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# Recent problems solved by 'acalgebra'

 Linear-systems/369608: I am supposed to solve a linear equation using the method of elimination, I have retried doing it over and over but when I go back to check my work it doesn't come out as the correct answer. So I need help solving this by using method of elimination. Please help me solve this equation: x+3y=14 x+2y=10 Hopefully you know this method, I do but this particular problem is causing me to struggle, so can you show me the steps to how you figured it out? Thank you!1 solutions Answer 263383 by acalgebra(30)   on 2010-11-11 13:25:39 (Show Source): You can put this solution on YOUR website!First, multiply the second equation by -1: Now, add the equations together: Combine like terms: Substitute y for 4 in one of the equations. I chose the first one: Multiply 3 by 4: Subtract 12 from both sides: So, and . -------- Check: First equation: Second equation:
 Angles/369585: Find the measure of the supplement to a 146° angle.1 solutions Answer 263370 by acalgebra(30)   on 2010-11-11 12:52:43 (Show Source): You can put this solution on YOUR website!The supplement and the angle should add up to 180°. Let the supplement be x, then: So, the measure of the supplement to a 146° angle has a measure of 34°.
 Coordinate-system/369591: The slope of a line is -7/6. What is the slope of any line perpendicular to this line?1 solutions Answer 263368 by acalgebra(30)   on 2010-11-11 12:48:00 (Show Source): You can put this solution on YOUR website!Because the slopes of perpendicular lines are opposite reciprocals, the slope of a line perpendicular to a line with a slope of is .
 Angles/369586: An angle is 10° more than the measure of its complement. Find the number of degrees in each angle.1 solutions Answer 263366 by acalgebra(30)   on 2010-11-11 12:45:40 (Show Source): You can put this solution on YOUR website!Let the angle be x and its complement be c, then: and . In the second equation, substitute x for : Now, solve: Now, in the first equation, substitute c for 40: So, the measure of the angle is 50°, and the measure of its complement is 40°.
 Graphs/369583: (5,-6);3x+5y=9 write an equation of the line perpendicular to the given line1 solutions Answer 263363 by acalgebra(30)   on 2010-11-11 12:39:36 (Show Source): You can put this solution on YOUR website!First, put the equation in slope-intercept form: Because perpendicular lines have slopes that are opposite reciprocals, the equation that is perpendicular to the given line is:
 Equations/369579: What is the value of k in this equation?1 solutions Answer 263359 by acalgebra(30)   on 2010-11-11 12:32:06 (Show Source): You can put this solution on YOUR website!Original equation: Add 40 to each side: Divide both sides by 8: So, the value of k in this equation is 7.
 Linear_Equations_And_Systems_Word_Problems/369560: The sum of twice one number and 3 times another is 41. If the second is subtracted from the first, the difference is 8. What are the numbers?1 solutions Answer 263357 by acalgebra(30)   on 2010-11-11 12:29:52 (Show Source): You can put this solution on YOUR website!Let the first number be x and the second number be y, then: and The easiest way to solve this is to multiply the second equation by 3: Now, add the equations: Combine like terms: Divide both sides by 5 to simplify: Now, substitute 13 for each x in one of the original equations. In this case, the second equation will be easier. Add y to each side: Subtract 8 from each side: So, and .
 Average/369374: Daniel ran 2 miles in 12 minutes. What was his average speed using the formula s=d/t?1 solutions Answer 263181 by acalgebra(30)   on 2010-11-10 21:48:10 (Show Source): You can put this solution on YOUR website! (Basic equation) (12 minutes is one-fifth of an hour, or .20 of an hour.) (Multiply both sides of the fraction to get whole numbers.) (Divide both sides of the fraction to simplify.) So, Daniel ran at an average speed of 10 miles per hour.
 Equations/369377: Please help me set up this equation, Mary has 22.75 in the bank. She only saves half dollars and quarters. She has \$10.50 in half dollars, how MANY quarters does she have? I know how to get to the answer but I don't know how to set up the equation to solve for x1 solutions Answer 263179 by acalgebra(30)   on 2010-11-10 21:42:36 (Show Source): You can put this solution on YOUR website!Let the number of quarters be x, then Now, divide 12.25 by 25 to get So, Mary has 49 quarters in the bank.
 Average/369370: Find the area of the triangle formed by the x-axis, the y-axis, and the line described by y = 6 - x.1 solutions Answer 263178 by acalgebra(30)   on 2010-11-10 21:39:52 (Show Source): You can put this solution on YOUR website!The triangle formed by the y-axis, x-axis, and the line defined by y=6-x is an isosceles right triangle with leg lengths of 6 and a hypotenuse length of . The area of the triangle is , which is 18.
 Quadratic_Equations/369361: Use the quadratic formula to solve the equation. 1 solutions Answer 263172 by acalgebra(30)   on 2010-11-10 21:27:26 (Show Source): You can put this solution on YOUR website!First, put the equation in standard form: Then, note a, b, and c: , , and Now, put a, b, and c into the quadratic equation: Then, solve: Because there is a square root of a negative number, there are no real number solutions.
 Mixture_Word_Problems/369367: If there were 60 problems on a test and Betty got 90% of the problems correct, how many problems did she answer correctly?1 solutions Answer 263168 by acalgebra(30)   on 2010-11-10 21:18:51 (Show Source):
 test/369328: Factor this expression completely: 1 solutions Answer 263165 by acalgebra(30)   on 2010-11-10 21:16:19 (Show Source):
 Graphs/369357: What would the graph be for: x + y = 2?1 solutions Answer 263162 by acalgebra(30)   on 2010-11-10 21:11:39 (Show Source): You can put this solution on YOUR website!Use the graphing calculator at http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html You'll need to copy and paste, because I can't type a link here. Sorry!
 Graphs/369358: What would the graph be for: y = x + 2?1 solutions Answer 263161 by acalgebra(30)   on 2010-11-10 21:11:21 (Show Source): You can put this solution on YOUR website!Use the graphing calculator at http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html You'll need to copy and paste, because I can't type a link here. Sorry!
 Triangles/369334: An isosceles right triangle has two 45° angles. The sides opposite those angles are equal in length Find the length of each of the equal sides if the length of the hypotenuse is 1.1 solutions Answer 263157 by acalgebra(30)   on 2010-11-10 21:08:30 (Show Source): You can put this solution on YOUR website!The hypotenuse is c, and the legs are a and b:
 Rectangles/369293: The length of a rectangle is 2 less than 3 times the width. If the perimeter is 68, what is the length of the rectangle?1 solutions Answer 263128 by acalgebra(30)   on 2010-11-10 20:02:17 (Show Source): You can put this solution on YOUR website!------ 3w-2=l perimeter=2(l+w) 2([3w-2]+w) 2(3w-2+w) 2(4w-2) 8w-4 perimeter=68 8w-4=68 8w=72 w=9 3w-2=l 3(9)-2=l 27-2=l 25=l l=25 So the length is 25.
 Linear_Equations_And_Systems_Word_Problems/369275: A bus traveled a distance of 180 km. How long will it take for a bus to make this trip if it has a speed of 45km/h?1 solutions Answer 263123 by acalgebra(30)   on 2010-11-10 19:51:33 (Show Source): You can put this solution on YOUR website! It would take 4 hours for the bus to make a 180 km trip at a speed of 45 km/h.
 Polynomials-and-rational-expressions/369268: (x^2y)^41 solutions Answer 263121 by acalgebra(30)   on 2010-11-10 19:47:31 (Show Source): You can put this solution on YOUR website! x^8y
 Triangles/369257: A right triangle has legs of 5 and x+2 and a hypotenuse of length x+3. What is the perimeter of the triangle?1 solutions Answer 263117 by acalgebra(30)   on 2010-11-10 19:41:42 (Show Source): You can put this solution on YOUR website!This right triangle uses the lengths of a common Pythagorean triple: 5, 12, and 13. x=10, so the perimeter is: 5+(10)+2+(10)+3 15+12+3 15+15 30 perimeter=30 Remember to include units in your answer!
 Geometric_formulas/369218: Prove the Right Angle Theorem: All right angles are congruent. Given: Angle 1 and Angle 2 are right angles. Prove: Angle 1 is congruent to angle 21 solutions Answer 263114 by acalgebra(30)   on 2010-11-10 19:30:53 (Show Source): You can put this solution on YOUR website!A right angle measures 90°, so by definition, both Angle 1 and Angle 2 have a measure of 90°. Angles that have the same measure are congruent, so Angle 1 is congruent to Angle 2.
 Graphs/369252: is there an easier way to graph linear equations 1 solutions Answer 263110 by acalgebra(30)   on 2010-11-10 19:27:40 (Show Source): You can put this solution on YOUR website!Yes. Use a graphing calculator. You can find an excellent one here: http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html You'll have to copy and paste into your browser, because I can't create a link in these text boxes. Sorry!
 Geometry_proofs/368763: Prove that midpoints of a quadrilateral form a parallelogram.1 solutions Answer 263108 by acalgebra(30)   on 2010-11-10 19:25:48 (Show Source): You can put this solution on YOUR website!The type of quadrilateral that is formed can either be a rhombus, a rectangle, or a square, but it will always be a parallelogram. This is because when the midpoints are connected to form the sides of the midpoint-verticed figure, each side of the original figure is bisected. Each newly formed side will be parallel to a diagonal of the original. Two of the newly formed sides are parallel to the same diagonal and therefore are parallel to each other. Along with the other two sides of the midpoint-verticed that are parallel to the other diagonal of the original, a parallelogram is formed.
 Graphs/369200: x+6=y y-x=-2 Are the lines parallel? 1 solutions Answer 263105 by acalgebra(30)   on 2010-11-10 19:19:34 (Show Source): You can put this solution on YOUR website!Take the first equation and switch the side, like this: Now, take the second equation and add x to each side: Because the slopes (coefficients of x) are the same, the lines are parallel.
 test/369209: Using each number only once, use 2,4,6 & 8 to write an expression with two proper fractions that have the largest possible sum.1 solutions Answer 263103 by acalgebra(30)   on 2010-11-10 19:16:02 (Show Source):
 Square-cubic-other-roots/369239: How to find the square root of 4x^10y^21 solutions Answer 263101 by acalgebra(30)   on 2010-11-10 19:13:22 (Show Source): You can put this solution on YOUR website!Well, 4x^10y^2 is a square, so simply get rid of the last exponent, like this: 4x^10y. There ya go!
 Problems-with-consecutive-odd-even-integers/369240: The sum of the least and greatest of three consecutive integers is equal to 35 plus the middle integer, what are the integers? 1 solutions Answer 263098 by acalgebra(30)   on 2010-11-10 19:11:00 (Show Source): You can put this solution on YOUR website!-------- x+x+2=35+x+1 2x+2=36+x 2x=34+x x=34 The three consecutive integers are 34, 35, and 36.
 Linear_Algebra/369229: What is the equation/function for if you enter 3 and the answer is 8 and you enter 10 and the answer is 29 and then you enter 20 and the answer is 59? How do I figure out the equation?1 solutions Answer 263091 by acalgebra(30)   on 2010-11-10 18:53:46 (Show Source): You can put this solution on YOUR website!3 >> 8 10 >> 29 20 >> 59 There is no set way to solve this, but here is the function: [output]=3[input]-1
 Systems-of-equations/369231: show me how to work out this equation. 5-3x+x=191 solutions Answer 263089 by acalgebra(30)   on 2010-11-10 18:51:12 (Show Source): You can put this solution on YOUR website!5-3x+x=19 5-4x=19 5=4x+19 -14=4x =x =x
 Numbers_Word_Problems/369226: A new high school has just been opened, with an enrollment of 1000 students. The school has 1000 lockers, numbered 1 to 1000, to accommodate them. On the first day of school, all 1000 lockers are closed and all 1000 students are outside waiting to be let into the building. The first student enters and opens all of the lockers. The second student follows and closes every second locker, beginning with the second locker. The third student enters the school and reverses every third locker beginning with locker 3 (e.g., if the locker is closed it is opened and vice versa). This procedure is continued until all 1000 students have passed by all the lockers. When they finish, which lockers will be open?1 solutions Answer 263087 by acalgebra(30)   on 2010-11-10 18:45:24 (Show Source): You can put this solution on YOUR website!The square numbered lockers (1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, and 961).