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# Recent problems solved by 'robertb'

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 Geometry_proofs/375079: Lets say that two triangles have one pair of congruent legs and the hypotenuses are congruent. What postulate or theorem would you use? 1 solutions Answer 266784 by robertb(4012)   on 2010-11-22 19:36:03 (Show Source): You can put this solution on YOUR website!They could be congruent by the LL, or HL theorem.
 Graphs/375132: i have to graph, y-3=0.6666666667(x+4),can you put it into slope-intercept form for me, i can then graph it thanks.1 solutions Answer 266782 by robertb(4012)   on 2010-11-22 19:32:19 (Show Source): You can put this solution on YOUR website!I'll just use . then , or , or, or .
 Graphs/375157: I can't remember graphing at all and am attempting to help my daughter with her home work. Can you explain how to solve the following problem so that I may understand and explain to her? x=3y Thank you! Sam1 solutions Answer 266779 by robertb(4012)   on 2010-11-22 19:28:51 (Show Source): You can put this solution on YOUR website!This is a linear equation. To graph a linear equation, you need two points on the line. If x = 0, then y = 0. (Just substitute x=0 into the eqution.) If x = 3, then 3 = 3y, or y = 1. Hence two points on the line are (0,0) and (3,1). Plot these two points on the line and try your best two draw a straight line through them.
 Travel_Word_Problems/375160: If I am traveling at 45mph, how long would it take me to travel 2 miles?1 solutions Answer 266774 by robertb(4012)   on 2010-11-22 19:25:07 (Show Source): You can put this solution on YOUR website!(2 miles)/(45 miles per hour) = 2/45 hr, or 2.67 minutes.
 Expressions-with-variables/375076: can anyone find the solution to this two part elimination method equation? 4x+5y=5 6x+7y=71 solutions Answer 266772 by robertb(4012)   on 2010-11-22 19:23:26 (Show Source): You can put this solution on YOUR website!Multiply the top equation by -6: -24x-30y = -30 Multiply the bottom equation by 4: 24x + 28y = 28. Add corresponding sides: -2y = -2, or y = 1. To find x, use either the top or the bottom equation. (I will use the top). 4x + 5 = 5, or 4x = 0, or x = 0.
 Graphs/375075: How do you find the slope of a line when you are given the line?1 solutions Answer 266769 by robertb(4012)   on 2010-11-22 19:20:19 (Show Source): You can put this solution on YOUR website!Pick any two points on the line (x1, y1) and (x2, y2), apply the slope formula: slope = .
 Linear_Equations_And_Systems_Word_Problems/375138: The sum of two numbers is 27. One number is 2 times as large as the other. What are the numbers?1 solutions Answer 266768 by robertb(4012)   on 2010-11-22 19:17:56 (Show Source): You can put this solution on YOUR website!Let x = one number, so 27 - x = other number. x = 2(27 - x), or x = 54 - 2x, 3x = 54, x = 18, one number, and 27 - 18 = 9, the other number.
 Probability-and-statistics/375151: an unbiased coin is tossed 5 times find the probability of the given event. the coin lands heads exactly once1 solutions Answer 266767 by robertb(4012)   on 2010-11-22 19:15:31 (Show Source):
 Probability-and-statistics/375146: Given the following set of data, find the value that corresponds to the 25th percentile. 10, 44, 15, 23, 13, 18, 72, 56 1 solutions Answer 266766 by robertb(4012)   on 2010-11-22 19:11:53 (Show Source): You can put this solution on YOUR website! 10, 13 , 15, 18, 23, 44, 56, 72. The 25th percentile should be the the average of 2nd and 3rd terms, i.e., (13+15)/2 = 14.
 Probability-and-statistics/375149: the probability that a bus will arrive late at the civic center is .35, and the probabalitiy that it will be on time or early is .601 solutions Answer 266765 by robertb(4012)   on 2010-11-22 19:08:04 (Show Source): You can put this solution on YOUR website!The two events are complementary, and so their probabilities must add up to 1. But 0.35 + 0.60 = 0.95 <1. That's what's wrong.
 Expressions-with-variables/375052: 2x+3y=8 x+2y=5 Can someone please help solve this two part equation using the elimination method?1 solutions Answer 266734 by robertb(4012)   on 2010-11-22 17:29:16 (Show Source): You can put this solution on YOUR website!Multiply the bottom eqn by -2: -2x - 4y = -10. Add corresponding sides: 3y + (-4y) = 8+(-10) -y = -2, or y = 2. Substitute into the bottom eqn; x + 2*2 = 5, or x + 4 = 5, or x = 1.
 Graphs/375072: x+y=4 x-y=21 solutions Answer 266732 by robertb(4012)   on 2010-11-22 17:26:14 (Show Source): You can put this solution on YOUR website!Add corresponding sides, to get 2x = 6, or x = 3. Substitute into the top equation: 3 + y = 4, or y = 1.
 Rational-functions/375060: x-0.05x=19 0.2a=0.05a+3 x/x+5=2/3 3/a+1/2=11/5a x/2=3/2x+11 solutions Answer 266731 by robertb(4012)   on 2010-11-22 17:23:37 (Show Source): You can put this solution on YOUR website!x-0.05x=19 => 0.95x = 19 => x = 20. 0.2a=0.05a+3 => 0.15a = 3 => a = 20. x/(x+5)=2/3 => 3x = 2(x+5) => 3x = 2x +10 => x = 10. 3/a+1/2=11/5a => 3/a + 0.5 = 2.2/a =>0.8/a = -0.5 => a = -1.6. x/2=3/(2x+1) => x(2x+1) = 6 => => (2x - 3)(x + 2) = 0, thus x = 3/2 or x = -2.
 Mixture_Word_Problems/375068: Please help me slove this word mixture problem. One canned juice drink is 15% orange juice, another is 5% orange juice. How many liters of each should be mixed together in order to get 10L that is 14% orange juice?1 solutions Answer 266730 by robertb(4012)   on 2010-11-22 17:15:24 (Show Source): You can put this solution on YOUR website!0.15x + 0.05(10 - x) = 0.14*10, 0.15x + 0.5 - 0.05x = 1.4, 0.10x = 0.9, x = 9 liters, the amount of 15% orange juice that must be mixed with 10 - x = 1 liter of 5% orange juice.
 Triangles/374530: the question is: given a right triangle with a perimeter of 60 and an altitude to the hypotnuse with a length of 12 what is the length of each side? i tried a lot using substitution its just too complicated i need an explanation too plz asap1 solutions Answer 266448 by robertb(4012)   on 2010-11-21 18:59:32 (Show Source): You can put this solution on YOUR website!A suggestion: Let x = the unknown leg, and y = the hypotenuse. Then from the perimeter condition, x+y+12 = 60, or x+y = 48, or y = 48 - x. From the right-triangle condition, use the Pythagorean identity : . Substituting, we get . Now see if there will be any progress...
 Rectangles/374595: The length of a rectangle is 3 meters longer than the width. If the area is 36 square meters, find the rectangle's dimensions. Round to the nearest tenth of a meter.1 solutions Answer 266445 by robertb(4012)   on 2010-11-21 18:53:13 (Show Source): You can put this solution on YOUR website!w(w+3) = 36, or . then by the quadratic formula, meters. We discard the negative value!) That's the width. The length is 4.7 + 3 = 7.7 meters.
 Rectangles/374580: how do i find the perimeter of a triangle when the lenght is 3x+5 and its width is 2x1 solutions Answer 266442 by robertb(4012)   on 2010-11-21 18:48:02 (Show Source): You can put this solution on YOUR website!Are you looking for the perimeter of a triangle or a rectangle??
 Rational-functions/374593: what is 3 to the power of 1/4 times 27 to the power of 1/41 solutions Answer 266441 by robertb(4012)   on 2010-11-21 18:46:07 (Show Source): You can put this solution on YOUR website!That is 3 times 27 to the power of 1/4, or 81 to the power of 1/4, or 3, the final answer!
 Quadratic-relations-and-conic-sections/374588: find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=4x^2-16x=8 what is the vertex1 solutions Answer 266439 by robertb(4012)   on 2010-11-21 18:44:49 (Show Source): You can put this solution on YOUR website!Is that +8 or -8??
 Triangles/374582: GIVEN 2 SIDES OF A TRIANGLE(4 AND 15) WHICH OTHER IS THE POSSIBLE SIDE LENGHT FOR THE TRIANGLE: 1, 2, 3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20 (CIRCLE THE POSSIBLE ONES)1 solutions Answer 266438 by robertb(4012)   on 2010-11-21 18:43:26 (Show Source): You can put this solution on YOUR website!Hmm. let's see: If x = unknown side, then the sides of the triangle are 4, 15, and x. By a combination of the use of the triangle inequality, 4 + 15 > x, or 19 > x; 4+x > 15, or x > 11; 15 +x > 4, or x > -11. This last inequality doesn't give us any new information. But from the first two, we get 19 > x > 11. There are 7 possibilities, looking at your list. Now you know...
 Exponential-and-logarithmic-functions/374584: Find the inverse of the logarithmic function f(x)=-ln(x-2). Steps I've done so far: 1. f(x)=-ln(x-2) 2. y=-ln(x-2) 3. x=-ln(y-2) What is the next step? I am not sure what to do with -ln. My instructor said the answer is: y=e^-x+2 but I don't know how he gets the -x. I know ln also stands for e. y=-e^x+2 makes more sense to me.1 solutions Answer 266436 by robertb(4012)   on 2010-11-21 18:36:45 (Show Source): You can put this solution on YOUR website!After x = -ln(y-2): -x = ln(y - 2). Then raise e to both these powers, , , . This is the inverse function.
 Equations/374571: suppose F(X)=AX+B, G(X)=BX+A,(A AND B INTEGERS), F(1)= 8, F(G(50))-G(F(50))=28 FIND THE PRODUCT OF A AND B. 1 solutions Answer 266434 by robertb(4012)   on 2010-11-21 18:32:29 (Show Source): You can put this solution on YOUR website!f(1) = 8 implies that a+b = 8. f(g(50)) - g(f(50)) = f(50b +a) - g(50a+b) = . From the very first equation, a+b-1 = 7, so that after substitution into the last equation above, (a-b)*7 = 28, or a-b = 4. So a-b = 4, and a+b = 8. It follows that 2a = 12, or a = 6, by elimination. Then b = 2. Therefore a*b = 12. BTW, just replace a by A, and b by B. :D
 Quadratic_Equations/374567: write a quadratic equation in the variable x having the given numbers as solutions. SOLUTION: 2, ONLY SOLUTION1 solutions Answer 266430 by robertb(4012)   on 2010-11-21 18:16:08 (Show Source):
 Equations/374105: Translate the following statement into an algebraic equation. Let x represent the number: 6 times a number is 14 more than that number1 solutions Answer 266348 by robertb(4012)   on 2010-11-21 02:46:14 (Show Source): You can put this solution on YOUR website!6x = x + 14
 testmodule/374060: Find the equation of the bisector of the acute angles and also the equation of the bisector of the obtuse angles formed by the line x+y =2 and x + 2y = 3.1 solutions Answer 266347 by robertb(4012)   on 2010-11-21 02:42:36 (Show Source): You can put this solution on YOUR website!Let (x,y) be a point in Quadrant 4 that is located in the angle bisector of the acute angle between the two lines. We use the distance formula between a point and a line: d = |Ax + By + C|/. Then the point (x,y)is BELOW the line x + 2y = 3, so its distance from the said line is . The point (x,y)is ABOVE the line x + y = 2, so its distance from the said line is . Hence ; . This the equation of the angle bisector of the ACUTE angle of intersection. The arguments for the equation of the angle bisector of the OBTUSE angle of intersection run along the same lines. (But choose (x,y) now to be in Q1, and such point will be ABOVE both lines, so use +'s in place of the absolute value bars.)
 Sequences-and-series/374209: The sequence is defined recursively. Write the first four terms a1 = 3; an = 3an-1 + 4 1 solutions Answer 266345 by robertb(4012)   on 2010-11-21 02:19:30 (Show Source): You can put this solution on YOUR website!a1 = 3, a2 = 3*3 + 4 = 13. a3 = 3*13+ 4 = 43, a4 = 3*43 + 4 = 133...
 Triangles/374219: In an equilateral triangle, if the lengths of the three sides are 5x − 2, 6x − 10, and 4x + c, what are the values of x and c? 1 solutions Answer 266343 by robertb(4012)   on 2010-11-21 02:09:31 (Show Source): You can put this solution on YOUR website!5x- 2 = 6x-10 = 4x+c. Equate the 1st and the 2nd expressions: 5x - 2 = 6x-10, or -2 + 10 = 6x-5x, or x = 8. Equate the 2nd and the 3rd expressions : 6x-10 = 4x+c, or 2x - 10= c, or c = 2*8-10 = 16-10 = 6. Therefore x = 8, and c = 6.
 Rectangles/374221: The width of a rectangular picture is one-half the length. The perimeter of the rectangle is 72 inches. Find the length of the picture.1 solutions Answer 266342 by robertb(4012)   on 2010-11-21 02:04:38 (Show Source): You can put this solution on YOUR website!l = length, w = l/2. Then PERIMETER = 2l + 2(l/2) = 72. 2l + l = 72, or 3l = 72, or l = 24 inches, the length of the rectangular picture, and w = 24/2 = 12 inches, the width of the picture.
 Numbers_Word_Problems/374252: Find how many quarts of 4% butterfat milk and 1% butterfat milk should be mixed to yield 60 quarts of 2% butterfat milk.1 solutions Answer 266341 by robertb(4012)   on 2010-11-21 01:59:09 (Show Source): You can put this solution on YOUR website!0.04x + 0.01(60-x) = 0.02*60 0.04x + 0.6 - 0.01x = 1.2, 0.03x = 0.6, x = 20 quarts, the amount of 4% butterfat milk, and 60 - 20 = 40 quarts, the amount of 2% butterfat milk.
 logarithm/374248: Solve the logarithmic equation algebraically. Approximate the result to three decimal places. (If there is no solution, enter NO SOLUTION.) ln x + ln(x + 1) = 21 solutions Answer 266340 by robertb(4012)   on 2010-11-21 01:48:19 (Show Source): You can put this solution on YOUR website!The logarithmic equation can be reduced to . Using the quadratic formula, we get. Only the value will satisfy the original equation, and so this is the final answer. And that my STUDENT, is how it's done...
 Rational-functions/374240: How do you find x... 2/x+3/5=22/5x1 solutions Answer 266339 by robertb(4012)   on 2010-11-21 01:43:15 (Show Source): You can put this solution on YOUR website! is the same as , or , or x = 2.4/0.6 = 4. Therefore x = 4.