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 Linear-equations/176737: How do I use Gauss-Jordan elimination to solve this linear system and find all solutions? x + y - 2z = 5 2x + 3y + 4z = 2 So far, I have placed each of the numbers into an augmented matrix. I do not know how to proceed from here.1 solutions Answer 131855 by solver91311(16897)   on 2009-01-14 22:58:15 (Show Source): You can put this solution on YOUR website!You can't solve this system. You have three variables but only two equations. Go find your other equation and we'll talk.
 Linear-equations/176742: I am a bit overwhelmed by the complexity of this question. Please help me to understand and answer the question. If matrix A is transformed into matrix B by means of an elementary row operation, is there an elementary row operation that transforms B into A?1 solutions Answer 131842 by solver91311(16897)   on 2009-01-14 22:19:10 (Show Source): You can put this solution on YOUR website!There are three elementary row operations: 1. Switching the position of two rows. Obviously, you can just switch them back again. 2. Multiplying each element of a row by a non-zero constant. Just multiply that row by the reciprocal of the non-zero constant. 3. Replacing a row with the sum of that row and a multiple of another row. Just subtract the multiple again. So, the answer to your question is yes.
 Probability-and-statistics/176732: Can someone double check my work please. Two dice are rolled. Find the probability that the score on the dice is 8? 8 = (1,7)(6,2)(4,4)(3,5)(5,3)(4,4)(2,6)(7,1) 8/36 = 2/91 solutions Answer 131808 by solver91311(16897)   on 2009-01-14 20:04:55 (Show Source): You can put this solution on YOUR website!First of all, how did you get (1, 7) or (7, 1)? DO NOT take that pair of dice to Vegas -- you might get your thumbs broken by some big casino security goon. Second of all, you counted (4,4) twice. Nope, (4,4) is a single outcome. So there are 8 = (6,2) or (5,3) or (4,4) or (3,5) or (2,6) = 5 ways to make an 8 and the probability of rolling 8 is .
 Probability-and-statistics/176736: If a coin is tossed three times, in how many different ways can the sequence of heads and tails appear?1 solutions Answer 131804 by solver91311(16897)   on 2009-01-14 19:59:35 (Show Source): You can put this solution on YOUR website!2 ways for the first toss times 2 ways for the second toss times 2 ways for the third toss = 6 ways.
 Probability-and-statistics/176735: Can someone double check my work please. Two dice are rolled. Find the odds that the score on the dice is either 6 or 12? 6 = (1,5)(2,4)(3,3)(3,3)(4,2)(5,1) = 6/36 = 1/6 12 = (6,6)(6,6) = 2/36 = 1/18 Did I do this right?1 solutions Answer 131802 by solver91311(16897)   on 2009-01-14 19:58:20 (Show Source): You can put this solution on YOUR website!Not quite. There are 5 ways to make a 6: (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1). There is 1 way to make a 12: (6, 6). There are a total of 36 different results: 6 ways one die can come up times 6 ways the other die can come up. Since you want the probability of rolling a 6 OR a 12, then you have a total of 6 different successes (5 ways to make 6 plus 1 way to make 12) out of 36 possible outcomes, so:
 Points-lines-and-rays/176733: Can someone double check my work please. Find the equation of the line passing through the two points.(2,9)and (0,6) slope = (y^2 - y1)(x^2 - x1) slope = (6 + 9)(0 + 2) slope = 15/2 Did I do this right?1 solutions Answer 131798 by solver91311(16897)   on 2009-01-14 19:52:51 (Show Source): You can put this solution on YOUR website!Not quite. slope = and and So: (you had + here instead of -)
 Equations/176729: Maggie makes a $9.25 purchase at a bookstore in Reno with a$20 bill. The store has no bills and gives her the change in quarters and fifty-cent pieces. There are 30 coins in all. How many of each kind are there? please help me! thank you!!1 solutions Answer 131795 by solver91311(16897)   on 2009-01-14 19:45:56 (Show Source): You can put this solution on YOUR website!The number of quarters: The number of 50c pieces: Given: The value of each quarter is 25 cents, so the value of all her quarters is in cents. Similarly the value of all her 50c pieces is The total value of her change is dollars which is the same as cents. The value of the quarters plus the value of the 50c pieces must equal the total value of the change, so: Solve the first equation for : → . Substitute this expression for into the second equation: Solve for So there were 13 half-dollars, and therefore quarters. Check: Checks.
 Divisibility_and_Prime_Numbers/176730: use two unit multipliers to convert 360 yards to inches1 solutions Answer 131793 by solver91311(16897)   on 2009-01-14 19:32:10 (Show Source): You can put this solution on YOUR website!Use 3 ft/yard and 12 inches/foot
 real-numbers/176727: A train traveled m miles at a speed of s mph. A bus following the same route traveled 5 mph slower. How much longer did the bus take than the train to make this trip? Write the answer as a single rational expression. 1 solutions Answer 131792 by solver91311(16897)   on 2009-01-14 19:30:18 (Show Source): You can put this solution on YOUR website!Use distance = rate times time. . Here, and is the speed of the train. is the speed of the bus. Since , and... for the train: for the bus: To find out how much longer the bus took, subtract the train's time from the bus' time:
 Rational-functions/176712: How do u solve this problem. Given: f(x)= x + 2 and g(x) = x^2 + 2 Problem: f(g(1)) how do i do this??1 solutions Answer 131791 by solver91311(16897)   on 2009-01-14 19:18:18 (Show Source): You can put this solution on YOUR website!For x in g(x) substitute 1 and do the arithmetic. Take this value for g(1) and substitute for x in f(x) and do the arithmetic. Alternatively, though I think it is a bit more work, you could substitute the expression for g(x) for the x in f(x) giving you an expression for (f◦g)(x). Then you can substitute 1 for x in the derived expression. In general, given a function f defined by f(x) = [some expression in x], you evaluate f(a) by substituting a for x in the expression. It doesn't matter whether a is a number, some other variable, or another function definition or composite of functions. Remember that f or g or h or some other letter is a function, f(x) or g(x) etc. is the value of the function at x. f(a), then, is the value of the function at a. Typically, things like f(x) are used to describe the general rule for the specific function whereas f(a) is used to examine the value of a particular function at a specific point, namely a.
 Numbers_Word_Problems/176685: 15 more than the square of a number is 8 times the number1 solutions Answer 131788 by solver91311(16897)   on 2009-01-14 18:44:33 (Show Source): You can put this solution on YOUR website!Although you don't specifically say, I assume that you want to determine the number. The number: The square of the number: 15 more than the square of the number: 8 times the number: 15 more than the square of the number is (=) 8 times the number: Put the quadratic into standard form and solve by factoring: Hint: -3 + (-5) = -8 and -3 X -5 = 15
 Inequalities/176686: how to solve this x-1<31 solutions Answer 131786 by solver91311(16897)   on 2009-01-14 18:39:13 (Show Source): You can put this solution on YOUR website!Add 1 to both sides.
 Exponents-negative-and-fractional/176692: This question is from textbook Can you please help me. the directions are evaluate the exponential expression. Write as a fraction in the simplest form. 14. 4(4-2) the -2 this is an exponent negative 2 thank you1 solutions Answer 131784 by solver91311(16897)   on 2009-01-14 18:38:01 (Show Source): You can put this solution on YOUR website!A negative exponent means the reciprocal. so
 Functions/176709: f(x) = 3x -8 for {-2, 3, 6}1 solutions Answer 131783 by solver91311(16897)   on 2009-01-14 18:35:25 (Show Source): You can put this solution on YOUR website!Just substitute the given values for x and do the arithmetic.
 Functions/176696: evaluate f(x)=3x - 8 for {-2,3,6}. Which set of numbers is the domain and which set of numbers is the range? 1 solutions Answer 131781 by solver91311(16897)   on 2009-01-14 18:34:12 (Show Source): You can put this solution on YOUR website!Substitute each of the values in the set for x in the function and then do the arithmetic. The values in the given set are elements of the domain and the values in your set of results are elements in the range.
 Graphs/176707: This question is from textbook Elementary and Intermediate Algebra Slope-Intercept Form Write an equation for each line. Use slope-intercept form if possible. 8. Points are (0, 3) and (2, -1) 10. Points are (0, -1) and (4, 1)1 solutions Answer 131779 by solver91311(16897)   on 2009-01-14 18:31:45 (Show Source): You can put this solution on YOUR website!Given two points, and , you can write the equation of the line using the two-point form of the equation of a line: . Just insert the values from the two ordered pairs and do the arithmetic. Once you have simplified things, solve the equation for y (that is, manipulate the equation so that y is by itself on the left and everything else is on the right) to put the equation in slope-intercept form.
 Complex_Numbers/176697: The imaginary number i is defined such that i^2 = –1. What does i + i^2 + i^3 + .... + i^23 equal? The answer is supposed to be -1, but I thought it should be -i according to another source. Is the answer key wrong?1 solutions Answer 131777 by solver91311(16897)   on 2009-01-14 18:28:03 (Show Source): You can put this solution on YOUR website! , and so on repeating the sequence every 4 increments of the exponent. The sum of the first 4 is: , so the sum of the each subsequent 4 must also be zero. Use integer division is 5 with a remainder of 3. So in your string of 23 terms there are 5 sets of 4 terms each of which sum to zero, so it is only the last three terms that make any difference: And that is your sum. It is your 'other source' that is incorrect.
 Functions/176699: f(x) = -x + 3 for -4 and 41 solutions Answer 131772 by solver91311(16897)   on 2009-01-14 18:17:09 (Show Source): You can put this solution on YOUR website!Just substitute the given values for x and do the arithmetic.
 Functions/176701: g(x) = -2x + 5 for 0 and 31 solutions Answer 131771 by solver91311(16897)   on 2009-01-14 18:16:45 (Show Source): You can put this solution on YOUR website!Just substitute the given values for x and do the arithmetic.
 Functions/176702: f(x) = -3x - 1 for -1 and 71 solutions Answer 131770 by solver91311(16897)   on 2009-01-14 18:16:21 (Show Source): You can put this solution on YOUR website!Just substitute the given values for x and do the arithmetic.
 Functions/176704: h(x) = 1.5x - 2 for -2 and 41 solutions Answer 131768 by solver91311(16897)   on 2009-01-14 18:15:52 (Show Source): You can put this solution on YOUR website!Just substitute the given values for x and do the arithmetic.
 Functions/176705: f(x) = 6 - x for 0 and 6 1 solutions Answer 131767 by solver91311(16897)   on 2009-01-14 18:15:19 (Show Source): You can put this solution on YOUR website!Just substitute the given values for x and do the arithmetic.
 Numbers_Word_Problems/176693: Farmer Billy Bob has 210m of fencing to enclose his pig pen on all 4 sides. What dimensions should his pig pen be to enclose the largest possible area?1 solutions Answer 131766 by solver91311(16897)   on 2009-01-14 18:14:12 (Show Source): You can put this solution on YOUR website!The area of a rectangle is given by the length times the width, and the perimeter is given by 2 times the length plus 2 times the width: and We want to maximize subject to the constraint that . → , so solve for either or . → Now substitute this expression for into the Area function: → Now we have a second degree polynomial with a negative lead coefficient, so the graph is a concave down parabola. The vertex of a concave down parabola is a maximum, so we need to find the value of the W coordinate for the vertex. The vertex of a parabola expressed in has an x-coordinate of . In this problem we have and , so the W-coordinate is at . Hence, for the maximum area, the width must be 52.5 meters. So if and , and the pig pen needs to be a square 52.5 meters on each side. As you may expect, it is true in general that a rectangle with maximum area for a given perimeter is a square. For extra credit, prove it.
 Equations/176690: Please help me solve this equation: Thanks 1 solutions Answer 131759 by solver91311(16897)   on 2009-01-14 17:48:18 (Show Source): You can put this solution on YOUR website!Multiply both sides by -9
 Numbers_Word_Problems/176694: Thank you for helping me but can you please go faster because i need now ok thanks 1 solutions Answer 131758 by solver91311(16897)   on 2009-01-14 17:39:45 (Show Source): You can put this solution on YOUR website!Exactly what is it you need? If you don't ask a question, you won't get an answer.
 Numbers_Word_Problems/176691: The area of a triangle is 126cm^2, and the altitude is 3 less than twice the base. Find the length of the base. 1 solutions Answer 131757 by solver91311(16897)   on 2009-01-14 17:38:32 (Show Source): You can put this solution on YOUR website!The area of a triangle is given by . Let the measure of the base be , then we are given that the altitude is , so and we are given that the area of this particular triangle is 126 square centimeters. Therefore: Solve the quadratic by ordinary means. You can factor, complete the square, or use the quadratic formula -- all three methods work. You will get two roots as you should expect, except that one of them will be < 0. This absurd result for the measure of a side of a triangle is an extraneous root caused by squaring the variable in the process of solving the problem. Exclude the negative root. The positive root is your answer.
 Rational-functions/176666: This question is from textbook McDougal Littell Algebra 2 How do you multiply and divide rational expressions?1 solutions Answer 131756 by solver91311(16897)   on 2009-01-14 17:15:40 (Show Source): You can put this solution on YOUR website!Just like any other fractions. regardless of whether a, b, c, and/or d are numbers or polynomial expressions. Of course, the result may need to be reduced to lowest terms. Likewise . Again, the result may need to be reduced to lowest terms. Lastly, you must exclude values of a variable that would cause any denominator to equal zero. For example: is undefined for
 real-numbers/176681: h=16t+251 solutions Answer 131754 by solver91311(16897)   on 2009-01-14 17:05:44 (Show Source): You can put this solution on YOUR website!Exactly what is it you would like to be able to do with this rather handsome little 2-variable linear equation?
 Polynomials-and-rational-expressions/176682: The length of a rectangular swimming pool is 2x-1m + the width is x+2 meters. Write a polynomial A(z represents the area) Could somebody please help me do this problem? I have tried and do no know how to do it. Thanks in advance. Judy1 solutions Answer 131753 by solver91311(16897)   on 2009-01-14 17:04:36 (Show Source): You can put this solution on YOUR website!The area of a rectangle is the length multiplied times the width. So just say: Then use FOIL to multiply the binomials to obtain the desired polynomial expression.
 Systems-of-equations/176631: Ramon mixes 12 liters of 8% acid solution with a 20% acid solution, which results in a 60% acid solution. Find the number of liters of 20% acid solution in the new mixture.1 solutions Answer 131703 by solver91311(16897)   on 2009-01-14 12:28:20 (Show Source): You can put this solution on YOUR website!The stated result is impossible. The mixture solution must be a smaller concentration than at least one of the constituents. Now if you meant "...12 liters of 80% acid..." you would have a solvable problem. Write back with the correct problem statement.
 Points-lines-and-rays/176638: This question is from textbook College Mathematics I How do I Find the distance between the pair of points (-1,-4) and (-5, -7)1 solutions Answer 131701 by solver91311(16897)   on 2009-01-14 12:23:11 (Show Source): You can put this solution on YOUR website!Use the distance formula: . Just plug in the coordinate values from your two points and do the arithmetic. Watch your signs carefully.