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 Linear-systems/264432: how do i slove this system 3x+5y=-3 10y-2z=2 x=-z1 solutions Answer 194686 by Alan3354(30993)   on 2010-02-02 11:12:52 (Show Source): You can put this solution on YOUR website!how do i slove this system 3x+5y=-3 10y-2z=2 x=-z ------------ Sub -x for z in the 2nd eqn, then it's a 2 eqn system. 3x+5y=-3 --> 6x+10y=-6 10y+2x=2 -------- 6x+10y=-6 2x+10y=2 -------- Subtract 4x = -8 -------- Take it from there.
 Polynomials-and-rational-expressions/264433: multiply. (a+1/3)(a+1/4) simplify answer. Please help....1 solutions Answer 194685 by Alan3354(30993)   on 2010-02-02 11:04:56 (Show Source): You can put this solution on YOUR website!(a+1/3)(a+1/4) = a*(a + 1/4) + (1/3)*(a + 1/4) = = ------------- Or
 Linear-equations/264426: How do you solve 2y=5x-1 and x=y+2? (Solve by graphing) How do you solve x=5 and 3y=2x-1 (Solve by graphing) How do you solve y=4 and 2x-y=1 (Solve by graphing) How do you solve y-5x=10 and x-5y=10 (Solve by graphing) i don't understand how to do these!:(1 solutions Answer 194681 by Alan3354(30993)   on 2010-02-02 10:16:04 (Show Source): You can put this solution on YOUR website!All of these are linear equations, so their graphs are straight lines. A straight needs only 2 points to graph it. ---------------------- How do you solve 2y=5x-1 and x=y+2? (Solve by graphing) 2y = 5x-1 y = (5/2)x - 1/2 Pick 2 values of x and find y x...y 1 2 --> (1,2) 3...7 --> (3,7) Plot those 2 points and draw a line thru them. Do the same for x=y+2 y = -x+2 Find 2 points, plot them draw the line. Where the 2 lines intersect is the solution. ------------------------- How do you solve x=5 and 3y=2x-1 (Solve by graphing) This one is easier as x=5 is a vertical line thru (5,0). 3y=2x-1 y = (2/3)x - 1/3 Do it like the 1st one. ------------------------- How do you solve y=4 and 2x-y=1 (Solve by graphing) How do you solve y-5x=10 and x-5y=10 (Solve by graphing) -------------- email me via the thank you note for help, or to check your work.
 Quadratic_Equations/264313: for each quadriatic function(a) find the vertex, the axis of symmetry, anf the maximum or minimum function value and (b) graph the function. f(x) = 4Xsquare + 16x +131 solutions Answer 194679 by Alan3354(30993)   on 2010-02-02 10:03:48 (Show Source): You can put this solution on YOUR website!a) find the vertex, the axis of symmetry, anf the maximum or minimum function value The axis of symmetry is x = -b/2a x = -16/8 = -2 x = -2 is the axis ---------- The minimum is at the vertex which is on the axis of symmetry f(-2) = 16 -32 + 13 = -3 Minimum at (-2,-3) Vertex at (-2,-3) ---------------- and (b) graph the function. f(x) = 4x^2 + 16x +13 dl the FREE graph software at http://www.padowan.dk.com
 Coordinate-system/264409: Find the slope of the line that passes through the given points (-2, 10), (6, 2) 1 solutions Answer 194675 by Alan3354(30993)   on 2010-02-02 09:39:31 (Show Source): You can put this solution on YOUR website!Do it like this: 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.
 Rate-of-work-word-problems/264416: It takes Mike 6 hours to paint a house. It takes Jim 4 hours to paint the same house. How long will it take them to paint the house together? 1 solutions Answer 194673 by Alan3354(30993)   on 2010-02-02 09:37:59 (Show Source): You can put this solution on YOUR website!Mike does 1/6 house per hour. Jim does 1/4 house per hour. Together, 1/6 + 1/4 = 5/12 per hour --> 12/5 = 2.4 hours together. ------------------------ Use the shortcut, product/sum 6*4/(6+4) = 24/10 = 2.4
 Problems-with-consecutive-odd-even-integers/247981: This is a quadratic word problem. A garden is to be laid out in such a way that 3 rectangular sections are created by fences. If the total amount of fencing available is 200 ft., find the dimensions that will maximize the total area. 1 solutions Answer 194672 by Alan3354(30993)   on 2010-02-02 09:35:04 (Show Source): You can put this solution on YOUR website!A garden is to be laid out in such a way that 3 rectangular sections are created by fences. If the total amount of fencing available is 200 ft., find the dimensions that will maximize the total area. --------------- I don't know why Tiff is here if she can't offer assistance. Anyway, The 200 feet of fence will be in 6 pieces. Call W the width of 2 pieces, and L the length of the 4 pieces. 2L + 4W = 200 The total area is L*W 2L + 4W = 200 --> L + 2W = 100 --> L = 100 - 2W Sub for L in the 2nd eqn Area = L*W Area = W*(100 - 2W) = 100W - 2W^2 Find W to maximize the area It's a parabola, and the max is at the vertex. The vertex is as W = -b/2a = -100/-4 W = 25 feet --------- L = 50 feet
 Rate-of-work-word-problems/264414: If a painter completes an entire house in 2x hours, then at what rate is she painting?1 solutions Answer 194670 by Alan3354(30993)   on 2010-02-02 09:27:03 (Show Source): You can put this solution on YOUR website!1/(2x) houses per hour, or 2x hours per house
 Linear-systems/264372: x-2y=-1 -x+5y=41 solutions Answer 194664 by Alan3354(30993)   on 2010-02-02 09:14:04 (Show Source): You can put this solution on YOUR website! x-2y=-1 -x+5y=4 ---------- Add them 3y = 3 Take it from there.
 Geometry_Word_Problems/264407: An ice cube that measures 4.5 centimeters on each side contains how many cubic centimeters of ice?1 solutions Answer 194662 by Alan3354(30993)   on 2010-02-02 09:12:36 (Show Source): You can put this solution on YOUR website!The volume of a cube is s^3
Graphs/264395: I am trying to solve for x (to find the x intercept) in the equation
y=(-1/2)x^2+2x+10. I got the y intercept (10) by "letting x=0", but when I try to do the same, "letting y=0", I get confused due to the fraction and exponent and do not know how to isolate the x. Can someone please explain this to me. Thank you!
1 solutions

Answer 194651 by Alan3354(30993)   on 2010-02-02 08:45:27 (Show Source):
You can put this solution on YOUR website!
y=(-1/2)x^2+2x+10
(-1/2)x^2+2x+10 = 0
Multiply by -2
x^2 - 4x - 20 = 0
 Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=96 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 6.89897948556636, -2.89897948556636. Here's your graph:

-----------
x = 2 +/- 2sqrt(3)

 Travel_Word_Problems/264374: if i am travelling @ 100 km/ph what distance will i Travel per second?1 solutions Answer 194647 by Alan3354(30993)   on 2010-02-02 08:31:25 (Show Source): You can put this solution on YOUR website!Is that 100 km per hour? If so, = 100000 meters/hour = 100000 m/3600 sec = 250/9 m/sec =~ 27.8 m/sec
 Linear-equations/263599: How do I find an equation of the line that contains the point (1,0) and is perpediclar to 2x+y=-4? 1 solutions Answer 194646 by Alan3354(30993)   on 2010-02-02 08:25:20 (Show Source): You can put this solution on YOUR website!Do it like this: 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.
 Linear-equations/264308: I am doing a problem on my math homework that says Write equation of line that passes through (8,-6) and is perpendicular to the line 6x - 3y = 6 Write answer in slope intercept form. How do I do that?1 solutions Answer 194595 by Alan3354(30993)   on 2010-02-01 22:12:42 (Show Source): You can put this solution on YOUR website!Do it like this one: 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.
 Polygons/264291: find the measure of one interior angle in each regular ploygon.Round to the nearest tenth if necessary. 7.pentagon 8.hexagon 9.24-gon 1 solutions Answer 194592 by Alan3354(30993)   on 2010-02-01 21:37:29 (Show Source): You can put this solution on YOUR website!find the measure of one interior angle in each regular ploygon.Round to the nearest tenth if necessary. 7.pentagon 8.hexagon 9.24-gon ------------------- The total of the interior angles in any polygon of n sides is: 180*(n-2) Each angle is 180*(n-2)/n ------------- You can do the arithmetic 7. n = 5 8. n = 6 9. n = 24
 Volume/264159: The volume of a cube with sides of length s is given by V = s^3. Find the rate of change of the volume with respect to s when s = 2 centimeters. V '(2) = _____ cm2 i found the derivative to be V'= 3s^2 so V'(2)= 36?1 solutions Answer 194591 by Alan3354(30993)   on 2010-02-01 21:34:03 (Show Source): You can put this solution on YOUR website!The volume of a cube with sides of length s is given by V = s^3. Find the rate of change of the volume with respect to s when s = 2 centimeters. V '(2) = _____ cm2 i found the derivative to be V'= 3s^2 so V'(2)= 36? -------------- Your method is good, but V'(2) = 3*2^2 = 12
 Linear_Equations_And_Systems_Word_Problems/264203: I need help converting to scientific notation the following... Use an x to indicate multiplication, but do not include spaces in your response. Don;t forget to use the ^ sign to indicate exponents.... 71500 Can someone help me please ? thank you!1 solutions Answer 194589 by Alan3354(30993)   on 2010-02-01 21:30:25 (Show Source): You can put this solution on YOUR website!71500 = 7.15*10^4 Using x for multiplication is not a good idea, x is often used as a variable. Use the asterisk instead. Even better, use 7.15E4
 Travel_Word_Problems/264288: A man travels 7 mi. due east, and then 4 mi. due North. How far is he from his starting point?1 solutions Answer 194588 by Alan3354(30993)   on 2010-02-01 21:28:47 (Show Source): You can put this solution on YOUR website!The distance is the hypotenuse of a right triangle with legs of 7 and 4. Use Pythagoras.
 Linear-systems/264282: how do you solve the system by substitution? 3X+2Y=11 x=13-3y1 solutions Answer 194586 by Alan3354(30993)   on 2010-02-01 21:27:33 (Show Source): You can put this solution on YOUR website!The 2nd eqn is already in terms of x. Sub for x into the 1st eqn.
 Surface-area/245118: 1. You are given 200 ft of fencing to enclose a rectangular garden plot. You can determine whatever dimensions you want for the rectangle as long as the perimeter is 200 ft. Will the garden always have the same area? Give examples. Is there any shape that could have a 200 ft perimeter and have more area than the rectangle? 1 solutions Answer 194584 by Alan3354(30993)   on 2010-02-01 21:26:23 (Show Source): You can put this solution on YOUR website!If it's a rectangle, the square will have the most area. ------------- If all shapes are considered, it's a circle.
 Proportions/261127: EXPRESS EACH RATE IN PER UNIT FORM solve and explain question if johnny drives at an average speed of 40 miles/hr, how long will it take for johnny to go 50 miles1 solutions Answer 194583 by Alan3354(30993)   on 2010-02-01 21:24:34 (Show Source): You can put this solution on YOUR website!There are only 2 numbers. What would you try?
 Evaluation_Word_Problems/264285: how do you turn a word problem to a algebraic form1 solutions Answer 194580 by Alan3354(30993)   on 2010-02-01 21:23:24 (Show Source): You can put this solution on YOUR website!You write down what it says.
 Polynomials-and-rational-expressions/264286: solve by factoring: x^2-18x+81=01 solutions Answer 194579 by Alan3354(30993)   on 2010-02-01 21:22:55 (Show Source): You can put this solution on YOUR website!81 = 9^2 Try that.
 Trigonometry-basics/264223: The pendulum of a clock swings through an angle of 2.5 radians as its tip travels through an arc of 50 centimeters. Find the lenght of the pendulum, in centimeters. 1 solutions Answer 194574 by Alan3354(30993)   on 2010-02-01 21:00:01 (Show Source): You can put this solution on YOUR website!The pendulum of a clock swings through an angle of 2.5 radians as its tip travels through an arc of 50 centimeters. Find the lenght of the pendulum, in centimeters. r = s/angle r = 50/2.5 = 20 cm ------------------------ Clock pendulums swing ±8º degrees or less, which is an included angle of ~0.28 radians. Have the authors of the books ever seen a clock?
 Average/264239: 1562 miles is equal how many hours?1 solutions Answer 194570 by Alan3354(30993)   on 2010-02-01 20:54:21 (Show Source): You can put this solution on YOUR website!As many as you like.
 Linear_Equations_And_Systems_Word_Problems/264257: With a tail wind, a helicopter traveled 300 miles in 1hour and 40 min. The return trip against the same wind took 20 min longer. Find the wind speed and also the air speed of the helicopter.1 solutions Answer 194568 by Alan3354(30993)   on 2010-02-01 20:53:15 (Show Source): You can put this solution on YOUR website!With a tail wind, a helicopter traveled 300 miles in 1hour and 40 min. The return trip against the same wind took 20 min longer. Find the wind speed and also the air speed of the helicopter. --------------- Downwind ground speed was 300/(5/3) = 180 mph Upwind ground speed was 300/2 = 150 mph The airspeed is the average, (180+150)/2 = 165 mph The windspeed is 15 mph --------------- PS My helicopter didn't go that fast.
 Trigonometry-basics/264225: the two legs of a right triangle have lenghts of 15 inches and 8 inches. Find the measure of the smaller acute angle. I tried to do tan=opp/adj, is it on the right path?1 solutions Answer 194555 by Alan3354(30993)   on 2010-02-01 20:20:02 (Show Source): You can put this solution on YOUR website!the two legs of a right triangle have lenghts of 15 inches and 8 inches. Find the measure of the smaller acute angle. ------------------- That's right, it's tan = 8/15 Angle =~ 28.07º
 Geometric_formulas/264231: The perimeter of a triangle is 20 cm. If all the sides are tripled, the new perimeter will be _____ cm.1 solutions Answer 194553 by Alan3354(30993)   on 2010-02-01 20:18:03 (Show Source): You can put this solution on YOUR website!20*3 cm
 Trigonometry-basics/264227: What is the number of degrees in an angle whose radian measure is 7pi/12?1 solutions Answer 194552 by Alan3354(30993)   on 2010-02-01 20:17:29 (Show Source): You can put this solution on YOUR website!Multiply radians by 180/pi to get degrees. 7pi/12 * 180/pi = 1260/12 = 105º
 Linear-systems/264229: Hi there, I was wondering whether or not there is a method to solving this called a graphing method.1 solutions Answer 194550 by Alan3354(30993)   on 2010-02-01 20:13:11 (Show Source): You can put this solution on YOUR website!To solving what?
 Exponents-negative-and-fractional/264165: How do u simplify 7s^0t^-5 over 2^-1m^2?1 solutions Answer 194546 by Alan3354(30993)   on 2010-02-01 20:05:37 (Show Source): You can put this solution on YOUR website!How do u simplify 7s^0t^-5 over 2^-1m^2? --------------- s^0 = 1. Anything to the power of zero (except infinity) is 1. = Multiply NUM and DEN by 2 = Multiply NUM and DEN by t^5 =