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 Equations/258057: Please answer this question. An object is launched upward at 45ft/Sec from a platform that is 40 feet high. What is the objects maximum height if the equation of the height(h) in terms of time (t) of the object is given by h(t) = -16t^2 + 45t + 40? 1 solutions Answer 189907 by Greenfinch(383)   on 2010-01-18 14:46:09 (Show Source): You can put this solution on YOUR website!h = 16t^2 + 45t + 40 dh/dt = 32t + 45. When dh/dt = 0, h is a stationary point this is at t = 45/32 = 1.406 seconds so h = 32 x(1.406^2 + 45x 1.406 + 40 = 63.25 + 63.27 + 40 = 166.52 feet
Quadratic_Equations/258053: Determine the number of solutions of 2x^2 - 3x - 5 = 0
1 solutions

Answer 189900 by Greenfinch(383)   on 2010-01-18 14:35:33 (Show Source):
You can put this solution on YOUR website!
The discriminant is 9 + 4x4x5 = 49
So 2 answers to 2X^2 - 3x -5 =0
 Solved by pluggable solver: SOLVE quadratic equation with variable 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=49 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 2.5, -1. Here's your graph:

Quadratic_Equations/258000: What is the points of intersection of these equations
x-2y-8=0
x^2=y^2-12x+6y+29=0
1 solutions

Answer 189894 by Greenfinch(383)   on 2010-01-18 14:31:05 (Show Source):
You can put this solution on YOUR website!
Second equation is a circle, so reorganise it
(x^2 + 12 x) - (y^2 - 6y)+ 29 = 0 and then complete the square
(x^2 + 12x + 36) - ( y^2 - 6y + 9) - 45 + 29 = 0 which becomes
(x + 6)^2 - (y - 3)^2 = 4^2 which is a circle centre at -6, 3 and radius 4
other equation is y = (1/2)x - 4 or x = 2y + 8
Probably solve for y is easier
(2y + 14)^2 - (y - 3)^2 = 4^2
4y^2 + 56 y + 196 -(y^2 - 6y +9) = 16
3y^2 + 62y + 187 = 16
3y^2 + 62y + 171 = 0
 Solved by pluggable solver: SOLVE quadratic equation with variable 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=1792 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -3.27799650382776, -17.3886701628389. Here's your graph:

Then use x = 2y + 8 to get the x figures

 Linear-equations/258033: slope and the vertical and horizontal intercept y=5x+2 can you show me the work so i know how to do this please thank you very much. 1 solutions Answer 189881 by Greenfinch(383)   on 2010-01-18 13:53:56 (Show Source): You can put this solution on YOUR website!y = 5x + 2 Gradient is 5 (every 1 added to the x creates 5 in the y direction) When x = 0, y = 2 when y = 0, x = -2/5
 Travel_Word_Problems/258026: A person travel 1600 miles by commercial jet, then an additional 500 miles by private plane. If the speed of the jet is 4 times the speed of the private plane, and total time in the air was 6 hours, determine the speed of each plane. I have tried the problem as: 4x/1600 + x/500 = 6, and also 1600/4x = 500/x - 6 , and a few other variations on this, but can't seem to come up with the correct answer, which the book has as 150 mph, and 600 mph. I'm think I'm close, but can't figure out what I'm doing wrong. Thanks for your help. Michelle1 solutions Answer 189878 by Greenfinch(383)   on 2010-01-18 13:51:18 (Show Source): You can put this solution on YOUR website!Private plane is travelling at v mph Jet is travelling at 4v mph Time on jet is 1600/4v and time on private plane is 500/v Total time is 6 = 1600/4v + 500/v Multiply by 4v throughout and get 24v = 1600 + 2000 so 24v = 3600 v = 150 So Private plane travels at 150 mph and jet at 600 1600/600 = 2 2/3 hours 500/150 = 3 1/3 hours Total = 6 hours
 Linear-equations/258027: Find the slope of the line determined by the following equation: x= 5-y/4 Please show steps to solving. Thank you.1 solutions Answer 189875 by Greenfinch(383)   on 2010-01-18 13:41:24 (Show Source): You can put this solution on YOUR website!x = 5 - y/4 multiply by 4 to get 4x = 20 - y rearrange y = 20 - 4x Gradient is therefore -4. When x = 0, y = 20 so y intercept +20
 Linear-equations/258030: i need to find the slope and vertical and horizontal intercepts for y=3x-71 solutions Answer 189874 by Greenfinch(383)   on 2010-01-18 13:38:06 (Show Source): You can put this solution on YOUR website!slope or gradient is +3 y - intercept is - 7 x - intercept is 2 1/3
 Quadratic_Equations/258001: y-9=0 x^2+y^2-24x-10y+153=01 solutions Answer 189873 by Greenfinch(383)   on 2010-01-18 13:36:13 (Show Source): You can put this solution on YOUR website!x^2 - 24x + y^2 - 10y + 153 = 0 is a circle with centre at 12,5 So rearranging (x^2 - 24x + 144) + (y^2 - 10y + 25) + 153 - 169 = 0 completing the square (x - 12)^2 + (y - 5)^2 = 16 = 4^2 Centre is there at 12, 5 and the radius is 4 Combining with the line y = 9 gives (x - 12)^2 + (y - 5)^2 - 16 =0 and y = 9 (x - 12)^2 + 4^2 - 16 = 0 (x - 12) ^2 = 0 x = 12 twice, so y = 9 is a tangent touching the circle at x = 12
 Linear-equations/258020: Write an equation of the line that passes through (-3,2) and is parallel to the line x-y=7. I dont understand how to do this problem. Or even start it for that matter.1 solutions Answer 189868 by Greenfinch(383)   on 2010-01-18 13:15:08 (Show Source): You can put this solution on YOUR website!The line x - y = 7 can be rewritten as y = x - 7 The gradient of the line is 1, because each increase of 1 in the value of x produces an increase in y of 1 as well. Any line parallel (||) will also have a gradient of 1, so all lines || to y = x -7 will be of the form y = x + c where c is a constant The line we are interested in goes through (-3,2) so we put these numbers into the equation so 2 = -3 + c so c = 5 The equation is y = x + 5
 Quadratic_Equations/257949: They give me this example:x squared -8x-20=0 (x-10)(x+2)=0 x-10=0 or x+2=0 x=10 or x=-2 I do not understand were they get -10 and +2. Why not 5 and 4. Also why is the 2 positive. 1 solutions Answer 189801 by Greenfinch(383)   on 2010-01-18 08:55:11 (Show Source): You can put this solution on YOUR website!x^2 - 8x - 20 = 0 ends up in the form (x + a)(x + b) = 0 which when expanded becomes x^2 + (a + b)x + (a x b) = 0 So a+b = -8 and a x b = -20 Either a or b is negative (but not both) since a x b is minus. So a + b is the difference in the quantities (since one is negative) If |a x b| is 20, a and b can be 1,20 : 2,10: 4,5. the differences are then 19, 8 and 1 We need the 8 and since the 8 is minus, the numbers we need are -10 and +2 giving a sum of -8, So the factors are (x - 10)(x + 2) = 0 Giving the roots x = 10 or -2
 Square-cubic-other-roots/257946: find the rational roots of 4x^3-3x-1=0. please & thanks.1 solutions Answer 189798 by Greenfinch(383)   on 2010-01-18 08:45:54 (Show Source): You can put this solution on YOUR website!Find first root using remainder theorem Try x = 1 f(1) = 0 So (x - 1) is a factor so x - 1 divided into 4x^3 - 3x -1 is 4x^2 -4x +1 = 4(x^2 -x + 1/4) = 4(x - 1/2)^2 So roots are x = 1 and 1/2 (twice)
 Angles/257945: Two angles are supplementary.If one angle measures 45 degrees less than twice the measure of its supplement, find the measure of each angle.1 solutions Answer 189796 by Greenfinch(383)   on 2010-01-18 08:39:01 (Show Source): You can put this solution on YOUR website!Call first angle y, then other angle is (180 - y) y + 45 = 2(180 - y) y + 45 = 360 - 2y 3y = 315 y = 105 So angles are 105 and 75 Check : y + 45 = 150 which is twice 75
 Linear_Algebra/257940: Can someone please help a Soldier out here. I am not sure how to set up this problem. Use the fundamental principles of counting or permutations to solve the problem. An auto manufacturer produces 7 models, each available in 6 different colors, with 4 different upholstery fabrics, and 5 interior colors. How many varieties of the auto are available?1 solutions Answer 189795 by Greenfinch(383)   on 2010-01-18 08:33:54 (Show Source): You can put this solution on YOUR website!Assuming all variations are permissible, 7 x 6 x 4 x 5 = 840
 Probability-and-statistics/257944: A factory manager surveys the owners of the cars parked in the car park. One of the question is: "when you drive to work how many people including yourself are in your car?" The responses are summarised in the table below. Number of people 1 2 3 4 5 6 Number of cars 42 26 12 2 0 1 Total 83 Calculate the mean number of people per car1 solutions Answer 189794 by Greenfinch(383)   on 2010-01-18 08:31:51 (Show Source): You can put this solution on YOUR website!No of People No of cars total 1 x 42 = 42 2 x 26 = 52 3 x 12 = 36 4 x 2 = 8 5 x 0 = 0 6 x 1 = 6 Total cars 83 Total people 144 Average 144/83 = 1.735
 Problems-with-consecutive-odd-even-integers/257941: Define the variable and write an equation. Do NOT solve. The sum of the squares of two consecutive integers is 9 greater than 8 times the smaller integer1 solutions Answer 189793 by Greenfinch(383)   on 2010-01-18 08:21:54 (Show Source): You can put this solution on YOUR website!Call the smaller integer n and the larger integer (n+1) n^2 + (n+1)^2 = 8n +9
 Geometry_Word_Problems/257683: one side of a regular pentagon measures 0.8 meter. What is the perimeter of the regular pentagon?1 solutions Answer 189579 by Greenfinch(383)   on 2010-01-17 13:37:41 (Show Source): You can put this solution on YOUR website!5 x 0.8 = 4 m
 Travel_Word_Problems/257699: Two cars leave town going in the same direction. One travels 55 mph and the other travels 65 mph How long will it take before they are 180 miles apart1 solutions Answer 189578 by Greenfinch(383)   on 2010-01-17 13:34:48 (Show Source): You can put this solution on YOUR website!One is travelling 10 mph faster than the other. It will therefore take 18 hours to be 180 miles apart
 Travel_Word_Problems/256407: Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking? 1 solutions Answer 188631 by Greenfinch(383)   on 2010-01-13 15:48:44 (Show Source): You can put this solution on YOUR website!After 3 hours, 1st cyclist (at 6 mph) in 18 miles. Second cyclist travels 4 mph faster than 1st cyclist. So time to move 18 miles at 4 mph is 4 1/2 hours
 Travel_Word_Problems/256472: A train leaves Los Angles headed for San Francisco traveling at an average speed of 60 miles per hour. Another train leaves San Francisco headed for Los Angles at the same time as the first train. The train leaving San Francisco is traveling at an average speed of 40 miles per hour. Both trains are traveling the same route. How far apart will the two trains be one hour before they meet?1 solutions Answer 188626 by Greenfinch(383)   on 2010-01-13 15:38:01 (Show Source): You can put this solution on YOUR website!The trains are approaching at 40 + 60 = 100 mph. One hour before they meet they will be 100 miles apart.
 Geometry_Word_Problems/256498: The problem is: An ant is 120 ft. from an 80ft. tall tree whose top is the visual line of a 600 ft. tall bldg. How far is tree from building? The teacher gave this: 280/3120 = 600/120 + x. Then he cross multiplied and got 240 + 2x = 1800 then he solved for x and got x = 780 ft. as answer. I have no idea where the 280 or 3120 came from...can anyone help? Thank you. This is for 9th grade Algebra I.1 solutions Answer 188620 by Greenfinch(383)   on 2010-01-13 15:30:19 (Show Source): You can put this solution on YOUR website!Think of this in terms of similar triangles. Tree is 80 ft high, building is 600 ft high, so ratio of 1 to 7 1/2. Distances are in the same ratio. Ant to tree is 120 so ant to building is 7 1/2 times 120. So ant to building is 900 feet. What they want is tree to building, which is ant to building less the 120 feet from ant to tree, so tree to building is 780 feet
 Linear-equations/256274: find the equation of a line that is perpindicular to the line 3x+2y=12 and passes through the point (-1,1)1 solutions Answer 188437 by Greenfinch(383)   on 2010-01-12 20:25:13 (Show Source): You can put this solution on YOUR website!Gradient of line is -3/2. The line perpendicular has a gradient +2/3 Gradient a x gradient b = -1 So line is y = 2/3 x + c If it passes through (-1,1) Then 1 - -2/3 + c c = 5/3 So line is 3y = 2x + 5
 Probability-and-statistics/256261: What is the formula for solving this: "If you draw 4 M&Ms from a bag containing 4 red, 4 yellow, 4 green, and 4 brown ones, what is the probability that you will get 1 of each color?" It boggles my mind. Thanks in advance! 1 solutions Answer 188434 by Greenfinch(383)   on 2010-01-12 20:21:30 (Show Source): You can put this solution on YOUR website!1st pick p = 1 (your are going to get a sweet and it doesn't matter which colour) 2nd pick p= 12/15 anything but 1st colour (of which 3 are left) 3rd pick p = 8/14 two colours left out of 4 4th p = 4/13 So probability is = 1 x 12/15 x 8/14 x 4/13 = 64/(5 x 7 x 13)= 64/455
 Sequences-and-series/256269: What is the function for the sequence 1,8,27,641 solutions Answer 188428 by Greenfinch(383)   on 2010-01-12 20:14:03 (Show Source): You can put this solution on YOUR website!This is 1^3, 2^3, 3^3, 4^3 etc There are various ways of writing this but U(n) = n^3 is one way
 Trigonometry-basics/256166: express tan 150 as the function of a positive acute angle1 solutions Answer 188427 by Greenfinch(383)   on 2010-01-12 20:12:00 (Show Source): You can put this solution on YOUR website!tan 150 = - tan 30
 Sequences-and-series/256266: Find the fifth, tenth, and hundredth term of each sequence... 4,14,24,34 I know that the way to solve the problem is to use the equation; A(n)= a+(n-1)d. But I just Do Not know which number goes to which variable? Since each term adds 10. Would the equation be. A(5)= A+(5-1)10?1 solutions Answer 188426 by Greenfinch(383)   on 2010-01-12 20:09:55 (Show Source): You can put this solution on YOUR website!a = 4 and d = 10 A(5 ) = 4 + 40 = 44 A(10) = 4 + 90 = 94 A(100)= 4 + 990 = 994
Miscellaneous_Word_Problems/256232: A rocket launched from ground level with an initial velocity of 224 ft/s. When will the rocket reach a height of 528 ft? I know that h=vt-16t^2 will be used. So what happens after I plug it all in? 528=224t-16t^2?
1 solutions

Answer 188425 by Greenfinch(383)   on 2010-01-12 20:05:29 (Show Source):
You can put this solution on YOUR website!
It is simpler dividing through by 16
33 = 14t -t^2 so
t^2 - 14t + 33 = 0
 Solved by pluggable solver: SOLVE quadratic equation with variable 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=64 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 3, 11. Here's your graph:

This gives t = 3 and t = 11. So it will pass 528 feet after three seconds, carry on until it runs out of speed after 7 seconds when it starts to drop until it passes 528 feet on the way down after 11 seconds hits the ground after 14 seconds

 Distributive-associative-commutative-properties/256248: factor completely: 4a^2-a-51 solutions Answer 188419 by Greenfinch(383)   on 2010-01-12 19:49:51 (Show Source): You can put this solution on YOUR website!4a^2 -a - 5 = (4a - 5)(a + 1 )
Quadratic_Equations/256251: solutions for x2 + 10x + 1 = -12 + 2x
1 solutions

Answer 188414 by Greenfinch(383)   on 2010-01-12 19:40:44 (Show Source):
You can put this solution on YOUR website!
I am assuming the equation is x^2 + 10x +1 = 2x - 12
If it is then x^2 + 8x + 13 = 0
 Solved by pluggable solver: SOLVE quadratic equation with variable 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=12 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -2.26794919243112, -5.73205080756888. Here's your graph:

 Linear_Equations_And_Systems_Word_Problems/255856: A poster is 25 cm taller than it is wide. It is mounted on a piece of cardboard so that there is a 5cm border on all sides. If the area of the boreder is 1350 cm squared what are the dimensions of the poster? 1 solutions Answer 188085 by Greenfinch(383)   on 2010-01-11 19:35:24 (Show Source): You can put this solution on YOUR website!Call smaller side x, then larger side is x + 25 small side + border is x + 10 ( border on each side) large side is x + 35 Area of border is (x + 10)(x + 35) -(x)(x+25) = 1350 Expanding ( x^2 + 45x + 350 ) - (x^2 + 25x) = 1350 20x + 350 = 1350 x = 1000/20 = 50 cm Check: Picture is 50 x 75 = 3750 cm sq with border is 60 x 85 = 8100 cm sq Difference is 1350 cm sq
 Equations/255848: At Gwen’s garage sale, all books were one price, and all magazines were another price. Harriet bought four books and three magazines for \$1.45, and June bought two books and five magazines for \$1.25. What was the price of a book and what was the price of a magazine? 1 solutions Answer 188079 by Greenfinch(383)   on 2010-01-11 19:24:12 (Show Source): You can put this solution on YOUR website!Call book price x and magazine price y Then 4x + 3y = 145 ..............A and 2x + 5y = 125 ..............B 4x +10y = 250 ..............C = 2B 7y = 105 ..............D = C - A 7 = 15 Sub in A 4x + 45 = 145 x = 25 Check in B 2 x 25 + 5 x 15 = 50 + 75 = 125 So books are 25cents and magazines are 15cents
 Expressions-with-variables/255799: I do not understand this at all. I know that I have to substitute the x and y values but I don't know how to solve it. It is solving systems using substitution. One of the problems is: y=3x-10 and the other equation that goes with it is y=2x-51 solutions Answer 188077 by Greenfinch(383)   on 2010-01-11 19:15:44 (Show Source): You can put this solution on YOUR website!These are simultaneous equations, which means that they can be solved if they are both true AT THE SAME TIME. This can either be done by getting rid of the x or y, or, in this case by substitution. If y = 3x - 10 and y = 2x - 5. then 3x - 10 = 2x - 5 because they both equal y and we can substitute 2x -5 for y This leads to x = 5 ( 3x - 2x and -5 -(-10)) Put that in one of the original equations and we get 3x5 -10 = 5 or 2 -5 = 5 So the answers are x=5 and y=5