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# Recent problems solved by 'ewatrrr'

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 logarithm/619721: Condense the expression: 3log(base3)15+2log(base3)x-log(base3)251 solutions Answer 389766 by ewatrrr(10682)   on 2012-06-11 11:46:34 (Show Source): You can put this solution on YOUR website! ``` Hi, ```
 Linear-equations/619745: How do you solve for the x-intercept in the equation x+2y=61 solutions Answer 389765 by ewatrrr(10682)   on 2012-06-11 11:36:41 (Show Source): You can put this solution on YOUR website! ``` Hi, How do you solve for the x-intercept in the equation x+2y=6 ||when y = 0 x = 6 Pt(6,0) is where the line cross the x-axis ```
 Expressions-with-variables/619743: 4x2 – 81y2 A. (2x + 9)(2x – 9) B. (2x + 9y)(2x – 9y) C. (2x + 9y)2 D. (2x – 9y)2 Thank you!1 solutions Answer 389764 by ewatrrr(10682)   on 2012-06-11 11:32:49 (Show Source): You can put this solution on YOUR website! ``` Hi, factoring (2x + 9y)(2x - 9y) Checking with FOIL F First terms 4x^2 O Outside terms -18xy I Inside terms +18xy L Last terms -81y^2 ```
 Triangles/619737: find the circumradius of triangle whose sides are 3,4 and 5?1 solutions Answer 389763 by ewatrrr(10682)   on 2012-06-11 11:26:50 (Show Source): You can put this solution on YOUR website! ``` Hi, the circumradius of triangle whose sides are 3,4 and 5? P = 12, s = 6 r = ```
 Rational-functions/619736: What is the sum of the solutions of |x -1| -4 = -21 solutions Answer 389762 by ewatrrr(10682)   on 2012-06-11 11:15:06 (Show Source): You can put this solution on YOUR website! ``` Hi, What is the sum of the solutions of |x -1| -4 = -2 |x -1| -4 = -2 |x -1| = 2 (x-1) = 2, x = 3 (x-1) = -2, x = -1 3 + -1 = 2 ```
 Rational-functions/619731: Solve the equation or formula for the indicated variable. S = 5r^2t; for t1 solutions Answer 389761 by ewatrrr(10682)   on 2012-06-11 11:12:58 (Show Source): You can put this solution on YOUR website! ``` Hi, did You mean or ||Solve the equation for ```
 Points-lines-and-rays/619725: What is the square feet inside a circumference of 438 feet? and What is the square feet inside a circumference of 502 feet?1 solutions Answer 389760 by ewatrrr(10682)   on 2012-06-11 11:05:59 (Show Source): You can put this solution on YOUR website! ``` Hi, What is the square feet inside a circumference of 438 feet? Similarily: ```
 Travel_Word_Problems/619728: How far can the members of a bicycling club ride out into the country at a speed of 12 mph and return over the same road at 8 mph if they travel a total of 10 hours? 1 solutions Answer 389759 by ewatrrr(10682)   on 2012-06-11 10:59:17 (Show Source): You can put this solution on YOUR website! ``` Hi, How far can the members of a bicycling club ride out into the country at a speed of 12 mph and return over the same road at 8 mph if they travel a total of 10 hours? D = rt or D/r = t x/12mph + x/8mph = 10hrs |Multiplying thru by 24 so as all denominators = 1 2x + 3x = 240 5x = 240 x = 48mi CHECKING our Answer*** 48mi/12mph + 48mi/8mph = 4hr + 6hr = 10hr ```
 Expressions-with-variables/619724: d^2 - 10d + 25 A.(d-5)^2 B. (d+5)^2 c. (d-5)(d+5) d. (d-25)(d-1) Thank you1 solutions Answer 389758 by ewatrrr(10682)   on 2012-06-11 10:53:31 (Show Source): You can put this solution on YOUR website! ``` Hi, d^2 - 10d + 25 (d-5)(d-5) = Check factoring Using FOIL F First terms d^2 O Outside terms -5d I Inside terms -5d L Last terms 25 ```
 Radicals/619696: What is the radical form of m^2.5? 1 solutions Answer 389757 by ewatrrr(10682)   on 2012-06-11 10:51:19 (Show Source): You can put this solution on YOUR website! ``` Hi, What is the radical form of: m^2.5 m^(5/2) ```
 Matrices-and-determiminant/619615: I want general solution for 6th degree polynomial. Thank You.1 solutions Answer 389752 by ewatrrr(10682)   on 2012-06-11 07:52:24 (Show Source): You can put this solution on YOUR website! ``` Hi, ```
 Matrices-and-determiminant/619641: Use cramer rule to solve .. x + y + z =12 x - y = 2 x - z = 4 1 solutions Answer 389751 by ewatrrr(10682)   on 2012-06-11 07:46:16 (Show Source): You can put this solution on YOUR website! ``` Hi, Previously Posted Solved by pluggable solver: Using Cramer's Rule to Solve Systems with 3 variables First let . This is the matrix formed by the coefficients of the given system of equations. Take note that the right hand values of the system are , , and and they are highlighted here: These values are important as they will be used to replace the columns of the matrix A. Now let's calculate the the determinant of the matrix A to get . To save space, I'm not showing the calculations for the determinant. However, if you need help with calculating the determinant of the matrix A, check out this solver. Notation note: denotes the determinant of the matrix A. --------------------------------------------------------- Now replace the first column of A (that corresponds to the variable 'x') with the values that form the right hand side of the system of equations. We will denote this new matrix (since we're replacing the 'x' column so to speak). Now compute the determinant of to get . Again, as a space saver, I didn't include the calculations of the determinant. Check out this solver to see how to find this determinant. To find the first solution, simply divide the determinant of by the determinant of to get: So the first solution is --------------------------------------------------------- We'll follow the same basic idea to find the other two solutions. Let's reset by letting again (this is the coefficient matrix). Now replace the second column of A (that corresponds to the variable 'y') with the values that form the right hand side of the system of equations. We will denote this new matrix (since we're replacing the 'y' column in a way). Now compute the determinant of to get . To find the second solution, divide the determinant of by the determinant of to get: So the second solution is --------------------------------------------------------- Let's reset again by letting which is the coefficient matrix. Replace the third column of A (that corresponds to the variable 'z') with the values that form the right hand side of the system of equations. We will denote this new matrix Now compute the determinant of to get . To find the third solution, divide the determinant of by the determinant of to get: So the third solution is ==================================================================================== Final Answer: So the three solutions are , , and giving the ordered triple (6, 4, 2) Note: there is a lot of work that is hidden in finding the determinants. Take a look at this 3x3 Determinant Solver to see how to get each determinant. ```
 Matrices-and-determiminant/619643: Use Cramer rule to solve. x + y + z = 12 x - y = 2 x - z = 41 solutions Answer 389750 by ewatrrr(10682)   on 2012-06-11 07:43:59 (Show Source): You can put this solution on YOUR website! ``` Hi, Solved by pluggable solver: Using Cramer's Rule to Solve Systems with 3 variables First let . This is the matrix formed by the coefficients of the given system of equations. Take note that the right hand values of the system are , , and and they are highlighted here: These values are important as they will be used to replace the columns of the matrix A. Now let's calculate the the determinant of the matrix A to get . To save space, I'm not showing the calculations for the determinant. However, if you need help with calculating the determinant of the matrix A, check out this solver. Notation note: denotes the determinant of the matrix A. --------------------------------------------------------- Now replace the first column of A (that corresponds to the variable 'x') with the values that form the right hand side of the system of equations. We will denote this new matrix (since we're replacing the 'x' column so to speak). Now compute the determinant of to get . Again, as a space saver, I didn't include the calculations of the determinant. Check out this solver to see how to find this determinant. To find the first solution, simply divide the determinant of by the determinant of to get: So the first solution is --------------------------------------------------------- We'll follow the same basic idea to find the other two solutions. Let's reset by letting again (this is the coefficient matrix). Now replace the second column of A (that corresponds to the variable 'y') with the values that form the right hand side of the system of equations. We will denote this new matrix (since we're replacing the 'y' column in a way). Now compute the determinant of to get . To find the second solution, divide the determinant of by the determinant of to get: So the second solution is --------------------------------------------------------- Let's reset again by letting which is the coefficient matrix. Replace the third column of A (that corresponds to the variable 'z') with the values that form the right hand side of the system of equations. We will denote this new matrix Now compute the determinant of to get . To find the third solution, divide the determinant of by the determinant of to get: So the third solution is ==================================================================================== Final Answer: So the three solutions are , , and giving the ordered triple (6, 4, 2) Note: there is a lot of work that is hidden in finding the determinants. Take a look at this 3x3 Determinant Solver to see how to get each determinant. ```
 Equations/619651: Solve the following problem. Round answer to two decimal places when necessary. E=120 I=3.5 R=E*I R=1 solutions Answer 389749 by ewatrrr(10682)   on 2012-06-11 07:40:39 (Show Source): You can put this solution on YOUR website! ``` Hi, E=120 I=3.5 = 7/2 R=E*I R= = = 420 ```
 Money_Word_Problems/619653: Solve the following problem. Round answer to two decimal places when necessary. I=240 w=I/3 A=I*W A=1 solutions Answer 389747 by ewatrrr(10682)   on 2012-06-11 07:37:35 (Show Source): You can put this solution on YOUR website! ``` Hi, I=240 w=I/3 A=I*W A= = 80 ```
 Polynomials-and-rational-expressions/619652: (125^2/3)1/2 if you could show steps like this that would be great! 4^3/2 * 4^5/2 4^3/2 + 5/2 4^8/2 4^4 256 That would be great 1 solutions Answer 389746 by ewatrrr(10682)   on 2012-06-11 07:36:07 (Show Source): You can put this solution on YOUR website! ``` Hi, (125^2/3)1/2 5^1 = 5 ```
 logarithm/619673: Write thhis expression as a single logarithm. 2(log(a)n - 4log(a)m) the logs have the a below them, couldn't figure out of to show them like that, but help in how to solve this problem would be very much appreciated. 1 solutions Answer 389744 by ewatrrr(10682)   on 2012-06-11 07:30:31 (Show Source): You can put this solution on YOUR website! ``` Hi ```
 Linear-systems/619661: 2x+y=12 what is the missing numbers in the ordered pairs ? 1 solutions Answer 389741 by ewatrrr(10682)   on 2012-06-11 07:27:14 (Show Source): You can put this solution on YOUR website! ``` Hi,previously Posted Use the equation 2x+y=12 what is the missing numbers in the ordered pairs ? Do not understand exactly Your Inquiry: a couple of ordered pairs would be the intercepts: (0,12) and ( 6,0) ```
 Linear-systems/619662: Use the equation 2x+y=12 what is the missing numbers in the ordered pairs ? 1 solutions Answer 389740 by ewatrrr(10682)   on 2012-06-11 07:26:12 (Show Source): You can put this solution on YOUR website! ``` Hi, Use the equation 2x+y=12 what is the missing numbers in the ordered pairs ? Do not understand exactly Your Inquiry: a couple of ordered pairs would be the intercepts: (0,12) and ( 6,0) ```
 Equations/619672: solve the equation. 2x/5 - x/3 = 5 1 solutions Answer 389738 by ewatrrr(10682)   on 2012-06-11 07:21:19 (Show Source): You can put this solution on YOUR website! ``` Hi, solve the equation |Multiplying thru by 15 so as all denominators = 1 6x - 5x = 75 x = 75 CHECKING our Answer*** 30-25=5 ```
 Money_Word_Problems/619655: Write this statement out as an equation and solve. If you multiply a number by 5 and then add 8, the result is 68. 1 solutions Answer 389737 by ewatrrr(10682)   on 2012-06-11 07:17:42 (Show Source): You can put this solution on YOUR website! ``` Hi, If you multiply a number by 5 and then add 8, the result is 68. Write as we Read: 5x + 8 = 68 5x = 60 x = 12 ```
 Length-and-distance/619663: find the length of the sides of tiangle whose vertices are (1,4),(-4,0),(3,-3).Classify the triangle1 solutions Answer 389736 by ewatrrr(10682)   on 2012-06-11 07:14:59 (Show Source): You can put this solution on YOUR website! ``` Hi, find the length of the sides of tiangle whose vertices are (1,4), (-4,0) D = sqrt(4^2 + 5^2) = sqrt(41) (3,-3 D = sqrt(3^2 + -7^2) = sqrt(58) longest side C (1,4), D = sqrt(-7^2 + 2^2) = sqrt(53) 41 + 53 = 94 > 58 If A, B and C are the sides of a triangle where C is the longest side, then we can say the following i) If A^2+B^2 = C^2 is true, then we have a right triangle ii) If A^2+B^2 > C^2 is the case, then we have an acute triangle.***** iii) If A^2+B^2 < C^2, then we have an obtuse triangle. ```
 Age_Word_Problems/619665: Percy is 47 years old and his son Zachary is 16 years old. In how many years' time will Percy be twice Zachary's age?1 solutions Answer 389732 by ewatrrr(10682)   on 2012-06-11 07:05:20 (Show Source): You can put this solution on YOUR website! ``` Hi, Percy is 47 years old and his son Zachary is 16 years old. In how many years' time will Percy be twice Zachary's age? 47 + x = 2(16+x) 47 + x = 32 + 2x 15yrs = x ```
 Rectangles/619667: if width of a reactangular field is 44 ft and height of a rectangular field is 39 ft,then area of a reactangular field is ?1 solutions Answer 389731 by ewatrrr(10682)   on 2012-06-11 07:01:51 (Show Source): You can put this solution on YOUR website! ``` Hi, if width of a reactangular field is 44 ft and height of a rectangular field is 39 ft, then area of a reactangular field is ? A = 44ft· 39ft = 1716 ft^2 ```
 Money_Word_Problems/619668: Sales at a local ice cream shop went up 60% in 5 years. If 37,000 ice cream cones were sold in the current year, find the number of ice cream cones sold 5 years ago.1 solutions Answer 389730 by ewatrrr(10682)   on 2012-06-11 06:59:53 (Show Source): You can put this solution on YOUR website! ``` Hi,re TY..Yes! typo on the extra zero. Note highlighted: amount + 60% increase = 37000. Sales at a local ice cream shop went up 60% in 5 years. 37,000 ice cream cones sold in the current year... x(1.60) = 37000 x = 37000/(1.60) x = 23,125, the number of ice cream cones sold 5 years ago. ```
 logarithm/619671: How can I calculate logbasex(logbase5(x+5))=01 solutions Answer 389729 by ewatrrr(10682)   on 2012-06-11 06:56:13 (Show Source): You can put this solution on YOUR website! ``` Hi,Re TY..sry misunderstood Your inquiry... Good work! x^0 = 5 = x+5 0 = x ```
 Money_Word_Problems/619669: There are 10 more sophmores than juniors in an algebra class. If there are 80 students in this class, find the number of sophmores and the numbers of juniors in the class.1 solutions Answer 389728 by ewatrrr(10682)   on 2012-06-11 06:53:29 (Show Source): You can put this solution on YOUR website! ``` Hi, There are 10 more sophmores than the number of juniorsin an algebra class. 80 students in this class (x+10)+ x = 80 2x + 10 = 80 2x = 70 x = 35, juniors and 45 sophmores CHECKING our Answer*** 35 + 45 = 80 ```
 Quadratic-relations-and-conic-sections/619477: I have the following equation: I need to identify the vertices and foci of the hyperbola. I also need to show my work. (y+5)^2/36 - (x+2)^2/25 =1 thank you1 solutions Answer 389681 by ewatrrr(10682)   on 2012-06-10 18:41:37 (Show Source): You can put this solution on YOUR website! ``` Hi, Note:Standard Form of an Equation of an Hyperbola opening up and down is: where Pt(h,k) is a center with vertices 'b' units up and down from center and foci from center along x = h (y+5)^2/36 - (x+2)^2/25 =1 C(-5,-2) V(,-5,-8) & V(-5,4), F(-5, -2±) See below descriptions of various conics Standard Form of an Equation of a Circle is where Pt(h,k) is the center and r is the radius Standard Form of an Equation of an Ellipse is where Pt(h,k) is the center. (a positioned to correspond with major axis) a and b are the respective vertices distances from center and ±are the foci distances from center: a > b Standard Form of an Equation of an Hyperbola opening right and left is: where Pt(h,k) is a center with vertices 'a' units right and left of center and foci {{sqrt(a^2+b^2) from center along y = k. Standard Form of an Equation of an Hyperbola opening up and down is: where Pt(h,k) is a center with vertices 'b' units up and down from center along x = h. the vertex form of a parabola opening up or down, where(h,k) is the vertex. The standard form is , where the focus is (h,k + p) the vertex form of a parabola opening right or left, where(h,k) is the vertex. The standard form is , where the focus is (h +p,k ) ```
 Subset/619442: If x1 = - 2; x2 = 5; y1 = 3; y2 = - 7, find the value of: (y2 - y1) / (x2 - x1) a. 10 / 7; b. - 10 / 3; c. 4 / 9; d. - 10 / 7 1 solutions Answer 389661 by ewatrrr(10682)   on 2012-06-10 15:17:13 (Show Source): You can put this solution on YOUR website! ``` Hi, If x1 = - 2; x2 = 5; y1 = 3; y2 = - 7, (5,-7) and (-2,3) = -10/7 ```
 Linear-equations/619449: Solve the following system by substitution. x=7y+24 x=(7/4)y My work: (7/4)y = 7y+24 multiply each side by 4 7y=28y+96 divide by 7 y= 4y+(96/7) move the Y and 96/7 to the other side -(96/7) = 3y I've multiplied 7 on both sides and then divided -672 = 21y which equals to -32 then input the -32 like this x=7(-32)+24 x=-200 but on the second equation it does not match x=(7/4)(-32) x=-56 and here are my choices: A. The solution set is {( _, _)} (Type an ordered pair) B. The system has dependent equations. The solution set is {x,y)| _____} c. The system is inconsisten. The solution set is undefined.1 solutions Answer 389658 by ewatrrr(10682)   on 2012-06-10 15:09:28 (Show Source): You can put this solution on YOUR website! ``` Hi, x=7y+24 x=(7/4)y My work: (7/4)y = 7y+24 multiply each side by 4 7y=28y+96 divide by 7 y= 4y+(96/7) move the Y and 96/7 to the other side Yes! -(96/7) = 3y and y = -32/7 and x = (7/4)(-32/7) = -8 (-8, -32/7) Independent system, one solution CHECKING our Answer*** -8 = 7(-32/7) + 24 = -8 A consistent system has at least one solution. An inconsistent system has no solutions. An independent system has exactly one solution. **** Andependent system has infinitely many solutions. ```
 Polynomials-and-rational-expressions/619445: 424 = x^2 + 36x1 solutions Answer 389655 by ewatrrr(10682)   on 2012-06-10 15:00:40 (Show Source): You can put this solution on YOUR website! ``` Hi, Re: TY, this is a trinomial (3 different type of terms) 424 = x^2 + 36x x^2 + 36x- 424 = 0 x is -45.35, 9.35 (rounded to 2 decimal points) ```