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# Recent problems solved by 'ewatrrr'

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 Matrices-and-determiminant/411588: Find X, Y, Z: 2X-3Y+ Z=5 X+3Y+8Z=22 3X- Y+2Z=12 1 solutions Answer 289287 by ewatrrr(10682)   on 2011-02-20 11:00:13 (Show Source): You can put this solution on YOUR website! ``` Hi D = = -48 D[x]= = -144 D[y]= = -48 D[z] ==-96 x = 3 and y = 1 and z = 2 ```
 Numbers_Word_Problems/411568: The product of two consecutive odd integers is seven thousand, fifty-five. What are the integers?1 solutions Answer 289282 by ewatrrr(10682)   on 2011-02-20 10:15:29 (Show Source): You can put this solution on YOUR website! ``` Hi Let x and (x+2) represent the two consecutive odd integers Question states*** x(x+2) = 7055 Solving for x x^2 + 2x - 7055 = 0 factoring (x+85)(x-83)=0 |Note:SUM of the inner product(85x) and the outer product(-83x) = 2x (x+85)=0 x = -85 |the two consecutive odd integers being -85,-83 (x-83)=0 x = 83 |the two consecutive odd integers being 83,85 CHECKING our Answer(s)*** -85*-83 = 83*85 = 7055 ```
 Quadratic-relations-and-conic-sections/411564: Please help me solve this equations,write the equations of the following ellipse in their cannonical forms and hence, determine their Foci and vertices: 1) 4x^2+5y^2-24x-20y+36=0 2) x^2+3y^2+2x-24y+46=01 solutions Answer 289281 by ewatrrr(10682)   on 2011-02-20 09:55:43 (Show Source): You can put this solution on YOUR website! ``` Hi Ellipses: 1) 4x^2+5y^2-24x-20y+36=0 4(x^2-6x) + 5(y^2-4y) +36 = 0 |completing squares 4[(x-3)^2 -9] + 5[(y-2)^2 -4] + 36 = 0 4(x-3)^2 -36 + 5(y-2)^2 -20 + 36 = 0 4(x-3)^2 + 5(y-2)^2 = 20 C(3,2) V(3,4)&V(3,0) and V(3+sqrt(5),2)&V(3-sqrt(5),2) sqrt(5-4)= 1 f(4,2) and f(2,2) 2) x^2+3y^2+2x-24y+46=0 |completing squares (x+1)^2 -1 +3[(y-4)^2 -16] + 46 = 0 (x+1)^2 +3(y-4)^2 -49 + 46 = 0 C(-1,4) V(-1,5)&V(-1,3) and V(-1+sqrt(3),4)&V(-1-sqrt(3),4) sqrt(3-1)=sqrt(2) f(-1 +sqrt(2),4) and f(-1-sqrt(2),4) ```
 Trigonometry-basics/411563: If the roots of quadratic equation are -7 and -5, write the equation in ax^2 + bx + c = 0 form. Here is what I've so far: x^2 + 12x + 35 = 0...then I don't know what to do next. Can you please help! Thank you so much!1 solutions Answer 289280 by ewatrrr(10682)   on 2011-02-20 09:20:23 (Show Source): You can put this solution on YOUR website! ``` Hi writing the equation in ax^2 + bx + c = 0 form. roots of quadratic equation are -7 and -5 (x+7)(x+5) = 0 x^2 + 12x + 35 = 0 |Yes! You have completed the instructions! ```
 Miscellaneous_Word_Problems/411552: Mark is 8 years younger than Jerry. In 10 yrs,he will be 10 yrs more than 1/2 as old as Jerry. Find their PRESENT ages.1 solutions Answer 289278 by ewatrrr(10682)   on 2011-02-20 09:08:07 (Show Source): You can put this solution on YOUR website! ``` Hi Mark is 8 years younger than Jerry Let x and (x-8) represent Jerry and Mark's ages respectively Question states*** In 10yrs... (x-8) + 10 = 1/2(x+10)+10 Solving for x (x-8) + 10 = 1/2*x + 5 +10 x/2 = 13 x = 26yr, Mark's age NOW. 'Jerry' is now 18yr. (26-8) CHECKING our Answer*** 28 = 1/2(36) + 10 = 18 + 10 ```
 Trigonometry-basics/411559: Find the solution set in a +bi form: 6x^2 + 4x +1 =0 I tried and here is what I have so far then I'm lost. Use the quadratic equation. The constants are a=6, b=4 and c=1. x = -b +/-sqrt(b^2-4ac)]/12 Thank you so much1 solutions Answer 289276 by ewatrrr(10682)   on 2011-02-20 08:54:26 (Show Source): You can put this solution on YOUR website! ``` Hi Finding the solution set in a +bi form: 6x^2 + 4x +1 =0 a=6, b=4 and c=1 |Yes! x = -b ± sqrt(b^2-4ac)]/12 |Yes! Finish substituting for b, b^2 and 4ac x = -4 ± sqrt(16-24)]/12 x = -4 ± sqrt(-8)]/12 x = -4 ± sqrt(-1*4*2)]/12 |sqrt(-1) = i x = -4 ± 2isqrt(2)]/12 x = -1/3 ± (1/6)isqrt(2) x = -1/3 + (1/6)isqrt(2) x = -1/3 - (1/6)isqrt(2) ```
 Human-and-algebraic-language/411557: A market research company finds that a the price of p=\$20, they would sell x=42 tiles each month. If they lower the price to p=\$10, then more people would purchase the tiles, and they can expect to sell x=52 tiles in a month's time. find the equation of the line for the demand equation. write the answer in the form p=mx +b. Hint: write an equation using points in the form (x,p).1 solutions Answer 289272 by ewatrrr(10682)   on 2011-02-20 08:36:42 (Show Source): You can put this solution on YOUR website! ``` Hi (42,20) (52,10) m = -10/10 = -1 p = -x + b |using ordered pair (42,20) to solve for x 20 = -42 + b 62 = b p = -x + 62 ```
 Quadratic_Equations/411341: Solve using the quadratic formula: 2x^2-11x-2=01 solutions Answer 289170 by ewatrrr(10682)   on 2011-02-19 14:17:28 (Show Source): You can put this solution on YOUR website! ``` Hi Solving using the quadratic formula: 2x^2-11x-2=0 ```
 logarithm/411324: please anyone help me with this question i have submitted a couple of times i just cant figure it out How do you simplify [5 x 4^(3n+1)] divided by [20 x 8^(2n)]1 solutions Answer 289169 by ewatrrr(10682)   on 2011-02-19 14:12:44 (Show Source): You can put this solution on YOUR website! ``` Hi = 20/20 = 1 ```
 Travel_Word_Problems/411334: A submarine let Hawaii two hours before an aircraft carrier. The vessels traveled in opposite directions. The aircraft carrier traveled at 25 mph for nine hours. After this time the vessels were 280 miles apart. Find the submarines speed.1 solutions Answer 289163 by ewatrrr(10682)   on 2011-02-19 13:51:37 (Show Source): You can put this solution on YOUR website! ``` Hi D = r*t Let x represent the submarines speed. Question states*** 280mi apart after traveling opposite directions 11hr*x + 25mph*9hr = 280mi |note:submarine left Hawaii two hours before an aircraft carrier Solving for x 11hrx = 55mi x = 5mph, the submarine's speed CHECKING our Answer*** 55mi + 225mi = 280mi ```
 Miscellaneous_Word_Problems/411336: Please help me solve this problem. I get 12.5 but I need to break this down so I understand it. I am not sure if I am right how I am arriving at the answer. 7 times the opposite of a number is 50 less than the product of 3 and the number. Thank you.1 solutions Answer 289161 by ewatrrr(10682)   on 2011-02-19 13:44:20 (Show Source): You can put this solution on YOUR website! ``` Hi Let x represent the number Question states*** 7*(-x) = 3x-50 Solving for x 50 = 10x x = 5 CHECKING our Answer*** -35 = 15-50 = 35 ```
 Linear-equations/411331: compute the discriminant. Then determine the number and type of solutions for the given equations 4x^2-8x+9=0 1 solutions Answer 289160 by ewatrrr(10682)   on 2011-02-19 13:42:05 (Show Source): You can put this solution on YOUR website! ``` Hi Finding the discriminant: b^2 - 4ac (ax^2 + bx + c = 0) 4x^2-8x+9=0 8^2 - 4*4*9 = 64 -144 = -80 Two imaginary roots ```
 Linear-equations/411330: solve: 2x^2+x=31 solutions Answer 289159 by ewatrrr(10682)   on 2011-02-19 13:37:10 (Show Source): You can put this solution on YOUR website! ``` Hi solving*** 2x^2+x = 3 2x^2 + x-3 = 0 factoring (2x+3)(x-1)=0 |Note:SUM of the inner product(3x) and the outer product(-2x) =x (2x+3)=0 x = -3/2 (x-1)=0 x = 1 CHECKING our Answer(s)*** 2*9/4 -3/2 = 18/4 - 6/4 = 12/4 = 0 2 + 1 = 3 ```
 Age_Word_Problems/411328: what is the total or fromula to use when you want to add each number up to 150?1 solutions Answer 289158 by ewatrrr(10682)   on 2011-02-19 13:31:16 (Show Source): You can put this solution on YOUR website! ``` Hi add each number up to 150. 'If' it is whole numbers from 1 to 150 you wish to add: = 75*151 = 11,325 ```
 Trigonometry-basics/411320: Determine the sum and product of the roots of 3y^2– 2y + 12 = 0 I need your help please. Thank you very much1 solutions Answer 289157 by ewatrrr(10682)   on 2011-02-19 13:25:34 (Show Source): You can put this solution on YOUR website! ``` Hi finding the roots using the quadratic formula 3y^2– 2y + 12 = 0 x = -.5 + 2isqrt(35)/6 x = -.5 - 2isqrt(35)/6 Sum of the roots = -1 Product: .25 + 4*35/36 Note i^2 = -1 ```
 Linear-systems/411312: 1.separate 46 into two parts so that one part is more than twice as much as the first part. find each part. 1 solutions Answer 289156 by ewatrrr(10682)   on 2011-02-19 13:10:25 (Show Source): You can put this solution on YOUR website! ``` Hi one part is more than twice as much as the first part Let x and 2x represent the parts Question states*** x + 2x = 46 Solving for x 3x = 46 x = 46/3. the parts are 46/3 and 92/3 CHECKING our Answer*** 46/3 + 92/3 = 138/3 = 46 ```
 Polynomials-and-rational-expressions/411311: Factor 30c^2+19c-631 solutions Answer 289154 by ewatrrr(10682)   on 2011-02-19 13:04:18 (Show Source): You can put this solution on YOUR website! ``` Hi Factoring 30c^2+19c-63 (5c+9)(6c-7) |Note:SUM of the inner product(54c) and the outer product(-35c) = 19c ```
 Travel_Word_Problems/411310: 2 cars leave pima county traveling in opposite directions. One car travels @80mph and other @ 54mph. in how many hour will they be 938 miles apart?1 solutions Answer 289153 by ewatrrr(10682)   on 2011-02-19 13:00:50 (Show Source): You can put this solution on YOUR website! ``` Hi D = r*t 80mph*t + 54mpn*t = 938mi t = 938mi/134mph t = 7hrs CHECKING our Answer*** 80mph*7hr + 54mpn*7hr = 560mi + 378mi = 938mi ```
 Numeric_Fractions/411304: I am having problems solving fractional equations.This is the problem i'm working on.5x/2+3=6. This is what i have done so far,5(5x+3)=2x,25x+15=2x,25x+2x=15,27x=15, x=15/27. However the answer is one and one-fifth. Can you please help me. thanks bob1 solutions Answer 289152 by ewatrrr(10682)   on 2011-02-19 12:57:21 (Show Source): You can put this solution on YOUR website! ``` Hi |multiplying thru by 2 so as all denominators= 1 5x + 6 = 12 5x = 6 x =6/5 OR 1 1/5 ```
 Polynomials-and-rational-expressions/411275: I solved this quadratic equation and wanted to make sure I wrote the answer correctly. Would you check it for me? 6p^2+5p+10=0 -5+-sqrt((5)^2-4(6)(10))/2(6) -5+-sqrt(25-240)/(12) -5+-sqrt(-215/12) -5+-sqrt(5(43))i/(12) -5+- i sqrt(5(43))/(12) 1 solutions Answer 289151 by ewatrrr(10682)   on 2011-02-19 12:51:18 (Show Source): You can put this solution on YOUR website! ``` Hi 6p^2+5p+10=0 may list as follows to meet requirements there may be for Your classroom ```
 Equations/411301: Solving by substitution or elimination:I need an ordered pair for the answer 2x+y=6 x-y=3 1 solutions Answer 289150 by ewatrrr(10682)   on 2011-02-19 12:35:30 (Show Source): You can put this solution on YOUR website! ``` Hi Solving by substitution x-y=3 OR y = x-3 2x+y=6 2x +(x-3) = 6 3x = 9 x = 3 and y = 0 (3-3) CHECKING our Answer*** 2x + y = 6 6 + 0 = 6 ```
 Linear-equations/410942: WITE AN EQUATION OF THE LINE THAT PASSES THROUGH(0,5) AND (1,3).1 solutions Answer 289149 by ewatrrr(10682)   on 2011-02-19 12:30:51 (Show Source): You can put this solution on YOUR website! ``` Hi Using the point-slope formula, (0,5) AND (1,3) m = 2/-1 = -2 y = -2x + b |using ordered pair Pt(0,5) to solve for b 5 = b y = -2x+5 ```
 Linear-equations/411292: solve by any method of your choice: 2x^2-3x=201 solutions Answer 289148 by ewatrrr(10682)   on 2011-02-19 12:25:25 (Show Source): You can put this solution on YOUR website! ``` Hi 2x^2-3x=20 2x^2-3x-20=0 x = (3 ± 13)/4 x = 4 x = -10/4 = -5/2 CHECKING our Answer*** (x-4)(x+5/2) = 0 2x^2 -3x-20 = 0 ```
 Expressions-with-variables/411267: hi, the length of a rectangle is 6 more than its witdth, the area is 72 cm^2, find the height. i did 1/2*b*h.... 1/2(b2+4B)=30 b2+4b=60 b2+4b-60=0 b-6 b+10 b=6 b+-10 is the answer 6 , i am having a hard time confirmting this answer. thank you in advance for your help1 solutions Answer 289134 by ewatrrr(10682)   on 2011-02-19 10:43:54 (Show Source): You can put this solution on YOUR website! ``` Hi length of a 'rectangle' is 6 more than its witdth Let x and (x+6) represent the width and length respectively Question states*** x(x+6) = 72 cm^2 |Area of a rectangle is w*l Solving for x x^2 + 6x - 72 = 0 factoring (x+12)(x-6) = 0 (x+12) = 0 x = -12 |tossing out negative solution for a measure (x -6) = 0 x = 6cm, the width. The length is 12cm (6cm+6) CHECKING our Answer*** 6cm*12cm = 72 cm^2 ```
 Probability-and-statistics/411265: how many different ways can a city health department inspector visit 3 restraurants in a city 0f 11 restraurants1 solutions Answer 289133 by ewatrrr(10682)   on 2011-02-19 10:32:03 (Show Source): You can put this solution on YOUR website! ``` Hi how many different ways can a city health department inspector visit 3 restraurants in a city 0f 11 restraurants 11C3 where nCx = 11*10*9/2*3 = 165 ways ```
 Evaluation_Word_Problems/411240: This is for a statistics class. On an exam with a mean of M=82, you obtain a score of X=86. a. Would you prefer a standard deviation of s=2 or s=10? (Hint: Sketch each distribution and find the location of your score.) b. If your score were X=78, would you prefer s=2 or s=10? c. Explain your answers.1 solutions Answer 289132 by ewatrrr(10682)   on 2011-02-19 10:28:50 (Show Source): You can put this solution on YOUR website! ``` Hi *Note: On an exam with a mean of M=82, you obtain a score of X=86 a. Would you prefer a standard deviation of s=2 or s=10? s = 2 z = 4/2 = 2 OR z= 4/10 = .4 b. If your score were X=78, would you prefer s=2 or s=10? s = 10 z = -4/2 = -2 OR z = -4/10 = -.4 c. If one scores below the mean, one wants the SD to be larger. If one scores above the mean , one would wish the SD to be smaller. That is: it will reflect a better position as to placement on the curve. ```
 Money_Word_Problems/411262: In a recent year the total sales at restrarant A were 350,000 more than restrarant B total sales at the two stores were 600,000,000 what were the sales for the year at each store.1 solutions Answer 289130 by ewatrrr(10682)   on 2011-02-19 10:10:34 (Show Source): You can put this solution on YOUR website! ``` Hi total sales at restrarant A were 350,000 more than restrarant B total sales Let x and (x + 350,00)represent the sales at A and B Question states*** x + (x+350,000) = 600,000,000 Solving for x 2x = 5,650,000 x = 2,825,000 at one store and 3,175,000 at the other (2,825,000+350,000) CHECKING our Answer*** 2,825,000 + 3,175,000 = 6,000,000,000 ```
 Money_Word_Problems/411247: if it is 250 km from karachi to nawabshah and 120 km from kotri to karachi, what percentage of distance from karachi to nawabshah is the distance from karachi to kotri?1 solutions Answer 289129 by ewatrrr(10682)   on 2011-02-19 10:02:31 (Show Source): You can put this solution on YOUR website! ``` Hi 250 km from karachi to nawabshah and 120 km from kotri to karachi. What percentage of distance from karachi to nawabshah is the distance from karachi to kotri 120/250 = .48 OR 48% distance from karachi to kotri is 48% of the distance from karachi to nawabshah ```
 Travel_Word_Problems/411244: Two jets leave an air base at the same time and travel in opposite directions. One jet travels 92 slower than the other. If the two jets are 10,602 apart after 9 hours, what is the rate of each jet? 1 solutions Answer 289126 by ewatrrr(10682)   on 2011-02-19 09:54:46 (Show Source): You can put this solution on YOUR website!``` Hi Let x and (x-92)represent the rates each of the jets are traveling Question states*** D= r*t 9x + 9(x-92) = 10,602mi Solving for x 18x = 10602+ 825 18x = 11430 x = 635mph. The other jet traveling at 543mph. (635-92) CHECKING our Answer*** 9hr*635mph + 9hr*543mph = 10,602mi ```
 Average/411254: Tom has taken 5 of the 8 equally weighted tests in his U.S. History class this semester, and he has an average score of exactly 78.0 points. How many points does he need to earn on the 6th test to bring his average score up to exactly 80.0 points? The answer is 90. Can someone explain how to get this answer?1 solutions Answer 289125 by ewatrrr(10682)   on 2011-02-19 09:49:30 (Show Source): You can put this solution on YOUR website! ``` Hi Averaged 78 pts on first 5 tests for a total of 390 Pts on these tests. Let x represent score on his 6th test. Question states*** (390+x)/6 = 80 Solving for x x = 480 -390 x = 90 CHECKING our Answer*** 480/6 = 80 ```
 Numbers_Word_Problems/411258: How much less is the sum of all odd digits between 24 and 308 than the sum of all even digits between 23 and 307?1 solutions Answer 289123 by ewatrrr(10682)   on 2011-02-19 09:43:48 (Show Source): You can put this solution on YOUR website! ``` Hi How much 'less' is the sum of all odd digits 'between' 24 and 308 than the sum of all even digits 'between' 23 and 307? 306 = 26 + (n-1)2 306 = 26 + 2n - 2 282 = 2n n = 141 = 23,406 |sum of evens 305 = 25 + 2n-2 141 = n 141/2(50 + 280) = 141/2*330 = 23,265 |sum of odds 23,406 - 23,265 = 141 ```