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Recent problems solved by 'orca'

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 Rational-functions/200673: 3x^3-12x=1 solutions Answer 150952 by orca(409)   on 2009-06-20 22:53:10 (Show Source): You can put this solution on YOUR website! = = = factor 3x out as it is the common factor of both terms = x^2-2^2 can be factored further =
 logarithm/200367: If a^(1/3)+b^(1/3)+c^(1/3)=0, then show that log[(a+b+c)/3]=1/3[loga+logb+logc]1 solutions Answer 150659 by orca(409)   on 2009-06-17 01:40:06 (Show Source): You can put this solution on YOUR website! cube both sides Noting that , we have So log[(a+b+c)/3]=1/3[loga+logb+logc]
 Polynomials-and-rational-expressions/200269: Factor the trinomial: 8x^2-16-28x1 solutions Answer 150601 by orca(409)   on 2009-06-16 16:58:31 (Show Source): You can put this solution on YOUR website! = re-arrange the terms in descending order = factor out the common factor 4 =
 Linear-systems/200112: x^2+y^2+2x-4y-4=0 complete square and state the center and the radius or the circle1 solutions Answer 150434 by orca(409)   on 2009-06-15 05:23:45 (Show Source): You can put this solution on YOUR website!First moving the constant term to the right side, we have Re-arranging the terms on the left side, we get Add 1 and 4 to both sides, we have So the center of the circle is (-1, 2). The radius is 3.
 Surface-area/200077: if a square has the side length 5 square root of 2 what is the area?1 solutions Answer 150426 by orca(409)   on 2009-06-14 23:14:54 (Show Source): You can put this solution on YOUR website!The length of the side is It area A is
 Inequalities/200080: What would be the correct solution to the inequality equation,: m/4+6<1/21 solutions Answer 150425 by orca(409)   on 2009-06-14 23:11:32 (Show Source): You can put this solution on YOUR website! Subtract 6 from both sides of the inequality multiply both sides by 4
 Numbers_Word_Problems/200088: Three times the opposite of a number is 40 greater than 5 times number. What is the number?1 solutions Answer 150423 by orca(409)   on 2009-06-14 23:06:47 (Show Source): You can put this solution on YOUR website!Suppose the unknown number is x. Then the opposite of the number is -x. **************************************************** Three time the opposite of the unknown number is -3x. Five times the unknown number is 5x. **************************************************** As their difference is 40, we have -3x - 5x = 40 **************************************************** Solving for x, we have -8x = 40 x = -5 **************************************************** So the number is -5.
 Bodies-in-space/200090: If the height of a right circular cylinder is quadrupled and the radius is divided by three, how is the volume changed? 1 solutions Answer 150422 by orca(409)   on 2009-06-14 23:01:00 (Show Source): You can put this solution on YOUR website!Suppose the height and the radius of the original cylinder are h and r respectively. Then the volume of the original cylinder is The height and the radius of the newly formed cylinder are 3h and r/3 respectively. Then the volume of the newly formed cylinder is = = = So the volume of the newly formed cylinder is only one third of the volume of the original cylinder.
 logarithm/197349: Simplify. log (subscript 6) 216^-31 solutions Answer 147975 by orca(409)   on 2009-05-22 15:11:50 (Show Source): You can put this solution on YOUR website!Note that So Therefore: log(6)216^-3 =log(6)6^-9 =-9
 Reduction-of-unit-multipliers/195943: Sue walked to her school at 2 mph, picked up her bike and rode home at 10 mph. If her round trip took 1.5 hours, how far is the school form Sue's home 1 solutions Answer 146938 by orca(409)   on 2009-05-12 02:40:11 (Show Source): You can put this solution on YOUR website!Let x be the distance between her home and the school. The time spent on the way to school is x/2 The time spent on the way from school to home is x/10. As the total time is 1.5, we have Solving the equation for x, we have multiply both sides by 10 to clear fractions
 Graphs/195239: What is the y-intercept of 4x+8y=12?1 solutions Answer 146434 by orca(409)   on 2009-05-07 00:21:15 (Show Source): You can put this solution on YOUR website!To find the y-intercept, let x = 0,then solve the equation for y. Letting x = 0, we have 8y = 12 Solving for y, we have y = 12/8 = 3/2
 Quadratic_Equations/194506: Solve using quadratic methods. x^2/3-3x^1/3-10=01 solutions Answer 145970 by orca(409)   on 2009-05-03 22:55:47 (Show Source): You can put this solution on YOUR website!Let then the equation becomes Solving for y, we have (y-5)(y+2)=0 y = 5 or y = -2 From , we get x=125 From , we get x = -8
 Radicals/194529: simplify 4/the square root of 101 solutions Answer 145968 by orca(409)   on 2009-05-03 22:50:29 (Show Source): You can put this solution on YOUR website! = = = =
 Square-cubic-other-roots/194357: please help Multiplying radicals and simplify 1) (3 square2)(-4 square 10) 2)(3-2 square 7)(3 +2 square 7)1 solutions Answer 145858 by orca(409)   on 2009-05-02 22:29:32 (Show Source): You can put this solution on YOUR website!1) = = = = = 2) Use the formula to simplify = = = = =
 Quadratic_Equations/194368: Factoring for quadratic equations. 6x^ + 3x - 18=0 1 solutions Answer 145857 by orca(409)   on 2009-05-02 22:21:57 (Show Source): You can put this solution on YOUR website!Note that 3 is a common factor of the three terms, we factor it out. Next factor So 2x - 3 = 0 or x + 2 = 0 From 2x-3 = 0 we get x = 3/2 From x+2=0 we get x = -2
 Radicals/193954: SIMPLIFY 1/1 + THE SQUARE ROOT OF 3=1 solutions Answer 145605 by orca(409)   on 2009-04-30 16:06:37 (Show Source): You can put this solution on YOUR website! = = = = =
 Sequences-and-series/193992: Which is the next number in the series: -1,0,3,8,15,24,35,...1 solutions Answer 145604 by orca(409)   on 2009-04-30 16:00:43 (Show Source): You can put this solution on YOUR website!Note that: 0 -(-1) =1 3 - 0 = 3 8 - 3 = 5 15-8 = 7 24-15 =9 35-24=11 ....... the differences are consecutive odd numbers. Therefore the next number - 35 will be 13. so the number is 48
 Radicals/193998: solve the following equation (√2 +√3)(√2-√3)=1 solutions Answer 145603 by orca(409)   on 2009-04-30 15:54:01 (Show Source): You can put this solution on YOUR website!Use the formula So = = =
 Exponential-and-logarithmic-functions/193849: rewite 3(ln)4 as the logarithm of a single number1 solutions Answer 145543 by orca(409)   on 2009-04-29 22:34:14 (Show Source): You can put this solution on YOUR website!Use the property of logarithm So
 Expressions-with-variables/193670: The sum of two numbers is 50. If twice the larger is subtracted by 4 times the smaller, the result is 8. Find the numbers.1 solutions Answer 145367 by orca(409)   on 2009-04-29 02:50:38 (Show Source): You can put this solution on YOUR website!Let the smaller one be x, then the larger one is 50 - x. Now use the given information" twice the larger is subtracted by 4 times the smaller, the result is 8 " to set up an equation: 2(50-x)-4x=8 Solving for x, we have 100 - 2x - 4x = 8 100-6x=8 100-8=6x 92=6x 6x=92 x=92/6=46/3 So the smaller number is 46/3 The larger one is 50-46/3=104/3
 Quadratic_Equations/193566: I'm stuck on this one: determine whether the following equation has a real or complex solution √2x^2 -4x-7√2=01 solutions Answer 145359 by orca(409)   on 2009-04-28 23:25:34 (Show Source): You can put this solution on YOUR website!You need to find the value of the discriminant of the equation. If the discriminant > = 0, then the equation has real solutions. Otherwise only complex solutions. Recall that The discriminant = for equation So The discriminant = = = = > 0 So the equation has 2 real roots
 expressions/193581: 5^-1 + 2^-1-3^0. ANSWER: -3/10 anyone knows why the answer is -3/10 please give a full break down 1 solutions Answer 145358 by orca(409)   on 2009-04-28 23:18:40 (Show Source): You can put this solution on YOUR website!Note that: And So = = = =
 real-numbers/193449: This question is from textbook is the quotient of two irrational numbers always an irrational number? why or why not?1 solutions Answer 145229 by orca(409)   on 2009-04-28 01:10:44 (Show Source): You can put this solution on YOUR website!consider two irrational numbers and Their quotient = is a rational number.
 Age_Word_Problems/193438: Tom buys \$20,000 worth of stock, and sells it eight months later for \$28,000. If he is required to pay 15% capital gains tax on his profits, how much tax will he pay? 1 solutions Answer 145224 by orca(409)   on 2009-04-27 22:50:01 (Show Source): You can put this solution on YOUR website!Note that the capital gain tax = profit*rate The profit = 28,000 - 20,000 = 8,000 The tax to be paid = 8,000*15% = 1,200
 Rectangles/193291: The length of a rectangle swimming pool is 2x-1 meters and the width is x+2 meters. Write a polynomial A(x) that represent the area. Find A(5)1 solutions Answer 145110 by orca(409)   on 2009-04-27 04:18:57 (Show Source): You can put this solution on YOUR website!Use the formula: Area of a rectangle = length*width So A = A can also be written in expanded form A = =
 Polynomials-and-rational-expressions/193287: This question is from textbook factor the trinomial x2+7x+121 solutions Answer 145109 by orca(409)   on 2009-04-27 04:14:01 (Show Source): You can put this solution on YOUR website!Note that 12 can be factored into 3*4. Because the sum of the two factors is 7 which is the coefficient of the second term, the quadratic can be factored into: =
 Triangles/193233: Hi, Thank you for the help. Layout for a soccer field: side A is 36' side B is 84'. A & B meet at 90o angle. what is the length of side C? Also like to know the formula for determining the length. thanks! This is a real life scenario. Gary B.1 solutions Answer 145089 by orca(409)   on 2009-04-26 23:35:38 (Show Source): You can put this solution on YOUR website!We are required to solve a right triangle. So apply the Pythagorean Theorem to it. The theorem states that the sum of the squares of the two legs a aand b is equal to the square of the hypotenuse c. Or Here we are given One leg = 36 Another leg = 84 We are required to find the length of the hypotenuse According to the Theorem, = = So c = = 91
 Geometry_Word_Problems/193102: A rectangular picture frame is 4 times as wide as its length with a perimeter of 80 inches. Find the dimensions.1 solutions Answer 144977 by orca(409)   on 2009-04-26 01:42:19 (Show Source): You can put this solution on YOUR website!Let x be the length. Then its width 4x So the perimeter in terms of x is 2(x + 4x) Setting it equal to 80, we have 2(x + 4x) = 80 Solving for x, we have 2*5x = 80 10x = 80 x = 8 Therefore the length is 8 the width is 4x = 4*8 = 32
 Radicals/192879: V7 TIMES V351 solutions Answer 144764 by orca(409)   on 2009-04-24 00:45:19 (Show Source): You can put this solution on YOUR website! = = = = =
 Average/192702: Factor each polynomial completely. Please show work. a^2b + 2ab - 15b1 solutions Answer 144638 by orca(409)   on 2009-04-23 03:11:01 (Show Source): You can put this solution on YOUR website!Note that b is the common factor of the three terms, we must factor it out first. = Next factor a^2+2a-15. = =
 test/192300: Two airplanes left the same airport traveling in opposite directions. If one airplane averages 400 miles per hour and the other airplane averages 250 miles per hour,in how many hours will the distance between the two planes be 1625 miles?1 solutions Answer 144347 by orca(409)   on 2009-04-21 02:24:37 (Show Source): You can put this solution on YOUR website!Suppose that in x hours the distance between the two planes will be 1625 miles. In x hours, the distance traveled by each plane is: Plane 1: 400x Plane 2: 250x The total distance covered is 400x + 250x. Setting it equal to 1625, we have 400x + 250x = 1625 Solving for x, we have 650x = 1625 x= 2.5 hours