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# Recent problems solved by 'fractalier'

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 Coordinate-system/45335: Find the midpoint of the segment that joins them. (2,3), (5,2)1 solutions Answer 30109 by fractalier(2101)   on 2006-07-10 21:03:26 (Show Source): You can put this solution on YOUR website!The midpoint of a segment joining two points is the average x- and y- values...so from (2,3) and (5,2), we add the x's and divide by two...then repeat with the y's to give us the point (7/2, 5/2)
 Expressions-with-variables/45354: 2x - 2(3x+7)=x - 51 solutions Answer 30108 by fractalier(2101)   on 2006-07-10 21:01:21 (Show Source): You can put this solution on YOUR website!Okay from 2x - 2(3x+7) = x - 5 let's expand, collect like terms and solve...like this 2x - 6x - 14 = x - 5 -4x - 14 = x - 5 -5x = 9 x = -9/5
 Expressions-with-variables/45351: Please write an algebraic expression for: The product of 3 and a number squared1 solutions Answer 30107 by fractalier(2101)   on 2006-07-10 20:59:06 (Show Source): You can put this solution on YOUR website!Product means multiplication, so we have, letting the number be x, 3x^2
 real-numbers/45353: If X is any real number than X to the power of 1 =1 solutions Answer 30106 by fractalier(2101)   on 2006-07-10 20:58:07 (Show Source): You can put this solution on YOUR website!Anything to the 1 power equals the anything...thus X^1 = X
 Equations/45370: find the value of y when y=.25x+21 solutions Answer 30105 by fractalier(2101)   on 2006-07-10 20:56:32 (Show Source): You can put this solution on YOUR website!It all depends on the value of x you choose... Choose a value for x and plug it in to this equation to get a corresponding value for y...
 Equations/45373: im havin trouble with this equation can you solve it and show me wat to do 5p+8(3p+4)=2641 solutions Answer 30104 by fractalier(2101)   on 2006-07-10 20:55:14 (Show Source): You can put this solution on YOUR website!Just posted this solution...p=8
 Equations/45374: im havin trouble with this equation can you solve it and show me wat to do 5p+8(3p+4)=2641 solutions Answer 30103 by fractalier(2101)   on 2006-07-10 20:53:44 (Show Source): You can put this solution on YOUR website!Okay from 5p + 8(3p + 4) = 264 let's expand, collect terms and solve...like this 5p + 24p + 32 = 264 29p + 32 = 264 subtract 32 from both sides 29p = 232 divude by 29 and get p = 8
 Equations/44673: SOlve the equation 3(n-1)^2+20=19(n-1)1 solutions Answer 29614 by fractalier(2101)   on 2006-07-04 12:33:22 (Show Source): You can put this solution on YOUR website!Okay from 3(n-1)^2 + 20 = 19(n-1) we expand and get 3n^2 - 6n + 3 + 20 = 19n - 19 now collect terms and solve, we get 3n^2 - 25n + 42 = 0 (3n - 7)(n - 6) = 0 n = 7/3 or n = 6
 Equations/44701: Evaulate (-3) second power -17 A) 39 B) 24 C) 27 D)301 solutions Answer 29613 by fractalier(2101)   on 2006-07-04 12:29:06 (Show Source): You can put this solution on YOUR website!(-3)^2 - 17 = 9 - 17 = -8 Even if you meant -3^2 - 17, that answer is -9 - 17 = -26 There is a mistake somewhere...
 Equations/44708: determine which two equations represent perpendicular lines A) y=5/3x-3 B) y=3x-5/3 C) y=-1/3x+5/3 D y=1/3x-5/31 solutions Answer 29612 by fractalier(2101)   on 2006-07-04 12:27:16 (Show Source): You can put this solution on YOUR website!Perpendicular lines have slopes which are negative reciprocals of each other... Notice that choices B and C have slopes which are 3 and -1/3, respectively... Thus B and C are perpendicular.
 Probability-and-statistics/44721: If the probability of any individual being in an airplane accident is .0005 in any given year, what is the probability of that same individual being in three separate, unrelated airplane accidents in a single year? Explain your answer. Please help me figure this one out. Thank you so much.1 solutions Answer 29611 by fractalier(2101)   on 2006-07-04 12:24:51 (Show Source): You can put this solution on YOUR website!Since the events are unrelated and independent of each other, their probabilities multiply...this is what is called the logical "AND" case...as in, what is the probability that this AND that will happen...in this particular problem there are three things...so the probability is P(3 accidents) = .0005^3 = .000000000125 = 1.25 x 10^-10
 Inequalities/44735: This question is from textbook College Algebra Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent. 5x -6y = 32 x = 6 - 3y1 solutions Answer 29609 by fractalier(2101)   on 2006-07-04 12:21:08 (Show Source): You can put this solution on YOUR website!Since the second one is already solved for x, we can substitute its value into the other equation. so from 5x - 6y = 32 x = 6 - 3y we get 5(6 - 3y) - 6y = 32 30 - 15y - 6y = 32 -21y = 2 y = -2/21 then plug that back into equation two and get x = 6 - 3y x = 6 - 3(-2/21) x = 6 + 6/21 x = 6 + 2/7 x = 6 2/7 or 44/7 Whenever you get one distinct solution, like we have here, (44/7, -2/21), we have a consistent and independent system...
 Inequalities/44736: This question is from textbook College algebra Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent. x + 2y =3 2x + y = 51 solutions Answer 29608 by fractalier(2101)   on 2006-07-04 12:16:43 (Show Source): You can put this solution on YOUR website!Let us solve the first one for x and substitute into the second one...we get x + 2y =3 2x + y = 5 and x = -2y + 3 and 2(-2y + 3) + y = 5 -4y + 6 + y = 5 -3y = -1 y = 1/3 then plugging this back into x = -2y + 3 we get x = -2/3 + 3 x = -2/3 + 9/3 x = 7/3
 Inequalities/44738: This question is from textbook College Algebra Solve each system by addition. Determine whether each system is independent, inconsistent, or dependent. 2x - y = 6 -4x + 2y =91 solutions Answer 29606 by fractalier(2101)   on 2006-07-04 12:13:53 (Show Source): You can put this solution on YOUR website!From 2x - y = 6 -4x + 2y = 9 let us multiply the top one by two and add them...we get 2(2x - y = 6) -4x + 2y =9 and 4x - 2y = 12 -4x + 2y = 9 adding we get 0 = 21 We ask, "When does 0 = 21?" Well never of course. Thus this system has no solution, the lines are parallel and the system is inconsisent.
 Radicals/44747: find the length x in the triangle and express in simplified radical form sides of the triangle are 10, 8, and x I get x^2 = 8^2 + 10^2 = 64 + 100 = 164 not sure if this is correct and I think I am missing the final step. Thanks for help1 solutions Answer 29604 by fractalier(2101)   on 2006-07-04 12:10:58 (Show Source): You can put this solution on YOUR website!Well, you are assuming that the x represents the hypotenuse...if it does you are correct and you get x^2 = 164 x = sqrt(164) = 2*sqrt(41) But if the x represents a leg, we get x^2 + 8^2 = 10^2 x^2 + 64 = 100 x^2 = 36 x = 6
 Probability-and-statistics/44685: Two dice are thrown. Determine the number of ways to obtain a score of at least 4. Hint In how many ways can you fail to obtain a score of at least 4? How many outcomes are possible all told?1 solutions Answer 29565 by fractalier(2101)   on 2006-07-03 19:51:23 (Show Source): You can put this solution on YOUR website!Well two dice can roll out a total of 6x6 = 36 ways... Of those 36 ways, only three ways are possible to be a total less than four, they are 1-1, 1-2, and 2-1. Thus 33 ways are possible for a total of at least four.
 Probability-and-statistics/44688: How many four letter code words can be formed using a standard 26 letter alphabet if repetition is allowed? and then if repetition is not allowed?1 solutions Answer 29564 by fractalier(2101)   on 2006-07-03 19:49:42 (Show Source): You can put this solution on YOUR website!Any of 26 letter can be in any of 4 spots, so there are 26^4 = 456,976 possibilities If there is no repeating, then the answer is less, because, even though 26 letters can be first, only 25 can be second, 24 can be third, and 23 can be last, so we get 26 x 25 x 24 x 23 = 358,800 possibilities
 Linear_Algebra/44691: Im sorry, i dont know what kind of algebra this is, but i am just learning that f(x)=y. Now we've started solving problems like f(g(2)) when f(x)=3x and g(x)= x-3. Please help me if you can!1 solutions Answer 29563 by fractalier(2101)   on 2006-07-03 19:45:53 (Show Source): You can put this solution on YOUR website!f(g(2)) is what is called a composite function...essentially a function of a function... First we evaluate g(2) and get g(2) = 2 - 3 = -1 Then we evaluate f(-1)...we get f(-1) = 3(-1) = -3
 Linear-equations/44693: Business and Finance. The cost of producing a number of items x is given by C= mx + b, in which b is the fixed cost and m is the variable cost (the cost of producing one or more item). (a) If the fixed cost is \$40.00 and the variable cost is \$10, write the cost equation. (b) Graph the cost equation. 1 solutions Answer 29562 by fractalier(2101)   on 2006-07-03 19:42:44 (Show Source): You can put this solution on YOUR website!Given C(x) = mx + b, we merely plug in for the fixed cost (b = \$40) and the incremental cost (m = \$10)...we get C(x) = 10x + 40 We know this is correct because if x = 0, that is no items produced, our fixed cost would still be \$40... To graph this, plot the point (0, 40), becaise when x = 0, C(x) = 40... Then let x = 1...C(x) = 10(1) + 40 = 50...thus graph the point (1, 50)... Connect the dots in a line and you're done...
 Linear-equations/44387: write an equation of the line.Express it in standard form. through (8,3)and(-4,3)1 solutions Answer 29336 by fractalier(2101)   on 2006-06-30 11:29:40 (Show Source): You can put this solution on YOUR website!If you quickly graph these, you will see that they are two points along a horizontal line. If you calculate the slope, you will find it to be zero. The equation of the this line is y = 3
 Radicals/44383: simplify by combining like terms. question 32. ^63-2^28+5^7 I don't have the signs on my computer for square roots. it is square root of 63, square root of 28, and square 7.1 solutions Answer 29335 by fractalier(2101)   on 2006-06-30 11:25:29 (Show Source): You can put this solution on YOUR website!Okay, we can use sqrt for square root....so we have sqrt(63) - 2*sqrt(28) + 5*sqrt(7) = now we pull out the largest perfect squares from each and get 3*sqrt(7) - 4*sqrt(7) + 5*sqrt(7) = 4*sqrt(7)
 Signed-numbers/44397: Can someone help me with this problem? I need to write the following number in expanded form: 684 is it (A) 6 + 8 + 4 (B) 600 + 80 + 4 (C) (6 x 100) + (8 x 10) + (4 x 1) (D) 600 x 80 x 4 Thanks, Sher1 solutions Answer 29334 by fractalier(2101)   on 2006-06-30 11:23:17 (Show Source): You can put this solution on YOUR website!Choice C is correct.
 Graphs/44405: Can I get some help here? Graph each function and state its domain and range. g(x)= x+2 Thanks1 solutions Answer 29333 by fractalier(2101)   on 2006-06-30 11:22:45 (Show Source): You can put this solution on YOUR website!First plot the point (0, 2) because when x = 0, g(x) = 2. Since the slope is one, we go up one and to the right one, and plot another point at (1, 3). For every x, we can find g(x) by adding 2. Connect them in a straight line. The domain is all real numbers since all values of x are allowed. The range is also all real numbers since all values of g(x) are possible.
 Numeric_Fractions/44418: Can someone help me with this problem? I need to perform the indicated operation: 11-6/7-7 Thank you , Ashley1 solutions Answer 29332 by fractalier(2101)   on 2006-06-30 11:20:06 (Show Source): You can put this solution on YOUR website!From 11 - 6/7 - 7 we can rearrange them to make it a bit easier (but you don't have to) and get 11 - 7 - 6/7 = 4 - 6/7 = 3 1/7
 Equations/44412: This question is from textbook Intermediate Algebra Solve using the quadratic formula: x2 – 2x = 15x – 101 solutions Answer 29331 by fractalier(2101)   on 2006-06-30 11:18:18 (Show Source): You can put this solution on YOUR website!From x^2 - 2x = 15x - 10 we collect terms and get x^2 - 17x + 10 = 0 Now using the quadratic we get x = (17 ± sqrt(289 - 40)) / 2 x = (17 ± sqrt(249)) / 2
 Polynomials-and-rational-expressions/44417: Can someone please help me factor x(2x-y) + y(2x-y) Thanks!1 solutions Answer 29330 by fractalier(2101)   on 2006-06-30 11:16:27 (Show Source): You can put this solution on YOUR website!Factor out the 2x-y from both terms and get x(2x-y) + y(2x-y) = (2x-y)(x+y)
 Equations/44345: -√[121]+(-1)³1 solutions Answer 29281 by fractalier(2101)   on 2006-06-29 16:35:42 (Show Source): You can put this solution on YOUR website!-√[121]+(-1)³ = -11 - 1 = -12
 expressions/44344: 4m-m-m1 solutions Answer 29279 by fractalier(2101)   on 2006-06-29 16:34:43 (Show Source): You can put this solution on YOUR website!4m - m - m = 2m
 Polynomials-and-rational-expressions/43902: By using the Factor Theorem, Find the Prime factors of the polynomial: x^3 - x^2 - 17x - 151 solutions Answer 29278 by fractalier(2101)   on 2006-06-29 16:34:01 (Show Source): You can put this solution on YOUR website!x^3 - x^2 - 17x - 15 has rational factors ±1, ±3, ±5, or ±15 Since 1 does not work, we try -1...and it works...so does -3 and 5 so that it factors into (x + 1)(x + 3)(x - 5)
 Trigonometry-basics/44190: Rewrite (9π)/5 radians in degree measure. Thanks1 solutions Answer 29276 by fractalier(2101)   on 2006-06-29 16:29:04 (Show Source): You can put this solution on YOUR website!To convert radians to degrees we multiply by 180/pi...so therefore 9(pi)/5 * 180/pi = 324°
 Equations/44242: 1 over 2x-7 + 3 over 7-2x show work isn't the bottom denominators the same?1 solutions Answer 29275 by fractalier(2101)   on 2006-06-29 16:26:27 (Show Source): You can put this solution on YOUR website!No they are not, but close, because 2x-7 / 7-2x = -1 I posted this solution about an hour ago...