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# Recent problems solved by 'ewatrrr'

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 Quadratic_Equations/619208: Complete the squre for the parabola y=3x^2+5x+171 solutions Answer 389465 by ewatrrr(10682)   on 2012-06-09 12:16:59 (Show Source): You can put this solution on YOUR website! ``` Hi, Complete the square for the parabola y=3x^2+5x+17 = 3(x+5/3)^2 - 25/3 + 17 = 3(x+5/3)^2 + 26/3 ```
 Geometry_Word_Problems/619210: I would just like to know the steps to solve this problem: A square's side is increased by 2 yards, which corresponds to an increase in the area by 36 square yards. How many yards is the side of the initial square? Thank you!1 solutions Answer 389464 by ewatrrr(10682)   on 2012-06-09 12:14:37 (Show Source): You can put this solution on YOUR website! ``` Hi, A square's side is increased by 2 yards, which corresponds to an *increase in the area by 36 square yards. How many yards is the side of the initial square? (x+2)^2 - x^2 = 36yd^2 x^2 + 4x + 4 - x^2 = 36 4x = 32 x = 8yds CHECKING our Answer*** 100- 64 = 36 ```
 Age_Word_Problems/619212: A father is 5 times as old as his son. In 18 years, the father will be twice as old as his son. How old is the father at present? 1 solutions Answer 389458 by ewatrrr(10682)   on 2012-06-09 11:58:33 (Show Source): You can put this solution on YOUR website! ``` Hi, A father is NOW 5 times as old as his son...yrs old NOW . In 18 years, the father will be twice as old as his son. 5x + 18 = 2(x+18) 3x = 18 x = 6yr, son's age NOW. Father is 30 years old at the present. ```
 Polynomials-and-rational-expressions/619196: DIVISION Find Quotient 6x^3 – x^2 – 7x – 9 2x + 3 I don't understand the division of polynomials. Thank you for your help.1 solutions Answer 389455 by ewatrrr(10682)   on 2012-06-09 11:03:18 (Show Source): You can put this solution on YOUR website! ``` Hi, May be accomplished much like any divsion Problem 3x^2 + (-5x) + 4 __________________________ 2x + 3 | 6x^3 - x^2 - 7x - 9 - (6x^3 + 9x^2) --------------- -10x^2 - 7x - (-10x^2 - 15x)) -------------- 8x - 9 - (8x +12) -------- -21 ```
 Problems-with-consecutive-odd-even-integers/619104: The Diagonal of a rectangular room is 13ft long. one wall measures 7ft longer than the adjacent wall. find the dimensions of the room the width of the room is____________1 solutions Answer 389454 by ewatrrr(10682)   on 2012-06-09 10:55:25 (Show Source): You can put this solution on YOUR website! ``` Hi, The Diagonal of a rectangular room is 13ft long. one wall measures 7ft longer than the adjacent wall. 13^2 = x^2 + (x+7)^2 169 = 2x^2 + 14x + 49 2x^2 + 14x - 120 = 0 x^2 + 7x - 60 = 0 factoring: (x-5)(x+12) = 0 x = 5 throwing out negative solution for unit measure Dimensions of the room are 5ft by 12ft ```
 Miscellaneous_Word_Problems/619193: A square is made up of section A and section B. Section A is 500 sq. ft. and section B is 750 sq. ft. What percent of the square is section A? 1 solutions Answer 389453 by ewatrrr(10682)   on 2012-06-09 10:49:33 (Show Source): You can put this solution on YOUR website! ``` Hi, A square is made up of section A and section B. Section A is 500 sq. ft. and section B is 750 sq. ft. What percent of the square is section A? 500/1250 = .40 or 40% ```
 Polynomials-and-rational-expressions/619195: (x³ + 2x² - 3x + 2) ÷ (x + 1) 1 solutions Answer 389452 by ewatrrr(10682)   on 2012-06-09 10:47:38 (Show Source): You can put this solution on YOUR website! ``` Hi, (x³ + 2x² - 3x + 2) ÷ (x + 1) Using synthetic Division: -1 1 2 -3 2 -1 -1 4 1 1 -4 6 x^2 + x - 4 R = 6 ```
 Linear-equations/619149: Fractions confuse me....I hope you can help (1/16x^4+6/7x^3+5/8^2+7) + (-9/16x^4+3/8x^2-7) Simplify your answer. Use integers or fractions for any numbers in the expression1 solutions Answer 389450 by ewatrrr(10682)   on 2012-06-09 10:42:15 (Show Source): You can put this solution on YOUR website! ``` Hi, Assuming highlighted (1/16x^4+6/7x^3++7) + (-9/16x^4+3/8x^2-7) ```
 Circles/619157: Write the equation of a circle in standard form. find the center, radius, intercepts, and graph the circle. x^2+y^2+16x+18y=-1291 solutions Answer 389448 by ewatrrr(10682)   on 2012-06-09 10:15:28 (Show Source): You can put this solution on YOUR website! ``` Hi, x^2+y^2+16x+18y=-129 (x+8)^2 -64 + (y+9) - 81 = -129 C( -8,-9) r = 4 ```
 Distributive-associative-commutative-properties/619146: Can someone please show me how to work out this problem? I need to show all work for this question which is to find the product. (x^2+7) (x^3-5x-4) 1 solutions Answer 389443 by ewatrrr(10682)   on 2012-06-09 09:59:48 (Show Source): You can put this solution on YOUR website! ``` Hi, In 3 steps... (x^2+7) (x^3-5x-4) = x^2(x^3-5x-4) + 7(x^3-5x-4) = x^5-5x^3-4x^2 + 7x^3-35x-28 = x^5+2x^3-4x^2 -35x-28 ```
 Linear-equations/619170: 4x-5=6x+111 solutions Answer 389442 by ewatrrr(10682)   on 2012-06-09 09:54:52 (Show Source): You can put this solution on YOUR website! ``` Hi, 4x-5=6x+11 -16 = 4x ||Isolating variable on side of the EQ -4 = x ```
 Triangles/619189: What is the hypotenuse of the right triangle if it's legs are 11 and 60 degrees1 solutions Answer 389440 by ewatrrr(10682)   on 2012-06-09 09:52:48 (Show Source): You can put this solution on YOUR website! ``` Hi, What is the hypotenuse of the right triangle if it's legs are 11 and 60 units ```
 test/619190: 3 square root of 5(-8+9 sqaure root of 5)1 solutions Answer 389439 by ewatrrr(10682)   on 2012-06-09 09:50:54 (Show Source): You can put this solution on YOUR website! ``` Hi, ```
 Triangles/619188: The height of a triangle is 6 m more than twice the length of the base. The area of the triangle is 28 m2. Find the height of the triangle.1 solutions Answer 389438 by ewatrrr(10682)   on 2012-06-09 09:48:19 (Show Source): You can put this solution on YOUR website! ``` Hi, The height of a triangle is 6 m more than twice the length of the base. The area of the triangle is 28 m^2 = L*H x(2x+6) =28 2x^2 + 6x -28 = 0 x^2 + 3x -14 = 0 = (-3 +8.06)/2 = 2.5 rounded to 1 decimal point (throwing out neg solution for unit measure length = 2.5m, height is 11m ```
 Quadratic_Equations/619119: The equation is y=(x+2)^2+k where k is a constant. a)Find k when its tangent at x=1 passes through (0,0). b)Find k when the quadratic is tangent to y=-x^21 solutions Answer 389436 by ewatrrr(10682)   on 2012-06-09 09:39:47 (Show Source): You can put this solution on YOUR website! ``` Hi, Re TY, Note: completed the exercise by demonstrating using the 1st derivative. The equation is y=(x+2)^2+k where k is a constant. a)Find k when its tangent at x=1 passes through (0,0). y=(x+2)^2+k , y' = 2(x+2), x=1, m = 6, tangent line is y = 6x, Tangent at(1,6) 6 = (1+2)^2 + k, k = b)Find k when the quadratic is tangent to y= -x^2, k = -2 (see 2nd graph) Taking 1st derivatives of both: 2(x+2) = -2x, x = -1, tangent at (-1,-1) -1 = (-1+2)^2 + k, k = -2 ```
 Money_Word_Problems/619038: if 6000 dollars is placed into an account with an annual interest rate of 3%,how long will it take the amount to triple if the interest is compounded annually?1 solutions Answer 389435 by ewatrrr(10682)   on 2012-06-09 09:22:09 (Show Source): You can put this solution on YOUR website! ``` Hi, In General A = Accumulated Amount P= principal = 6000 r= annual rate = .03 n= periods per year = 1 t= years = log3/log(1.03) = t ```
 Quadratic_Equations/619187: Please help me graph 2x^2+6x+5=0 1 solutions Answer 389433 by ewatrrr(10682)   on 2012-06-09 09:15:07 (Show Source): You can put this solution on YOUR website! ``` Hi, Please help me graph 2x^2+6x+5=0 ||Recommend completing Square y = 2(x+3/2)^2 - 9/2 + 5 y = 2(x+3/2)^2 +1/2 Parabola Opening Upward as 2>0, V(-3/2,1/2) Axis of symmetry x = -3/2 ```
 Money_Word_Problems/619171: a person has deposited rs 25,000 in an inverstment which yields 14% simple interest annually. do these amounts (principal+interest) form an arithmatic progression? if so, determine the amount of inverstment after 20 years.1 solutions Answer 389432 by ewatrrr(10682)   on 2012-06-09 08:56:48 (Show Source): You can put this solution on YOUR website! ``` Hi, a person has deposited rs 25,000 in an investment which yields 14% simple interest annually. do these amounts (principal+interest) form an arithmatic progression? if so, determine the amount of inverstment after 20 years In General A = Accumulated Amount P= principal = 25,000 r= annual rate = .14 n= periods per year = 1 t= years = 20 = \$343,587.25 ```
 Travel_Word_Problems/619181: a man travels in a motorized boat at the rate of 15 kph from his barrio to the city and comes back at the rate of 12 kph. if his total time of travel is 3 hrs. find the distance from the barrio to the city1 solutions Answer 389429 by ewatrrr(10682)   on 2012-06-09 08:38:45 (Show Source): You can put this solution on YOUR website! ``` Hi, a man travels in a motorized boat at the rate of 15 kph from his barrio to the city and comes back at the rate of 12 kph. if his total time of travel is 3 hrs. find the distance from the barrio to the city D = rt OR D/r = t |Multiplying thru by 60 so as all denominators = 1 4x + 5x = 180 9x = 180 x = 20mi, the distance from the barrio to the city ```
 Radicals/619180: what is the value of 'x' in this radical equation of 4{sqrt(3x+6)}-x=14.1 solutions Answer 389427 by ewatrrr(10682)   on 2012-06-09 08:34:35 (Show Source): You can put this solution on YOUR website! ``` Hi, ||Isolate the radical ||Square both sides of the EQ 3x+6 = (x+14)^2/16 48x + 96 = x^2 + 28x + 196 x^2 -20x + 100 = 0 (x-10)(x-10) = 0 x = 10 ```
 Mixture_Word_Problems/619184: How much demineralized water do you add to 36% HCl to make 1 m3 of 15% HCl. 1 solutions Answer 389426 by ewatrrr(10682)   on 2012-06-09 08:22:59 (Show Source): You can put this solution on YOUR website! ``` Hi, How much demineralized water do you add to 36% HCl to make 1 m3 of 15% HCl. water = water .36x = .21 x = .583 C^3 water needs to be added ```
 Quadratic_Equations/619182: Please help me solve 2x^2+6x+5=0 1 solutions Answer 389425 by ewatrrr(10682)   on 2012-06-09 08:18:40 (Show Source): You can put this solution on YOUR website! ``` Hi, Please help me solve 2x^2+6x+5=0 Note: Using the Quadratic formula is ALWAYS a sure thing: ```
 Finance/619064: John bought a number of notepads for \$70. Four of the notepads got spoiled. He sold the remaining notepads at \$3 more per pad than he paid, and made a total profit of \$10. How many notepads did John buy?1 solutions Answer 389327 by ewatrrr(10682)   on 2012-06-08 16:47:17 (Show Source): You can put this solution on YOUR website! ``` Hi, John bought a number of notepads for \$70. \$70/x per pad Four of the notepads got spoiled. He sold the remaining notepads at \$3 more per pad than he paid, and made a total profit of \$10. How many notepads did John buy? **** |||Multiplying thru by x so as all denominators = 1 70(x-4) + 3x(x-4) = 80x 3x^2 + 58x -200 = 80x 3x^2 -22x - 280 = 0 x = 14, throwing out the negative solution for count CHECKING our Answer*** 70/14 = \$5 pd for the notepads originally 10· \$8 - \$70 = \$10 ```
 Proportions/619049: in a scale drawing of a city the distance of 45 kilometers is represented by a line sector 3 inches long . on the same drawing what distance is represented by a line sector 2 inches long1 solutions Answer 389319 by ewatrrr(10682)   on 2012-06-08 16:30:28 (Show Source): You can put this solution on YOUR website! ``` Hi in a scale drawing of a city the distance of 45 kilometers is represented by a line sector 3 inches long . on the same drawing what distance is represented by a line sector 2 inches long ||Cross Multiplying to solve 3x = 90 x = 30Km ```
 Human-and-algebraic-language/619071: Can someone help me to translate the following: Find three consecutive odd integers such that 3 times the second minus the third is 11 more than the first?1 solutions Answer 389317 by ewatrrr(10682)   on 2012-06-08 16:26:25 (Show Source): You can put this solution on YOUR website! ``` Hi, Find three consecutive odd integers, , such that 3 times the second minus the third is 11 more than the first? 3(x+2) - (x+4) = x+11 3x + 6 -x-4 = x + 11 2x + 2 = x + 11 x = 9 9, 11 , 13 CHECKING our Answer*** 3·11 - 13 = 20 ```
 Rectangles/619062: The perimeter of a rectangle is 44 meters the length is 10 meters more than twice the width. Find the dimensions.1 solutions Answer 389302 by ewatrrr(10682)   on 2012-06-08 15:12:49 (Show Source): You can put this solution on YOUR website! ``` Hi, The perimeter of a rectangle is 44 meters the length is 10 meters more than twice the width. P = 2L + 2W = 2(2x+10) + 2x = 44m 2(2x+10) + 2x = 44m 6x = 24m x = 4m, the width. The length is 18m ```
 Probability-and-statistics/619059: a two-tailed test is conducted at the 5% significance level. What is the right tail percentile required to reject the null hypothesis? 1 solutions Answer 389301 by ewatrrr(10682)   on 2012-06-08 15:09:00 (Show Source): You can put this solution on YOUR website! ``` Hi, a two-tailed test is conducted at the 5% significance level. What is the right tail percentile required to reject the null hypothesis? 2.5% ```
 Permutations/619061: In how many ways can 40 contestants in a spelling bee finish first through third?1 solutions Answer 389300 by ewatrrr(10682)   on 2012-06-08 15:07:11 (Show Source): You can put this solution on YOUR website! ``` Hi, In how many ways can 40 contestants in a spelling bee finish first through third? Order Important: 40P3 = 40!/37! = 59,280 ways ```
 Word_Problems_With_Coins/619056: If i have a total of 16 coins using only nickles and quarters to equal \$3, how many quarters will i have?1 solutions Answer 389299 by ewatrrr(10682)   on 2012-06-08 15:05:38 (Show Source): You can put this solution on YOUR website! ``` Hi, If i have a total of 16 coins using only nickles and quarters to equal \$3, how many quarters will i have? Note: CENTS makes sense 25x + 5(16-x) = 300¢ 20x = 220 x = 11, number of quarters. There are 5 nickels CHECKING our Answer*** 25*11 + 5*5 = 300¢ or \$3.00 ```
 Probability-and-statistics/618949: The mean time taken by all participants to run a road race was found to be 220 minutes with a standard deviation of 20 minutes. Using the 68 – 95 – 99.7 Rule, find the percentage of runners who ran this race: a. In less than 180 minutes b. In more than 220 minutes c. In between 160 and 280 minutes d. In at least 240 minutes e. In no more than 200 minutes1 solutions Answer 389287 by ewatrrr(10682)   on 2012-06-08 13:49:39 (Show Source): You can put this solution on YOUR website! ``` Hi, The mean time taken by all participants to run a road race was found to be 220 minutes with SD= 20min Using the 68 – 95 – 99.7 Rule, find the percentage of runners who ran this race: a. In less than 180 minutes (2 SD) (1-.95)/2 = 2.5% b. In more than 220 minutes 50% c. In between 160 and 280 minutes (3 SD) 99.7% d. In at least 240 minutes 84% e. In no more than 200 minutes 16% ```
 Sequences-and-series/619018: what is the sum of the series S28 for -143+(-134)+(-125)+(-116)+..1 solutions Answer 389272 by ewatrrr(10682)   on 2012-06-08 12:22:27 (Show Source): You can put this solution on YOUR website!``` Hi, sum of the series S28 for -143+(-134)+(-125)+(-116)+.. Arithmetic Series, d = 9 ```