3 = (11x + 9)/(x + 3) Then I distributed the exponent to the 10 and multiplied (x + 3) to both sides: 1,000(x + 3) =(11x +9) 1,000x + 3,000 = 11x + 9 Then I put the x's on the same side & all whole numbers: 989x = -2991 Then I divided to find x: X = -2991/989; x = -3.024266936. Now I realize I did something wrong to come up with this answer so could you please help me?1 solutions Answer 364878 by richard1234(5390)   on 2012-01-26 21:55:18 (Show Source): You can put this solution on YOUR website!Assuming log is in base 10, your solution is correct. You want to make sure if the log is in base 10 or in base e (i.e. ln)
 Triangles/563460: How do i find the base of a triangle when im given the hieght of 13 and the area of 69?1 solutions Answer 364877 by richard1234(5390)   on 2012-01-26 21:47:55 (Show Source): You can put this solution on YOUR website!Use A = (1/2)bh 69 = (1/2)(13)b Solve for b
 logarithm/562946: In a logarithm, why would you let it equal 1, for example, log(8)4=1 , rather than having it equal 1/2 ? I just want to understand logarithms a little bit more. Thank you1 solutions Answer 364797 by richard1234(5390)   on 2012-01-26 16:17:17 (Show Source): You can put this solution on YOUR website! is not equal to 1. You should ask yourself, "8 to what power equals 4?" It turns out that the logarithm is equal to 2/3.
 real-numbers/563024: 1. What is the difference between natural numbers and rational numbers? 2. What is the difference between rational numbers and real numbers? 3. What is the difference between whole numbers and integers? 4. Why is there a rule that says x^0=1? 5. Why is there a rule that says 5/0 = undefined? 1 solutions Answer 364794 by richard1234(5390)   on 2012-01-26 16:14:41 (Show Source): You can put this solution on YOUR website!For #1-3, review what natural numbers, rational numbers, integers, etc. are defined as. For #4, x^0 = 1 because x^(a-b) = (x^a)(x^b), so if a = b, x^0 = (x^a)/(x^a) = 1 (assume x is not 0). For #5, 5/0 is undefined because we cannot divide 5 into groups of zero.
 Parallelograms/563081: Can u tell me the formulae for finding area of parallelogram with 4 coordinates?1 solutions Answer 364791 by richard1234(5390)   on 2012-01-26 16:12:01 (Show Source): You can put this solution on YOUR website!Suppose the coordinates are (0,0), (a,b), (c,d) and (a+c,b+d) (we may assume one of the coordinates is (0,0) in order to fix a point). Then the area is equal to the determinant of the matrix |a b| |c d| or ad-bc.
 Numbers_Word_Problems/563033: what are two integers less than 30?1 solutions Answer 364787 by richard1234(5390)   on 2012-01-26 16:08:21 (Show Source): You can put this solution on YOUR website!17 and 24, for example.
 Unit_Conversion_Word_Problems/563061: 1)How many miles are in 4 furlongs? 1 solutions Answer 364786 by richard1234(5390)   on 2012-01-26 16:07:43 (Show Source): You can put this solution on YOUR website!1 furlong = 1/8 mile 4 furlongs = 4/8 = 1/2 mile
 Parallelograms/563124: what is the perimeter of a parallelogram that is 30 cm by 20cm? 1 solutions Answer 364783 by richard1234(5390)   on 2012-01-26 16:04:51 (Show Source): You can put this solution on YOUR website!Perimeter = 30+30+20+20 = 100 cm
 test/563172: The sum of two squares of two consecutive odd positive integers is1301 solutions Answer 364780 by richard1234(5390)   on 2012-01-26 16:01:56 (Show Source): You can put this solution on YOUR website!7^2 + 9^2 = 130 You could do it by letting x^2 + (x+2)^2 = 130, but since we're given that they're integers, we do not need to use the longer method.
 Sequences-and-series/563150: How can we show if the sequence αn = 2cos(nπ) is monotone or not?1 solutions Answer 364779 by richard1234(5390)   on 2012-01-26 16:00:20 (Show Source): You can put this solution on YOUR website!2 cos (n*pi) is not monotonic. Monotonic means that the function is either strictly increasing or strictly decreasing.
 Probability-and-statistics/562680: a date picked at random is february 301 solutions Answer 364722 by richard1234(5390)   on 2012-01-25 23:17:21 (Show Source): You can put this solution on YOUR website!There is no February 30...
 Trigonometry-basics/562854: how would you find slope of a tangent of a distance vs time graph?1 solutions Answer 364721 by richard1234(5390)   on 2012-01-25 23:09:02 (Show Source): You can put this solution on YOUR website!You could find the derivative of the function, i.e. velocity vs. time.
 test/562857: 9x + 9y. Use distributive law to factor.1 solutions Answer 364720 by richard1234(5390)   on 2012-01-25 23:08:22 (Show Source): You can put this solution on YOUR website!9(x+y)
 Sequences-and-series/562232: What is the common difference in the arithmetic sequence of 1, 1/4, 1/9, 1/16?1 solutions Answer 364542 by richard1234(5390)   on 2012-01-25 08:38:37 (Show Source): You can put this solution on YOUR website!1, 1/4, 1/9, 1/16, ... is not an arithmetic sequence.
 Trigonometry-basics/562308: Please explain the minimun value of cosx = -1 i know but plz explain the value ??1 solutions Answer 364541 by richard1234(5390)   on 2012-01-25 08:32:53 (Show Source): You can put this solution on YOUR website!Cosine alternates between -1 and 1. cos x = 1 when x = -pi, -3pi, -5pi, etc.
 Sequences-and-series/562209: What is the arithmetic sequence of 1, 1/4, 1/9, 1/16?1 solutions Answer 364493 by richard1234(5390)   on 2012-01-24 22:25:28 (Show Source): You can put this solution on YOUR website!That is not an arithmetic sequence. Arithmetic sequences have consecutive terms that differ by a constant number.
 Numbers_Word_Problems/561896: What number is the sum of 17 times its first digit, 34 times its second digit, and 51 times its third digit? Why?1 solutions Answer 364490 by richard1234(5390)   on 2012-01-24 22:22:32 (Show Source): You can put this solution on YOUR website!If a,b,c denote the digits, then (right away we know the number is a multiple of 17) Here, we conclude that a is even (since RHS is even). Now consider the equation mod 10 (if you don't know modular arithmetic, think of it as "matching the units digits on LHS and RHS"). If a = 2, then b = 4 or 9, but neither allows for an integer value of c. If a = 4, then b = 3 or 8, but likewise, there are no integer solutions for c. If a = 6, then b = 2 or 7, and it can be checked that b = 2 allows for the number 629. If a = 8, then b = 1 or 6, but neither allows for integer solutions. Hence the only number is 629.
 Travel_Word_Problems/562205: maria can run laps around the school in the time it takes Susan to run 3 times around the track. how many laps will maria have run when Susan has run 12 laps 1 solutions Answer 364487 by richard1234(5390)   on 2012-01-24 22:14:38 (Show Source): You can put this solution on YOUR website!Maria can run (how many) laps in the time it takes Susan to run three times around the track?
 Functions/562038: Find g(x)+5 I'm not sure how to go about finding the value of g(x)+5 since there is still a variable and the +5 is on the outside of the parenthesis, but on the left side of the "equation."1 solutions Answer 364483 by richard1234(5390)   on 2012-01-24 22:07:49 (Show Source): You can put this solution on YOUR website!We know what g(x) is, so g(x) + 5 is just "5 more than g(x)."