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# Recent problems solved by 'ewatrrr'

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 Permutations/636253: What is the Five digIt nUmber we can make using the digits 5,4,0,8 ? 1 solutions Answer 400872 by ewatrrr(10682)   on 2012-08-10 06:37:17 (Show Source): You can put this solution on YOUR website! ``` Hi, 5 - digit numbers using the 4 digits: 5, 4 , 0, 8 (first digit cannot be zero) There are = 768 of them ```
 Graphs/636262: find the x- and y-intercepts of the graph of the equatiion. y=x-31 solutions Answer 400869 by ewatrrr(10682)   on 2012-08-10 06:29:39 (Show Source): You can put this solution on YOUR website! ``` Hi, y= x-3 line: slope m = 1 x-intercepts ( 3,0) || when y = 0 y-intercepts (0,-3) ```
 Graphs/636263: find the x- and y-intercepts of the graph of the equation. y=x^2-91 solutions Answer 400868 by ewatrrr(10682)   on 2012-08-10 06:27:06 (Show Source): You can put this solution on YOUR website! ``` Hi, y=x^2-9 parabola: V(0,-9), line of symmetry x = 0(y-axis) x-intercepts (± 3,0) || when y = 0 y-intercepts (0,-9) ```
 Graphs/636264: find the x- and y-intercepts of the graph of the equation. x^2+y^2=41 solutions Answer 400867 by ewatrrr(10682)   on 2012-08-10 06:23:14 (Show Source): You can put this solution on YOUR website! ``` Hi, x^2+y^2=4 Circle: C(0,0), r = 2 x-intercepts (± 2,0) y-intercepts (0,± 2) ```
 Graphs/636142: You might want to draw up a number line and then place two points on that line. Multiply each number by -1 and see where that new point ends up. Look at the relationship between the original points, and compare that with the relationship of the last two points.1 solutions Answer 400774 by ewatrrr(10682)   on 2012-08-09 16:22:57 (Show Source): You can put this solution on YOUR website! ``` Hi, 2 and 7 placed on the line 2(-1) = -2 and 7(-1)= -7 also placed on the line Original numbers are on the opposite side of 0, but the same distance from 0 ```
 percentage/636119: A TV originally priced at \$2,400 is on sale for 20% off. What is the sale price? 1 solutions Answer 400773 by ewatrrr(10682)   on 2012-08-09 16:17:20 (Show Source): You can put this solution on YOUR website! ``` Hi, A TV originally priced at \$2,400 is on sale for 20% off. (paying 80%) What is the sale price = \$1920 ```
 Triangles/636139: Hello im a bit itchy about this question : Three sides of a triangle are are 2, 4, and 5. the two smallest size of a similar triangle are 6 and 12. find the measure of the missing side. Do I just do this: 6^2+12^2= c^2 and solve? But then what was the point of the other triangle and it's side? Thanks~ 1 solutions Answer 400772 by ewatrrr(10682)   on 2012-08-09 16:12:53 (Show Source): You can put this solution on YOUR website! ``` Hi, Three sides of a triangle are are 2, 4, and 5 the two smallest size of a similar triangle are 6 and 12 and , ```
 Age_Word_Problems/636138: alisha brother is 6 yearsyounger than alisha.alisha is 5 years younger thanher sister,alisha brother is 10 years old what is the equation 1 solutions Answer 400770 by ewatrrr(10682)   on 2012-08-09 16:09:20 (Show Source): You can put this solution on YOUR website! ``` Hi, Note: Important to read entire question before planning a way of solving. alisha brother is 10 years old alisha brother is 6 years younger than alisha: alisha is 16 alisha is 5 years younger than her sister: sister is 21 ```
 Linear-systems/636130: How do I do a 3 variable equation in Linear system. Example: 3x + 3y + 6z = 27 along with two other 3 variable equations.1 solutions Answer 400769 by ewatrrr(10682)   on 2012-08-09 16:05:25 (Show Source): You can put this solution on YOUR website! ``` Hi, 3x+3y+6z=27 x-y+5z=-1 5x+y+z=-2 using Crame'sr rule is one way of solving 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 (-23/10, 77/10, 9/5) 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/636122: solve the following system of equations using matrices: x+y+z=-9 x-y+5z=-19 5x+y+z=-291 solutions Answer 400768 by ewatrrr(10682)   on 2012-08-09 16:01:03 (Show Source): You can put this solution on YOUR website! ``` Hi, x+y+z=-9 x-y+5z=-19 5x+y+z=-29 x = -5, y = -1, z = -3 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 (-5, -1, -3) 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. ```
 test/636137: x+y=8 x+3.25y=171 solutions Answer 400766 by ewatrrr(10682)   on 2012-08-09 15:57:43 (Show Source): You can put this solution on YOUR website! ``` Hi, x +y = 8 x +3.25y = 17 | Subtracting the 2nd EQ from 1st EQ to eliminate x -2.25y = - 9 y = 4 and x = 4 ```
 Equations/636096: 3(x+5)-2(y-1)=6 x+4(y+3)=131 solutions Answer 400764 by ewatrrr(10682)   on 2012-08-09 15:53:59 (Show Source): You can put this solution on YOUR website! ``` Hi, 3(x+5)-2(y-1)=6 x+4(y+3)=13 3x+15-2y+2=6 x+4y+ 12=13 3x-2y = -11 |multiplying 1st EQ by 2 and adding to the second x+4y = 1 7x = -21 x = -3 and y = 1 ```
 Travel_Word_Problems/636125: If an object is thrown upward with an initial velocity of 112ft/sec, it's height after t sec is given by h=112t-16t^2. how long will it take for the object to reach it's maximum height?1 solutions Answer 400759 by ewatrrr(10682)   on 2012-08-09 15:42:28 (Show Source): You can put this solution on YOUR website! ``` Hi, h= -16t^ + 112t Note: h = -16(t-7/2)^2 + 16*49/4 h = -16(t-7/2)^2 + 196 Note: vertex form of a Parabola opening up(a>0) or down(a<0), where(h,k) is the vertex Parabola opening Downward V(3.5,196) how long will it take for the object to reach it's maximum height? will take 3.5 sec to reach max height of 196 ft ```
 Probability-and-statistics/636114: A pizza place offers 3 different cheeses and 8 different toppings. In how many ways can a pizza be made with 1 cheese and 3 toppings?1 solutions Answer 400757 by ewatrrr(10682)   on 2012-08-09 15:35:20 (Show Source): You can put this solution on YOUR website! ``` Hi, A pizza place offers 3 different cheeses and 8 different toppings. In how many ways can a pizza be made with 1 cheese and 3 toppings? WAYS ```
 Probability-and-statistics/636115: A delicatessen offers 4 different breads, 4 cheeses, and 6 different meats. In how many ways can a sandwich be made with 1 bread,1 cheese and 2 meats?1 solutions Answer 400751 by ewatrrr(10682)   on 2012-08-09 15:19:32 (Show Source): You can put this solution on YOUR website! ``` Hi, A delicatessen offers 4 different breads, 4 cheeses, and 6 different meats. In how many ways can a sandwich be made with 1 bread,1 cheese and 2 meats? ```
 Quadratic-relations-and-conic-sections/636108: Write the equation of a circle that has the center on the x-axis, a radius of 1, and passes through the point (((square root of 2)/2),((square root of 2)/2)).1 solutions Answer 400749 by ewatrrr(10682)   on 2012-08-09 15:15:34 (Show Source): You can put this solution on YOUR website! ``` Hi, Write the equation of a circle that has the center on the x-axis, a radius of 1, and passes through the point (,) (x,0) D = = 1 , -x =± , x = ```
 Quadratic-relations-and-conic-sections/636106: Write the equation of a circle in which the endpoints of the diameter are at (-2,-3) and at (4,5).1 solutions Answer 400742 by ewatrrr(10682)   on 2012-08-09 14:54:17 (Show Source): You can put this solution on YOUR website! ``` Hi, Write the equation of a circle in which the endpoints of the diameter are at (-2,-3) and at (4,5) D = r = 5 M = (2/2, 2/2) = (1,1) the center ```
 Quadratic_Equations/636080: Write an equation of a line in the form y=mx+b that passes through the points (-4, -1) and (2, -4).1 solutions Answer 400706 by ewatrrr(10682)   on 2012-08-09 12:29:56 (Show Source): You can put this solution on YOUR website! ``` Hi, Using the standard slope-intercept form for an equation of a line y = mx + b where m is the slope and b the y-intercept. Line thatpasses through the points (-4, -1) and (2, -4) m = 3/-6 = -1/2 y = (-1/2)x + b |Using ordered pair (x,y): (2,-4) to solve for b -2 = b y = (-1/2)x - 2 ```
 Miscellaneous_Word_Problems/636068: The admission fee at a county fair is \$1.50 for children and \$4.00 for adults. On a particular day, 2200 people enter the fair and \$5050 is collected. How many children and how many adults attended? 1 solutions Answer 400703 by ewatrrr(10682)   on 2012-08-09 12:24:32 (Show Source): You can put this solution on YOUR website! ``` Hi, The admission fee at a county fair is \$1.50 for children and \$4.00 for adults. On a particular day, 2200 people enter the fair and \$5050 is collected. How many children and how many adults attended? Question states*** y + x = 2200 0r 4.00y + 1.50x = \$5050 4y + 1.5(2200-y) = 5050 2.5y = 1750 y = 700 , the number of adult tickets, children 1500 and... ```
 logarithm/636067: Find the exact value log[27](6)+log[27](18)-log[27](4) 1 solutions Answer 400700 by ewatrrr(10682)   on 2012-08-09 12:09:18 (Show Source): You can put this solution on YOUR website! ``` Hi, log[27](6)+log[27](18)-log[27](4) = ```
 Quadratic_Equations/636066: p-2the square root of p then =8 the answer should be 16. i cleared the p and got rid of the -2 and ended up with 2p=64-16p+p^2. i ended up with p=9+sqrt17, p=9-sqrt17. it says to check the answer it is supposed to ended up with one answer.1 solutions Answer 400699 by ewatrrr(10682)   on 2012-08-09 12:06:05 (Show Source): You can put this solution on YOUR website! ``` Hi, let x^2 = p (x-4)(x+2) = 0 x = 4 ⇒ p = x^2 = 16 and... Note: x = -2( p = 4) is an extraneous solution as 4 -4 - 8 ≠ 0 ```
 Exponents/636065: I was having trouble with this problem. I need to write it using only positive exponents. Here is the problem: m^4 multiplied by n^-2. Thanks!1 solutions Answer 400698 by ewatrrr(10682)   on 2012-08-09 11:56:31 (Show Source): You can put this solution on YOUR website! ``` Hi, Note: ```
 Polynomials-and-rational-expressions/636061: Multiply and simplify by factoring. Assume that all expressions under radicals represent non-negative numbers 3 3 √y^10 √16y^11 (Simplify, type in radical form)1 solutions Answer 400696 by ewatrrr(10682)   on 2012-08-09 11:53:29 (Show Source): You can put this solution on YOUR website! ``` Hi, ```
 Expressions-with-variables/636057: Can you help me with this problem? Consider the funcetion f(x)=3x^-24x-3 a. Is it minimum or maximun b. What is the value? c. The domain of f is? d. The range of f is? Please help. Thank you1 solutions Answer 400693 by ewatrrr(10682)   on 2012-08-09 11:45:05 (Show Source): You can put this solution on YOUR website! ``` Hi, Note: the vertex form of a Parabola opening up(a>0) or down(a<0), where(h,k) is the vertex Assume you meant: parabola opening Upward a = 3 > 0, Vmin(4,-51) a. Is f(4) a minimum or maximun b. What is the value? -51 c. The domain of f is? x is any real number d. The range of f is? f(x) > -51 ```
 Evaluation_Word_Problems/636051: Find the discriminant and determine the number of real solutions then solve. x^2-2x+10=0 & Simplify: 7+2i/4+i 1 solutions Answer 400691 by ewatrrr(10682)   on 2012-08-09 11:24:11 (Show Source): You can put this solution on YOUR website! ``` Hi, ax^2 +bx + c = 0 x^2-2x+10=0 discriminant || i^2 = -1 = ± 6i , NO real solutions, Note: parabola will NOT cross x-axis Simplify: || multiplying both numerator and denominator by conjugate (4-i). Note: i^2 = -1 ```
 Coordinate-system/636044: I need assistance with writing point-slope form for an equation with the slope and one point already given. one example is "what is the point-slope form of a line through (4,-4) with a slope of -9/4?" I don't even know how to begin solving this problem. I practically need a lesson on how to do this kind of thing in general.1 solutions Answer 400687 by ewatrrr(10682)   on 2012-08-09 11:08:30 (Show Source): You can put this solution on YOUR website! ``` Hi, Using the standard slope-intercept form for an equation of a line y = mx + b where m is the slope and b the y-intercept. line through (4,-4) with a slope m = -9/4 |Using ordered pair (x,y): (4,-4) to solve for b 5 = b y = (-9/4)x + 5 (Note: line slants to the left (back 4 Up 9) from point(4,-4) using point-slope form as the directions state || which also says: y = (-9/4)x + 5) ```
 Linear-equations/636032: Explain, in complete sentences, whether or not the expression x2 + 24x + 144 fits one of the special patterns. If so, which one? Explain how the polynomial is factored. Provide the factors.1 solutions Answer 400685 by ewatrrr(10682)   on 2012-08-09 10:47:46 (Show Source): You can put this solution on YOUR website! ``` Hi, If the following can be factored... What 2 numbers have a product of 144 and sum of 24??? F First terms O Outside terms I Inside terms + x = 24x L Last terms another: What 2 numbers have a product of 9 and sum of 6??? F First terms O Outside terms I Inside terms + = 6x L Last terms ```
 Quadratic_Equations/635988: The hypotenuse of a right triangle is 4 cm less than twice as long as one of the other side. If the third side is 16 cm long, find the length of the hypotenuse.1 solutions Answer 400684 by ewatrrr(10682)   on 2012-08-09 08:59:14 (Show Source): You can put this solution on YOUR website! ``` Hi, Previously Posted The hypotenuse of a right triangle is 4cm less than twice as long as one of the other side If the third side is 16 cm long, find the length of the hypotenuse. Applying the Pythagorean Theorem 16^2 + x^2 = y^2 | y = (2x-4) 256 + x^2 = 4x^2 - 16x + 16 3x^2 -16x - 240 = 0 x = 12cm, the other leg (throwing out negative solution for unit measure) Hypotenuse is 20cm and... ```
 Pythagorean-theorem/636003: The hypotenuse of a right triangle is 4cm less than twice as long as one of the other side. If the third side is 16 cm long, find the length of the hypotenuse.1 solutions Answer 400683 by ewatrrr(10682)   on 2012-08-09 08:56:10 (Show Source): You can put this solution on YOUR website! ``` Hi, The hypotenuse of a right triangle is 4cm less than twice as long as one of the other side If the third side is 16 cm long, find the length of the hypotenuse. Applying the Pythagorean Theorem 16^2 + x^2 = y^2 | 256 + x^2 = 4x^2 - 16x + 16 3x^2 -16x - 240 = 0 x = 12cm, the other leg (throwing out negative solution for unit measure) Hypotenuse is 20cm and... ```
 Linear_Equations_And_Systems_Word_Problems/636010: A test consists of multiple choice questions worth 3 points and essay questions worth 5 points. The test has 17 questions that are worth a total of 65 points. Use a model to determine how many multiple choice questions are on the test 1 solutions Answer 400682 by ewatrrr(10682)   on 2012-08-09 08:45:11 (Show Source): You can put this solution on YOUR website! ``` Hi, A test consists of multiple choice questions worth 3 points and essay questions worth 5 points. The test has 17 questions that are worth a total of 65 points. 3x + 5y = 65 | x+y = 17 0r y = 17-x 3x + 5(17-x) = 65 -2x = -20 x = 10, number of multiple choice questons, 7 essay questions and... ```
 Circles/635995: A circle with the equation (x + 4)2 + (y - 3)2 = 9 is reflected over the line y = -1. What is the equation of the image?1 solutions Answer 400680 by ewatrrr(10682)   on 2012-08-09 08:37:28 (Show Source): You can put this solution on YOUR website! ``` Hi, A circle with the equation (x + 4)2 + (y - 3)2 = 9 is reflected over the line y = -1. ```