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# Recent problems solved by 'robertb'

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 Geometry_Word_Problems/356682: a triangle has two equal sides,and the third side of the triangle is 5 feet shorter than the first side. if the perimeter of the triangle is 40 feet, find the dimension of each side.1 solutions Answer 254645 by robertb(4012)   on 2010-10-15 02:19:52 (Show Source): You can put this solution on YOUR website!The lengths of the sides of the triangle would be x, x, x - 5. The perimeter would be x+x+x-5 = 40, 3x = 45, x = 15. Therefore the lengths of the sides of the triangle are 15, 15, 10.
 Numbers_Word_Problems/356710: Find a four-digit number that meets all these conditions: a. No two digits are the same. b. The sum of the two middle digits = the sum of the first and last digits. c. The thousands digit is the smallest. d. No digit is even. e. The units digit is the largest.1 solutions Answer 254640 by robertb(4012)   on 2010-10-15 01:54:25 (Show Source): You can put this solution on YOUR website!Find a four-digit number that meets all these conditions: a. No two digits are the same. b. The sum of the two middle digits = the sum of the first and last digits. c. The thousands digit is the smallest. d. No digit is even. e. The units digit is the largest. 1357 is an example. (This is just by trial and error.) Or 1537.
 Expressions-with-variables/356714: Solve and check. 3/4-3/5x=23/20 x=?1 solutions Answer 254638 by robertb(4012)   on 2010-10-15 01:48:44 (Show Source): You can put this solution on YOUR website!, , , , , , , .
 Linear_Equations_And_Systems_Word_Problems/356719: Simplify and express in terms of i Square root of -491 solutions Answer 254636 by robertb(4012)   on 2010-10-15 01:43:04 (Show Source):
 Unit_Conversion_Word_Problems/356697: how many liters of a 40% alcohol solution must be mixed with 65% solution to obtain 20 liters of a 50% solution?1 solutions Answer 254635 by robertb(4012)   on 2010-10-15 01:41:57 (Show Source): You can put this solution on YOUR website!, , , , # liters 40% alcohol solution, and 20 - 12 = 8 liters 65% alcohol solution.
 Money_Word_Problems/356622: Roberto invested some money at 8%. and then invested \$5000 more than twice this amount at 12%. His total annual income from the two investments was \$4440. How much was invested at 12%?1 solutions Answer 254556 by robertb(4012)   on 2010-10-14 21:07:20 (Show Source): You can put this solution on YOUR website!let x = amount invested at 8%. Then the amount invested at 12% is 2x + 5000, from the given. Then 0.08x + 0.12(2x + 5000) = 4440. 0.08x+0.24x + 600 = 4440. 0.32x = 3840 x = 12,000. Thus the amount invested at 12 is \$29,000.
 Expressions-with-variables/356620: 3x+y=10 y=-2x+4 solve this by using substitution1 solutions Answer 254555 by robertb(4012)   on 2010-10-14 21:02:30 (Show Source): You can put this solution on YOUR website!Substitute the bottom equation into the top equation: 3x+(-2x+4)=10. 3x-2x+4 = 10. x = 6. Then y = -2(6) + 4 = -12+4 = -8.
 Graphs/356611: Nine is subtracted from a number, and then the difference is multiplied by 5. The result is 75. What is the number?1 solutions Answer 254552 by robertb(4012)   on 2010-10-14 20:58:08 (Show Source): You can put this solution on YOUR website!, , .
 Permutations/356613: how many 6 letter words can be formed using the word Alaska?1 solutions Answer 254549 by robertb(4012)   on 2010-10-14 20:55:51 (Show Source): You can put this solution on YOUR website!That would be
 Travel_Word_Problems/356607: at the beginning of a bicycle ride for charity, roberto and juana are 30 miles apart. If they Leave at the same time and ride in the same direction, roberto overtakes juana in 6 hours. if they ride toward each other, they meet in 1 hour. what are their speeds?1 solutions Answer 254545 by robertb(4012)   on 2010-10-14 20:49:25 (Show Source): You can put this solution on YOUR website!Let r = speed of roberto, j = speed of juana. Using the formula D = RT, (distance = rate x time), the 1st and 2nd sentences give . The 3rd sentence implies that . The first equation is the same as , after transposition and dividing both sides by 6. The 2nd equation is just . Adding corresponding sides of these 2 equations, we get , or r = 17.5 miles per hour. Then j=30 - r = 12.5 miles per hour.
 Square-cubic-other-roots/356606: how do you find the square root of 1369.1 solutions Answer 254543 by robertb(4012)   on 2010-10-14 20:41:49 (Show Source):
 Linear-equations/356602: Write the equation of the line parallel to y=5x-8 and going through the origin.1 solutions Answer 254542 by robertb(4012)   on 2010-10-14 20:41:10 (Show Source): You can put this solution on YOUR website!The equation is already written in slope-intercept form, so the slope of the line parallel to it must also be 5. Since the parallel line passes through the origin, the y-intercept must be 0. Therefore the equation of the parallel line must be y = 5x.
 Linear_Algebra/356605: solve the system. then classify the system as consistent and independent, consistent and dependent, or inconsistent 4x-5y=0 3x-5y=-51 solutions Answer 254540 by robertb(4012)   on 2010-10-14 20:38:18 (Show Source): You can put this solution on YOUR website!The system is consistent and independent. Solving by elimination, subtract the bottom from the top equation, to get : x = 5. For the y-value: 4(5) - 5y = 0, 20 - 5y = 0, 5y = 20, y = 4.
 Linear_Algebra/356603: solve the system. then classify the system as consistent and independent, consistent and dependent, or inconsistent y=2x-1 -6x+3y=-31 solutions Answer 254539 by robertb(4012)   on 2010-10-14 20:35:29 (Show Source): You can put this solution on YOUR website!The system is consistent and dependent, because the bottom equation is a multiple of the top equation (the top equation is multiplied by -3). The two equations represent only one line on the cartesian plane, and thus would have all of the points on that line as solution points. There is not a single point of intersection only, but infinitely many.
 Geometry_Word_Problems/356597: if a regular octahedron has a surfacce area of 48 square inches,what is the area of each face?1 solutions Answer 254538 by robertb(4012)   on 2010-10-14 20:33:27 (Show Source): You can put this solution on YOUR website!Since a regular octahedron would have 8 congruent faces, the area of each face would be 48 sq.in./8 = 6 sq.in.
 Linear-equations/356600: undefined slope passes through (4,2). find the equation.1 solutions Answer 254536 by robertb(4012)   on 2010-10-14 20:30:09 (Show Source): You can put this solution on YOUR website!A line having undefined slope is a vertical line, so the equation is .
 Problems-with-consecutive-odd-even-integers/356593: The largest of 2 integers is one more than three times the smaller. If the sum of the two integers is 37, find the larger integer. 1 solutions Answer 254535 by robertb(4012)   on 2010-10-14 20:29:09 (Show Source): You can put this solution on YOUR website!Let L = the larger ineteger, S = the smaller. Then from the given, , and . Substituting the first equation into the second, we get . , , and .
 Geometry_proofs/356581: if AC=DB and AC and DB bisect each other at E, then AE=EB1 solutions Answer 254523 by robertb(4012)   on 2010-10-14 20:01:28 (Show Source): You can put this solution on YOUR website!Let x = ac = db. Since ac and db bisect each other at e, then e is the midpoint both of ac and db. Hence each of ae and eb will have length equal to x/2, and thus ac = db.
 Travel_Word_Problems/356580: two cars leave town at the same time going in the same direction on the same road. one travels 30 mph, the other travels at 45 mph. in how many hours will they be 150 miles apart?1 solutions Answer 254521 by robertb(4012)   on 2010-10-14 19:56:46 (Show Source): You can put this solution on YOUR website!let t = # hours the two cars are in motion. Then by the formula D = RT, . , . Therefore the two cars will be 150 miles apart after 10 hours.
 Mixture_Word_Problems/356169: On an airplane that was two-thirds full, 20% of the passengers were boys, one-fourth of the passengers were women, one-eighth of the passengers were girls, and there were 68 men. How many seats are on the plane? 1 solutions Answer 254238 by robertb(4012)   on 2010-10-14 00:23:00 (Show Source): You can put this solution on YOUR website!Let x = #number of seats in the airplane. Only seats are occupied. Of these, are boys, are women, are girls, and 68 are men. Hence, , or , or , . Therefore there are 240 seats in the airplane all-in-all.
 test/356167: 5x-3y=6 5x-4y=31 solutions Answer 254235 by robertb(4012)   on 2010-10-14 00:14:02 (Show Source): You can put this solution on YOUR website!Subtract the bottom equation from the top equation, to get: y = 3. Substitute into the top equation: 5x-3(3) = 6, 5x = 6+9, 5x = 15, x = 3.
 Linear_Algebra/356160: Let A be an m x n matrix. Show that if A has linearly independent column vectors, then Null(A) = 0.1 solutions Answer 254234 by robertb(4012)   on 2010-10-14 00:11:13 (Show Source): You can put this solution on YOUR website!Rank of column space of A = rank of A. Thus rank(A) = n (which is the number of columns of A). By the Rank-Nullity theorem, rank(A)+null(A) = n, again the number of columns of A. Therefore n + null(A) = n, and null(A) = 0.
 Linear_Algebra/356159: I need help with this proof: Let x1....xk be linearly independent vectors in R^n, and let A be a nonsingular nXn matrix. Define yi = Axi for i = 1,...k. show that y1,.... yk are linearly independent. Thanks!1 solutions Answer 254231 by robertb(4012)   on 2010-10-13 23:57:08 (Show Source): You can put this solution on YOUR website!Consider the linear combination: (a1)(y1)+(a2)(y2)+(a3)(y3)+....+(a(n-1))(y(n-1))+(an)(yn)= 0, a1, a2, a3,...an are scalar coefficients. For the purpose of contradiction, suppose that {y1, y2, y3,...,yn} is a linearly dependent set. Therefore not all of a1, a2, a3, ...an are equal to zero, by definition. Since A is nonsingular, exists. Now (a1)(y1)+(a2)(y2)+(a3)(y3)+....+(a(n-1))(y(n-1))+(an)(yn)= (a1)(Ax1)+(a2)(Ax2)+(a3)(Ax3)+....+(a(n-1))(Ax(n-1))+(an)(Axn)= A((a1)(x1)+(a2)(x2)+(a3)(x3)+....+(a(n-1))(x(n-1))+(an)(xn))= 0. Since A is nonsingular, this means that exists. Left-multiply the equation A((a1)(x1)+(a2)(x2)+(a3)(x3)+....+(a(n-1))(x(n-1))+(an)(xn))= 0 by . This means that (a1)(x1)+(a2)(x2)+(a3)(x3)+....+(a(n-1))(x(n-1))+(an)(xn)= 0,and not all a1, a2, a3, ...an are equal to zero, CONTRADICTION, because {x1, x2, x3, ...xn} is a linearly independent set. Therefore {y1, y2, y3,...,yn} has to be a linearly independent set.
 Travel_Word_Problems/356149: a boat goes 14 km/h in still water. The boat is paddled 6 km downstream in a river in the same time it takes to go 3 km upstream. What is the speed of the river?1 solutions Answer 254229 by robertb(4012)   on 2010-10-13 23:44:35 (Show Source): You can put this solution on YOUR website!let x = speed of the river. Then 14 + x = speed of boat relative to the river DOWNSTREAM, and 14 - x = speed of the boat relative to the river upstream. Using the formula D = RT, and knowing the fact that the times upstream and downstream are the same, then , , , , km/hr, the speed of the river.
 Equations/356097: forty pounds of cashews costing 6\$ per pound were mixed woth 100 pound of peanuts costing 3.32 per pound. find the cost of the mixture 1 solutions Answer 254174 by robertb(4012)   on 2010-10-13 21:08:56 (Show Source): You can put this solution on YOUR website!40lb * \$6/lb = \$240 100lb * \$3.32/lb = \$332. Total cost of mixture is \$240 + \$332 = \$572.
 Square-cubic-other-roots/356071: Subtract & simplify: ³√(270x)-³√(10x^4) 1 solutions Answer 254167 by robertb(4012)   on 2010-10-13 20:54:19 (Show Source): You can put this solution on YOUR website!³√(270x)-³√ ³√-³√ 3³√-x³√ (3-x)³√
 Human-and-algebraic-language/356069: West Highschool has 250 fewer students than twice the amount of East Highschool. Together they have 2858 students, how many students does each school have?1 solutions Answer 254153 by robertb(4012)   on 2010-10-13 20:33:23 (Show Source): You can put this solution on YOUR website!let w = #students in West, e = # students in East. Then from the given, w = 2e -250. Also, w +e = 2858. from the 2nd equation, w = 2858 - e. Substituting into the 1st equation, 2858 -e = 2e - 250. 3108 = 2e +e, after transposition. 3108 = 3e, 1036 = e, and w = 2858-1036 = 1822.
 Numbers_Word_Problems/356048: the sum of two number is 15. three times one number is 11 less than five times the other. find the numbers. please help1 solutions Answer 254152 by robertb(4012)   on 2010-10-13 20:29:17 (Show Source): You can put this solution on YOUR website!let x be one number. Then the other number is 15-x. From the given, 3x = 5(15-x)-11. Then 3x = 75 -5x-11, 8x = 64, x = 8. The other number is 15-8 = 7.
 Miscellaneous_Word_Problems/356050: if a tank holds 640 gallons and is 3/4 full how many gallons are left?1 solutions Answer 254150 by robertb(4012)   on 2010-10-13 20:19:55 (Show Source): You can put this solution on YOUR website!gallons.
 Angles/356059: whats is the supplementary angle for 15 degrees1 solutions Answer 254149 by robertb(4012)   on 2010-10-13 20:16:44 (Show Source): You can put this solution on YOUR website!degrees.
 Travel_Word_Problems/356055: how far would you travel in 2.4 hours at 25 mph?1 solutions Answer 254148 by robertb(4012)   on 2010-10-13 20:16:08 (Show Source): You can put this solution on YOUR website! miles.