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Greenfinch answered: 383 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389, >>NextEquations/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
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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:
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Then use x = 2y + 8 to get the x figures
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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. Michelle
1 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
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Quadratic_Equations/258001: y-9=0
x^2+y^2-24x-10y+153=0
1 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
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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
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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
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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
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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):
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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 car
1 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
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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
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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):
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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
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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
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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
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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):
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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):
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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
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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
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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-5
1 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
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