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# Recent problems solved by 'Alan3354'

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 Linear_Algebra/271696: Solve the following 3 by 3 system algebraically. x+y+2z=0 1/4x-1/4y+1/8z=1 3/2x+y+1/2z=11 solutions Answer 198931 by Alan3354(30959)   on 2010-02-19 16:05:27 (Show Source): You can put this solution on YOUR website!I'm not sure what "algebraically" means. ------------- x+y+2z=0 1/4x-1/4y+1/8z=1 --> 2x-2y+z = 8 3/2x+y+1/2z=1 --> 3x+2y+z = 2 --------------- x + y+2z = 0 2x-2y +z = 8 3x+2y +z = 2 Eliminate y ------------ Add eqns 2 and 3 2x-2y +z = 8 3x+2y +z = 2 ------------- Add 5x + 2z = 10 eqn A -------------- Add 2x 1st eqn to 2nd 2x+2y+4z = 0 2x-2y +z = 8 ------------Add 4x + 5z = 8 eqn B 20x +25z = 40 eqn B x 5 20x + 8z = 40 eqn A x 4 ------------------------ Subtract 17z = 0 z = 0 ------ x = 2 ----- y = -2
 Equations/271652: can you teach me how to solve parallel and perpendicular lines please?1 solutions Answer 198916 by Alan3354(30959)   on 2010-02-19 14:47:22 (Show Source): You can put this solution on YOUR website!Here are 2 examples: Given 2 points example. Find the equation of the line thru the points (2,1) and (3,5) --------------------- This is a 2 step process. First find the slope of the line thru the points. slope, m = diffy/diffx m = (5-1)/(3-2) m = 4 --------- Now use y = mx + b with either point to find b, the y-intercept. y = mx + b 5 = 4*3 + b b = -7 ------- y = mx + b y = 4x - 7 is the answer. ------------------------ For further assistance, or to check your work, email me via the thank you note. ---------------------- A line and a point example. Write in standard form the eqation of a line that satisfies the given conditions. Perpendicular to 9x+3y=36, through (1,2) ----------------- Find the slope of the line. Do that by putting the equation in slope-intercept form, y = mx + b. That means solve for y. 9x+3y = 36 3y= - 9x + 36 y = -3x + 13 The slope, m = -3 ------------------ The slope of lines parallel have the same slope. The slope of lines perpendicular is the negative inverse, m = +1/3 ---------------- Use y = mx + b and the point (1,2) to find b. 2 = (1/3)*1 + b b = 5/3 The equation is y = (1/3)x + 5/3 (slope-intercept form) x - 3y = -5 (standard form) ------------------------ For further assistance, or to check your work, email me via the thank you note.
 Triangles/271703: If you know the measurements of two sides of and angle how do you find the missing measurement1 solutions Answer 198912 by Alan3354(30959)   on 2010-02-19 14:30:20 (Show Source): You can put this solution on YOUR website!If the angle is between the 2 known sides, use the Cosine Law. If not, use the Law of Sines.
 Graphs/271763: 8x-4y=12 4y-8x=-12 What is the solution of the system? a. no solution b. infinitely many solutions c. A point Is the system consistent or inconsistent? Are the equations dependent or independent?1 solutions Answer 198906 by Alan3354(30959)   on 2010-02-19 14:06:32 (Show Source): You can put this solution on YOUR website!It's the same equation twice, multiplied by -1. --> dependent infinite solutions consistent
 Polynomials-and-rational-expressions/271733: Solve the system of equaations by graphing. x + y = 4, x + y = -41 solutions Answer 198877 by Alan3354(30959)   on 2010-02-19 11:41:30 (Show Source): You can put this solution on YOUR website!Notice both have x + y on one side. The graphs are 2 parallel lines, no intersection, no solution.
 Linear-equations/271687: What is the slope of the line determined by the coordinates (2, 3) and (-6, -4)?1 solutions Answer 198848 by Alan3354(30959)   on 2010-02-19 09:19:42 (Show Source): You can put this solution on YOUR website!What is the slope of the line determined by the coordinates (2, 3) and (-6, -4)? ------------- Slope, m = diffy/diffx m = (-4-3)/(-6-2) = -7/-8 m = 7/8
 Quadratic_Equations/270067: Combine like terms where possible. 8y^4 - 3y^4 1 solutions Answer 198792 by Alan3354(30959)   on 2010-02-18 22:07:07 (Show Source): You can put this solution on YOUR website!= 5y^4
 Numbers_Word_Problems/269933: What is the smallest perfect number?1 solutions Answer 198790 by Alan3354(30959)   on 2010-02-18 22:04:17 (Show Source): You can put this solution on YOUR website!I think that means it's the sum of its factors. 6 = 1 + 2 + 3
 Rate-of-work-word-problems/270075: If it take 5 workers 6 hours to paint an office, how long does it take 8 workers to paint the same office assuming all the workers work at the same rate?1 solutions Answer 198789 by Alan3354(30959)   on 2010-02-18 22:03:36 (Show Source): You can put this solution on YOUR website!5 workers * 6 hours = 30 man-hours of work 30 man-hours/8 men = 15/4 hours = 3.75 hours
 Graphs/270083: Graph the following linear equation by finding x- and y-intercepts. 2x – 4y = -8 Describe the graph verbally by showing the calculation of the two intercepts and giving the ordered pair for each. Describe the line you have graphed. The description should include the quadrants through which the line passes, and the direction the line leans (forward or backward). 1 solutions Answer 198788 by Alan3354(30959)   on 2010-02-18 22:02:00 (Show Source): You can put this solution on YOUR website!Graph the following linear equation by finding x- and y-intercepts. 2x – 4y = -8 ------------------- set x = 0 to find the y-intercepts, and vice versa x - 2y = -4 (I reduced it) x = 0: -2y = -4 y = 2 --> (0,2) y-intercept ------------------ y=0: x = -4 --> (-4,0) x-intercept Draw a line thru the 2 points
 Travel_Word_Problems/271556: the sum of four consecutive even integers is 308. Write and solve an equation to find the integers. Show all work.1 solutions Answer 198783 by Alan3354(30959)   on 2010-02-18 21:48:27 (Show Source): You can put this solution on YOUR website!308/4 = 77, which is in the center of the numbers. --> 74, 76, 78 and 80 ---------------------- There are other ways to do it that take more time and more space.
 Linear-equations/271479: state the slope of a line parallel to x=2 1 solutions Answer 198782 by Alan3354(30959)   on 2010-02-18 21:46:38 (Show Source): You can put this solution on YOUR website!x=2 is "vertical", parallel to the y-axis. All lines parallel to it have the same slope, = infinite, or undefined.
 absolute-value/271574: I need help with 8 and the radius is 3 so we have to find the area 1 solutions Answer 198779 by Alan3354(30959)   on 2010-02-18 21:44:35 (Show Source): You can put this solution on YOUR website!8 what? What sort of shape is it?
 Polynomials-and-rational-expressions/271535: Could I have help with this problem please. The speed of train A is 16 mph's slower than the speed of train B. Train A travels 200 miles in the same time it takes train B to travel 280 miles. Find the speed of each train. Speed of Train A is ? Speed of Train B is ?1 solutions Answer 198764 by Alan3354(30959)   on 2010-02-18 21:01:43 (Show Source): You can put this solution on YOUR website!diff in distance = 80 miles diff in speed = 16 mph 80/16 = 5 hours A = 200/5 = 40 mph B = 280/5 = 56 mph
 Volume/271525: find the square root Use the square root key on your calculator if necesary Round your answer to the thousandth place square root 5 and square root 96 thanks1 solutions Answer 198757 by Alan3354(30959)   on 2010-02-18 20:37:40 (Show Source): You can put this solution on YOUR website! ------------------------ Do you not have a calculator? There's one on Windows click Start, All Programs, Accessories, Calculator
 Polynomials-and-rational-expressions/271476: how do i simplify 10-(-3+6)?1 solutions Answer 198755 by Alan3354(30959)   on 2010-02-18 20:20:24 (Show Source): You can put this solution on YOUR website!10-(-3+6)? = 10 - (3) = 7
 Equations/271514: (2x+9)/(3x-1) Show me how to simplify this equation. Thanks.1 solutions Answer 198754 by Alan3354(30959)   on 2010-02-18 20:19:11 (Show Source): You can put this solution on YOUR website!No simplification is possible. Ignore tobias, he's wrong most of the time.
 Polynomials-and-rational-expressions/271502: What is the slope of a binomial 2x+3(4-2)1 solutions Answer 198753 by Alan3354(30959)   on 2010-02-18 20:15:04 (Show Source): You can put this solution on YOUR website!A binomial does not have a slope.
 Triangles/271509: Can a triangle have the following measures:4,9, and 8?1 solutions Answer 198752 by Alan3354(30959)   on 2010-02-18 20:14:10 (Show Source): You can put this solution on YOUR website!Yes, it can have those sides. ----------------------------- If any side is >= the sum of the other 2 sides, or <= the difference of the other 2 sides, it's not possible to form a triangle. ----------------- I can only guess that tobias checked to see it 4, 9 and 8 made a right triangle. They don't, but they can make a triangle.
 Travel_Word_Problems/270967: a plane is flying at 174 miles per hour with a heading of 50.5 degrees from due north. the wind is blowing a constant 23 miles per hour at 140.5 degrees from due north. find the ground speed and true course of the plane. 1 solutions Answer 198750 by Alan3354(30959)   on 2010-02-18 20:13:04 (Show Source): You can put this solution on YOUR website!Is the plane flying a heading of 50.5º? If it's 50.5 "from due north", it could be 309.5º --------------- Wind direction in aviation is the direction the wind is coming from. Is this wind from 140.5º? ------------------- The people writing textbooks should stick to subjects they know. Headings are given to the whole degree, no 50.5 degs ---------------------- I'll solve this, using that plane heading of 50.5, and the wind direction of 140.5 (coming from 140.5). ----------------- Notice they're 90º apart, so it's a right triangle with sides of 174 and 23. The resultang groundspeed is the hypotenuse: g = 175.5 mph -------------- The angle between the plane's heading and it course is the arctan(23/174) =~ 7.53º If the wind direction uses from, that makes the ground track 43º If the wind direction uses to, it's 58º --------------------------------- PS miles per hour is not used in aviation, it's knots. It would be the "wind is 140 at 20 knots"
 Graphs/271371: what is the x-intercept of the line 5x-3y=-151 solutions Answer 198701 by Alan3354(30959)   on 2010-02-18 16:58:34 (Show Source): You can put this solution on YOUR website!what is the x-intercept of the line 5x-3y=-15 It's the point where the line crosses the x-axis. That means y = 0. -------- 5x-3y = -15 5x-3*0 = -15 5x = -15 x = -3 The point is (-3,0)
 Rectangles/271379: explain (to a 5th grader) how to find the area of a rectangle where 1 side = 1m and the other =34cm???? 1 solutions Answer 198700 by Alan3354(30959)   on 2010-02-18 16:56:38 (Show Source): You can put this solution on YOUR website!explain (to a 5th grader) how to find the area of a rectangle where 1 side = 1m and the other =34cm? ------------------------ The area is the product of the 2 sides, or length times width. Which side is called length and width doesn't matter. The 2 sides must have the same units. In this case, either both meters or both cm. 1 meter = 100 cm The area is 34 cm * 100 cm = 3400 square cm --------------------- Or, 34 cm = 0.34 meters The area is 1 m * 0.34 m = 0.34 square meters Both are correct. I prefer 3400 sq cm
 Quadratic_Equations/271355: solve 8/z=9/z-1/z1 solutions Answer 198683 by Alan3354(30959)   on 2010-02-18 16:09:36 (Show Source): You can put this solution on YOUR website!8/z=9/z-1/z ---------- 8/z = 8/z z <> 0, all other values are valid
 Triangles/271194: how can i work out the coordinates if i got a angle of 25 and one side 601 solutions Answer 198584 by Alan3354(30959)   on 2010-02-18 09:34:10 (Show Source): You can put this solution on YOUR website!That's not enough info. Is there a drawing?
 Money_Word_Problems/271181: 1. The backyard can be mapped onto a Cartesian coordinate (x,y) graph. Using the various items described in the yard below, answer the following questions. a) A water line is given by the equation: Suppose you want to put a pink flamingo lawn ornament in your backyard, but you want to avoid placing it directly over the water line, in case you need to excavate the line for repairs in the future. Could you place it at the point ? Demonstrate how you arrived at your answer with the detail calculations. 1 solutions Answer 198581 by Alan3354(30959)   on 2010-02-18 09:27:57 (Show Source): You can put this solution on YOUR website!I don't see the equation.
 Travel_Word_Problems/271183: 10.6 secs1 solutions Answer 198578 by Alan3354(30959)   on 2010-02-18 09:22:41 (Show Source): You can put this solution on YOUR website!They approach at the sum, 110 mph. 110 mph = 110*5280 ft/hour = 110*5280/3600 ft/sec t = 500/(110*5280/3600) seconds t =~ 3.099 seconds ------------------ 15 mph = 22 ft/sec If you remember that, you can shorten the time needed to do a lot of problems.
 Volume/271176: AN OVERSIZED CONTAINER IS 3m. IT'S DIAMETER IS 2m.WHAT IS THE VOLUME?1 solutions Answer 198573 by Alan3354(30959)   on 2010-02-18 09:11:13 (Show Source): You can put this solution on YOUR website!If it's a cylinder, radius 1 meter, h = 3 meters. ----------------- IT'S = IT IS. IT IS DIAMETER... is not good.
 Distributive-associative-commutative-properties/271089: I am trying to factor the combination x^3-3x^2-x+3 1 solutions Answer 198485 by Alan3354(30959)   on 2010-02-17 22:28:07 (Show Source): You can put this solution on YOUR website!The 3 is a clue, its only factors are 1 and 3 (plus or minus). See if 3 or -3 is a root.
 logarithm/270973: e x+ e -x=51 solutions Answer 198483 by Alan3354(30959)   on 2010-02-17 22:11:09 (Show Source): You can put this solution on YOUR website!If you mean e^x + e^-x = 5 then x = inv hyperbolic cosine (2.5) x =~ 1.566799 (via calculator) ------------- The long way e^x + e^-x = 5 Multiply by e^x e^2x + 1 = 5e^x e^2x - 5e^x + 1 = 0 It's a quadratic in e^x e^x = (1/2)*(5 ± sqrt(21)) e^x =~ 4.7912878, 0.2087 x = log(4.79..., 0.2087) x = ± 1.566799
 Trigonometry-basics/271061: Give the exact value of theta in degrees rounded to the nearest tenth if sin theta=.3 and 901 solutions Answer 198477 by Alan3354(30959)   on 2010-02-17 21:41:11 (Show Source): You can put this solution on YOUR website!It can't be both an exact value and rounded. theta = 162.5º
 percentage/271065: find the percent of change. tell whether the change is an increase or decrease. round to the nearest tenth of a percent. from 87 to 108 1 solutions Answer 198475 by Alan3354(30959)   on 2010-02-17 21:39:10 (Show Source): You can put this solution on YOUR website!from 87 to 108 Change = 21 21/87 =~ 0.2412 increase = 24.1%