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Rectangles/95169: I have been trying this problem for three days now and still can not come up with anything. Please Help show me the light. I was asked to find two different rectangles with the same perimeter and the same area. Tried all kinds of different combos of numbers. I know sides of 0 will work, but that isn't a rectangle. Thank you much, Rich
1 solutions
Answer 69246 by ankor@dixie-net.com(15639)   on 2007-08-29 20:57:27 (Show Source):
You can put this solution on YOUR website! find two different rectangles with the same perimeter and the same area. Tried all kinds of different combos of numbers. I know sides of 0 will work, but that isn't a rectangle.
:
Let x = length and y = width
;
Perimeter = area
2x + 2y = x*y
:
2y - xy = -2x
:
y(2-x) = -2x
:
y =  ; plot this equation
:
Here is a graph which plots the length as x and the width as y, which has
perimeter = area (for x > 2).
:
I should have added here the statement,
"Any value greater than 2, that you plug in for x in the above equation, will yield a value for y which will satisfy the problem."
;
:
A couple integer values 6 by 3, 4 by 4, non-integers are unlimited,
10 by 2.5, 12 by 2.4, 22 by 2.2, etc.
:
Did this help you?
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Graphs/95066: The path of a falling object is given by the function s=16t^2+v0t+s0 where Vo represents the initial velocity in ft/sec and s0 represents the initial heigth in feet.
If a rock is throne upward with an initial velocity of 64 ft per sec. from the top of a 25 ft building, write the height (s) equation using this information.
a) how high is the rock after 1 sec?
b)after how many sec will the graph reach max heigth?
c) what is the max. heigth?
1 solutions
Answer 69173 by ankor@dixie-net.com(15639) on 2007-08-29 15:33:26 (Show Source):
You can put this solution on YOUR website!The path of a falling object is given by the function s=16t^2+v0t+s0 where Vo represents the initial velocity in ft/sec and s0 represents the initial height in feet.
If a rock is throne upward with an initial velocity of 64 ft per sec. from the top of a 25 ft building, write the height (s) equation using this information.
:
s = -16t2 + 64t + 25
:
Reviewing the Three parts of this equation
-16t^2 is the force of gravity, hence it is negative
64t is the initial upward velocity, it is positive
25 is the initial height of the building where this starts
:
:
a) how high is the rock after 1 sec?
Substitute 1 for t in the above equation and find s:
s = -16(1^2) + 64(1) + 25
s = -16 + 64 + 25
s = 73 ft above ground after 1 second
:
:
b)after how many sec will the graph reach max height?
:
Max height will occur at the axis of symmetry of this equation:
:
Formula for that is: x = -b/(2a)
:
In our equation this would be:
s = -64/(2*-16)
s = -64/-32
s = +2 seconds to reach max height
:
:
c) what is the max. height?
Find the this by substituting 2 for t in the equation:
s = -16(2^2) + 64(2) + 25
s = -16(4) + 128 + 25
s = -64 + 128 + 25
s = 89 ft is the max height occurring after 2 second
:
A graphical presentation would show this clearly.
x axis in seconds and y axis in feet
:
Note after 1 sec it looks like it is about 70 ft and after 2 sec it's over 88 ft
:
Did I succeed in making this understandable to you?
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Miscellaneous_Word_Problems/94986: If the sides of a square are decreased by 2 cm, the area is decreased by 36 cm2. What were the dimensions of the original square?
1 solutions
Answer 69161 by ankor@dixie-net.com(15639) on 2007-08-29 13:20:40 (Show Source):
You can put this solution on YOUR website!If the sides of a square are decreased by 2 cm, the area is decreased by 36 cm2. What were the dimensions of the original square?
:
Let x = side of original square
Then
(x-2) = side of the new square
:
Original square area - new square area = 36
x^2 - (x-2)^2 = 36
:
x^2 - (x^2 - 4x + 4) = 36: FOILed (x-2)(x-2)
:
x^2 - x^2 + 4x - 4 = 36; removing bracket changes the signs
:
4x = 36 + 4; x^2's cancel out
:
4x = 40
:
x = 40/4
:
x = 10 cm, side of original square:
:
:
Check: 10^2 - 8^2 = 36
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Equations/95028: Business and finance. If the total bill at a restaurant, including a 15% tip, is
$65.32, what was the cost of the meal alone?
1 solutions
Answer 69160 by ankor@dixie-net.com(15639) on 2007-08-29 13:14:20 (Show Source):
You can put this solution on YOUR website!If the total bill at a restaurant, including a 15% tip, is
$65.32, what was the cost of the meal alone?
;
Let x = cost of the meal; tip would be .15x
x + .15x = 65.32
1.15x = 65.32
x = 65.32/1.15
x = $56.80
:
Check solution:
56.80 + .15(56.80) = 65.32
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Polynomials-and-rational-expressions/94748: This question is from textbook Beginning Algebra
Good evening tutor,
I do not understand multiplying polynomials. Could someone please help me with this problem?
Multiply the following:
(x/3 + 3/4)(3x/4 - 3/5)
Thank you in advance for your help I am going crazy trying to understand this.
1 solutions
Answer 69083 by ankor@dixie-net.com(15639) on 2007-08-28 18:28:53 (Show Source):
You can put this solution on YOUR website!Multiply the following:
 * 
:
We need to put each pair of fractions over a single denominator, using a common
denominator much as you do in numerical fractions:
:
Find the common denominator of the 1st pair: It would be 12, right?
=  = 
:
Do the same with the 2nd pair of fractions, the common denominator would be 20:
=  = 
:
Now we have a single fraction times a single fraction
*
:
FOIL the numerators:
 = 
:
Factor out 3 in the numerator, then cancel it into the denominator:
 =  ; that's about all you can do with this
:
Did this help you understand this?
|
Expressions-with-variables/94727: find a value for y so that the value of 10y^3 is the same as the value for
(10y)^3 ?
1 solutions
Answer 69051 by ankor@dixie-net.com(15639) on 2007-08-28 16:06:21 (Show Source):
You can put this solution on YOUR website!find a value for y so that the value of 10y^3 is the same as the value for
(10y)^3 ?
:
 = 
:
I inadvertently sent this in, but worse than that I have not come up with a solution. I will keep trying but perhaps you can resubmit it, someone smarter than me may come up with it. Sorry. A
:
On further effort on this, I am going to say only y = 0 will satisfy this
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Percentage-and-ratio-word-problems/94722: Step right up anad guess the nimber of candies in the jar?
Three people have already guessed, and their guesses are 315, 350, and 327. Now here's the big clue: One of the guesses is off by 26, one is off by 14, and one is close, but off by 9 candies?
How many candies are in the jar?
1 solutions
Answer 69044 by ankor@dixie-net.com(15639) on 2007-08-28 15:55:37 (Show Source):
You can put this solution on YOUR website!Three people have already guessed, and their guesses are 315, 350, and 327. Now here's the big clue: One of the guesses is off by 26, one is off by 14, and one is close, but off by 9 candies?
How many candies are in the jar?
:
The "Brute Force" method
:
x +/- 14 = 315; x = 301 or 329
x +/- 26 = 350; x = 376 or 324
x +/- 9 = 327; x = 336 or 318
No matches here:
:
x +/- 14 = 327; x = 341 or 313
x +/- 26 = 315; x = 341 or 289
x +/- 9 = 350; x = 359 or 341
:
No need to go any further: the number is 341
:
There is probably a more elegant method, but have to admit, I can't come up with it.
|
Complex_Numbers/94817: I have a worded problem that is giving me trouble and I would really appreciate if someone could assist me in making sense of it all. It goes like this.
Four brothers are born in successive intervals of three years. The eldest is twice the age of the youngest. What is the age of their father, who is eighteen years older than the eldest son?
I have given this a go, but all I am able to come up with is this
B1= Brother 1 =9
B2= Brother 2 =12
B3=Brother 3 =15
B4=Brother 4 =18
F=Father =36
B1+B2+3+B3+6B4+9
4B=+18
F=2B4+9
My problem is even though I think I can get an answer to this problem in my head. I am unable to sort it into an algebraic equation, which is what I desperately need. Any help would be greatly appreciated. Thank you so much.
1 solutions
Answer 69038 by ankor@dixie-net.com(15639) on 2007-08-28 15:28:17 (Show Source):
You can put this solution on YOUR website!Four brothers are born in successive intervals of three years. The eldest is twice the age of the youngest. What is the age of their father, who is eighteen years older than the eldest son?
:
Let x = age of the youngest
Then the remaining brothers' ages would be: x+3, x+6, x+9
:
It says,"The eldest is twice the age of the youngest."
(x+9) = 2x; you can do this in your head, but continuing in algebra
9 = 2x - x
x = 9 age of the youngest
:
Oldest, obviously is x + 9 = 18, + 18 = 36 is father
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Graphs/94818: The equation of the line with y-intercept of 3 and perpendicular to the graph of 2x+y=5 is?
This is an sample test questions for my math assessment test. I will be taking in a few hours and this is my last question that I don't know how it works. I know the answer but I don't know how to get to that answer. Thank you very much!
1 solutions
Answer 69036 by ankor@dixie-net.com(15639) on 2007-08-28 15:20:35 (Show Source):
You can put this solution on YOUR website!The equation of the line with y-intercept of 3 and perpendicular to the graph of 2x+y=5 is?
:
y intercept occurs when x = 0, therefore the equation in the form y = mx + b
would be y = mx + 3
:
Now we want to find the slope (m) of the given equation:
Put equation in the slope/intercept (y = mx + b) form:
2x + y = 5
y = -2x + 5
The slope m = -2
:
Slope relationship between perpendicular lines is given as: m1*m2 = -1
Assume the m1 = -2 from the above equation,
find m2 (the slope of the perpendicular line) y = mx + 3
:
-2 * m2 = -1
Divide both sides by -1 and you have:
m2 = -1/-2
m2 = +1/2
:
The equation of the perpendicular line: y =  x + 3
:
It will help you to memorize the perpendicular lines slope relationship
m1 * m2 = 1, and that y intercept occurs when x = 0
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Graphs/94773: 1/9x-1/5y=20/9
-10x+18=-200
Solve the system
I can't get this? Please I need help, thanks
1 solutions
Answer 69032 by ankor@dixie-net.com(15639) on 2007-08-28 13:43:30 (Show Source):
You can put this solution on YOUR website!
The first thing we want to do here is get rid of those annoying denominators.
Multiplying each term in the equation by 9*5 or 45, would do this, leaving us with:
5x - 9y = 5(20)
5x - 9y = 100
:
On this equation I assume you mean:
-10x + 18y = -200
:
Now it becomes apparent that this system cannot be solved. See what happens if
we multiply the 1st equation by 2, and add to the 2nd equation:
:
10x - 18y = 200
-10x + 18y = -200
------------------- adding eliminates everything!
0x + 0y = 0
:
This is just a form of "math student harassment" don't you think?
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Radicals/94797: the equation d=1.2 square root h, gives the distance, D, in miles that a person can see to the horizon from a height ,h, in feet.
A. solve equation for h,
B. a national park peak is 14,255 feet in elevation. How far can you see to the horizon from the top of peak.
I am lost on how to solve the equation and then figure out the steps to take to come up with the answer for B.
1 solutions
Answer 69027 by ankor@dixie-net.com(15639) on 2007-08-28 13:27:26 (Show Source):
You can put this solution on YOUR website!the equation d=1.2 square root h, gives the distance, D, in miles that a person can see to the horizon from a height ,h, in feet.
:
A. solve equation for h,
1.2  = d
Divide both sides by 1.2
= 
Square both sides:
h = 
:
B. a national park peak is 14,255 feet in elevation. How far can you see to the horizon from the top of peak.
Given the formula: d = 1.2*
d = 1.2*  ; find Square Root on a calculator
d = 1.2 * 119.3943
d = 143.273 miles to the horizon from an elevation of 14,255 ft
:
:
Did this help you understand this?
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Probability-and-statistics/94739: This question is from textbook Introductory algebra
A triangular region has a perimeter of 66 meters. The first side is two-thirds of the second side. The third side is 14 meters shorter than the second side. What are the lengths of the three sides of the triangular region?
1 solutions
Answer 69021 by ankor@dixie-net.com(15639) on 2007-08-28 12:55:36 (Show Source):
You can put this solution on YOUR website!Let x = length of the 2nd side
:
It says," The first side is two-thirds of the second side." Therefore:
1st side = 2x/3
:
It also says,"The third side is 14 meters shorter than the second side." Therefore:
3rd side = (x-14)
:
What are the lengths of the three sides of the triangular region?
It says "A triangular region has a perimeter of 66 meters." Therefore:
:
side 1 + side 2 + side 3 = 66
(2x/3) + x + (x-14) = 66
:
Multiply equation by 3 to get rid of the denominator:
2x + 3x + 3(x-14) = 3(66)
2x + 3x + 3x - 42 = 198
8x = 198 + 42
8x = 240
x = 240/8
x = 30 m, the length of side 2
:
2/3(30) = 20 m, the length of side 1
:
30 - 14 = 16m, the length of side 3
:
:
Check solution, using the perimeter:
20 + 16 + 30 = 66
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Polynomials-and-rational-expressions/94584: Science and Nutrition. A passenger train can travel 325 mi in the same time a freight train takes to travel 200 mi. If the speed of the passenger train is 25 mi faster than the speed of the freight train, find the speed of each.
1 solutions
Answer 68986 by ankor@dixie-net.com(15639) on 2007-08-27 21:51:48 (Show Source):
You can put this solution on YOUR website!A passenger train can travel 325 mi in the same time a freight train takes to travel 200 mi. If the speed of the passenger train is 25 mi faster than the speed of the freight train, find the speed of each.
:
Let s = speed of the freight
Then
(s+25) = speed of the pass train
:
They are giving the time as the same for both trains, make a time equation from this fact:
Time = Dist/speed
:
 = 
:
Cross multiply and you have:
:
325s = 200(s+25)
:
325s = 200s + 5000
:
325s - 200s = 5000
:
125s = 5000
:
s = 5000/125
:
s = 40 mph, speed of the freight
and
(s+25) = 65 mph, speed of the pass train
:
:
Check solutions, is the time the same?
200/40 = 325/65
5 = 5
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Polynomials-and-rational-expressions/94575: solve and check the equation for x
x/6 - x/8 = 1
1 solutions
Answer 68985 by ankor@dixie-net.com(15639) on 2007-08-27 21:37:36 (Show Source):
You can put this solution on YOUR website!solve and check the equation for x
 = 1
;
This is so easy, multiply by a number that will cancel out the denominators
24 would do this, Right?
:
24*  - 24*  = 24*1
:
You have:
4x - 3x = 24
:
x = 24
:
:
Check solution, substitute 24 for x in the original equation
 = 1
:
4 - 3 = 1
:
How about that, do you think you got a handle on this stuff now?
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Trigonometry-basics/94596: please help me solve this. thank you so much.p.s. i put each part of the equation on a separate line so that it would not all squish together. it reads: equation 1 plus equation 2 equals equation 3
2x-10
---------
3x^2-x-14
plus
7
----
3x-7
equals
8
---
x+2
thank you so much and God bless.
1 solutions
Answer 68962 by ankor@dixie-net.com(15639) on 2007-08-27 19:48:17 (Show Source):
You can put this solution on YOUR website!Assume you mean:
 +  = 
:
factor the quadratic and you have:
 + =
:
Multiply the equation by (3x-7)(x+2) to get rid of the denominators, you have:
:
(2x-10) + 7(x+2) = 8(3x-7)
:
2x - 10 + 7x + 14 = 24x - 56; multiplied what's inside the brackets
:
9x + 4 = 24x - 56
:
9x - 24x = -56 - 4
:
-15x = -60
:
x = -60/-15
:
x = + 4
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Linear-equations/94572: the equation y - 2 =3(x + 2) is in point-slpoe form
write the equation in stadard form
1 solutions
Answer 68961 by ankor@dixie-net.com(15639) on 2007-08-27 19:42:48 (Show Source):
You can put this solution on YOUR website!the equation y - 2 =3(x + 2) is in point-slope form
write the equation in standard form; that's Ax + By = C
;
y - 2 = 3(x + 2)
:
multiply what's inside the brackets:
y - 2 = 3x + 6
:
Add 2 to both sides:
y = 3x + 6 + 2
y = 3x + 8
:
Subtract 3x from both sides:
-3x + y = 8 is the standard form
:
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Quadratic_Equations/94570: Some students planned for a get-together. The budget for food was $500. Five of the students failed to come because of the distance and therefore the cost of food for each member increased by $5. How many students attended the get-together?
1 solutions
Answer 68959 by ankor@dixie-net.com(15639) on 2007-08-27 19:20:21 (Show Source):
You can put this solution on YOUR website!Some students planned for a get-together. The budget for food was $500. Five of the students failed to come because of the distance and therefore the cost of food for each member increased by $5. How many students attended the get-together?
:
Let x = Number of students, who actually attended
Then
(x+5) = Original number of students expected
:
Actual cost per person: = 
:
Expected cost per person = 
:
It said the cost increased by $5, because of of 5 less students:
Actual cost - expected cost = $5
- = 5
:
multiply equation by x(x+5) to get rid of the denominators, resulting in:
500(x+5) - 500x = 5(x(x+5)
:
500x + 2500 - 500x = 5x^2 + 25x
:
Arrange as a quadratic equation:
5x^2 + 25x - 2500 = 0
:
Simplify divide by 5:
x^2 + 5x - 500 = 0
:
Factors to:
(x+25)(x-20) = 0
:
x = +20, the positive solution is what we want here.
:
20 Students actually attended
:
:
Check our solution. Actual = 20, Expected no. of student = 25
500/20 - 500/25 =
25 - 20 = $5
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Linear-systems/94475: Solve the system of equations. Check your solution.
-x+y-3z= -4
3x-2y+8z= 14
2x-6y+5z= -3
1 solutions
Answer 68955 by ankor@dixie-net.com(15639) on 2007-08-27 18:51:02 (Show Source):
You can put this solution on YOUR website!-x + y - 3z = -4
3x - 2y+ 8z = 14
2x- 6y+ 5z = -3
:
Multiply the 3rd equation by -1 and add all three equations
-x + y - 3z = -4
3x - 2y+ 8z = 14
-2x +6y- 5z = +3
-------------------Adding eliminates x and z, find y:
0x + 5y + 0z = +13
y = 13/5
y = 2.6
:
substitute 2.6 for y in the 1st equation
-x + 2.6 - 3z = -4
-x - 3z = -4 - 2.6
-x - 3z = -6.6
x + 3z = 6.6: multiplied by -1 to get rid all those negatives
:
Do the same in the 2nd equation
3x -2(2.6) + 8z = 14
3x - 5.2 + 8z = 14
3x + 8z = 14 + 5.2
3x + 8z = 19.2
:
Multiply 1st two unknown equation by 3, subtract from the 2nd two unk equaiton
3x + 9z = 19.8
3x + 8z = 19.2
-------------------subtracting eliminates x, find z
0x + 1z = +.6
z = .6
:
Use 3x - 2y + 8z = 14 to find x
3x - 2(2.6) + 8(.6) = 14
3x - 5.2 + 4.8 = 14
3x - .4 = 14
3x = 14 + .4
3x = 14.4
x = 14.4/3
x = 4.8
:
Our solution: x = 4.8; y = 2.6; z = .6
:
You should check our solutions in one of the original equations
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Quadratic_Equations/94567: A professor started a project with a group of students, 60% of whom were boys. Due to some unavoidable reasons, six girls couldn't turn up, so the professor had to make some changes in the group. He admitted six boys. In doing so, the percentage of boys in the project increased to 75%. Find the number of boys and girls involved in the project initially.
1 solutions
Answer 68936 by ankor@dixie-net.com(15639) on 2007-08-27 15:53:24 (Show Source):
You can put this solution on YOUR website!A professor started a project with a group of students, 60% of whom were boys. Due to some unavoidable reasons, six girls couldn't turn up, so the professor had to make some changes in the group. He admitted six boys. In doing so, the percentage of boys in the project increased to 75%. Find the number of boys and girls involved in the project initially.
:
Let t = total number of students,
.6t = number of boys originally
:
(.6t + 6) = actual number of boys (which the problem says became 75%)
:
From all this we have one simple equation:
.6t + 6 = .75t
.6t - .75t = -6
-.15t = -6
t = -6/-.15
t = +40 kids
:
.6 * 40 = 24 boys originally
.4 * 40 = 16 girls "
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Quadratic_Equations/94569: A designer, attemptng to arrange the characters of his artwork in the form of a square grid with equal number of rows and columns, found that 24 characters were left out. When he tried to add one more row and column, he found that he was short of 25 characters. Can you find the number of characters used by the designer?
1 solutions
Answer 68933 by ankor@dixie-net.com(15639) on 2007-08-27 15:44:37 (Show Source):
You can put this solution on YOUR website!A designer, attempting to arrange the characters of his artwork in the form of a square grid with equal number of rows and columns, found that 24 characters were left out. When he tried to add one more row and column, he found that he was short of 25 characters. Can you find the number of characters used by the designer?
:
Let x^2 = no. of characters in the original square
:
Then the total number of characters = x^2 + 24
:
Add one column and row and you have (x+1)^2 in the new square
:
Original square + 24 = new square - 25
x^2 + 24 = (x+1)^2 - 25
x^2 + 24 = x^2 + 2x + 1 - 25
:
Arrange the unknowns on the left and the numerals on the right:
x^2 - x^2 - 2x = 1 - 25 - 24
-2x = - 48
x = -48/-2
x = +24
:
The number of characters = x^2 + 24
24^2 + 24
576 + 24 = 600 characters used by the designer
:
Check by using the new square
25^2 - 25
625 - 25 = 600 also
:
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Numbers_Word_Problems/94583: number problem. If one-half of one integer is subtracted from three fifths of the next consecutive integer the defference is 3. What are the two integers.
1 solutions
Answer 68925 by ankor@dixie-net.com(15639) on 2007-08-27 14:58:59 (Show Source):
You can put this solution on YOUR website!If one-half of one integer is subtracted from three fifths of the next consecutive integer the difference is 3. What are the two integers.
:
One integer = x; next integer = (x+1)
:
Change 3/5 to decimal: .6
:
.6(x+1) - .5x = 3
.6x + .6 - .5x = 3
.6x - .5x = 3 - .6
.1x = 2.4
x = 2.4/.1
x = 24 and 25 are the two integers
:
:
Check
.6(25) - .5(24) =
15 - 12 = 3
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absolute-value/94447: I need help with the following question. My book does not have any examples or show any thing on this type of questions. [] is supposed to be a staight line up and down but I do not know how to due it.
Solve the absolute value equation or indication the equation has no solution. The answers are in solution sets with square roots in them
[2x^2-x-1]=3
Thank you
1 solutions
Answer 68923 by ankor@dixie-net.com(15639) on 2007-08-27 14:38:20 (Show Source):
You can put this solution on YOUR website!Solve the absolute value equation or indication the equation has no solution. The answers are in solution sets with square roots in them:
|2x^2 - x - 1| = 3; vertical lines are uppercase back-slash on my keyboard
:
We have two quadratic equation to solve
2x^2 - x - 1 = +3
2x^2 - x - 1 - 3 = 0
2x^2 - x - 4 = 0
and
2x^2 - x - 1 = -3
2x^2 - x - 1 + 3 = 0
2x^2 - x + 2 = 0
:
The first one can be solved using the quadratic formula:
a = 2; b = -1; c = -4
:
:
:
:
:
:
Two solutions:
and
:
:
The 2nd equation: 2x^2 - x + 2; has no real roots. We can see that by looking
at the discriminant: b^2 - 4*a*c. In this equation: a=2, b=-1, c=+2 so we have:
-1^2 - 4*2*2 = 1 - 16 = -15
Remember the discriminant rules. Less than 0, no real roots.
:
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Polynomials-and-rational-expressions/94590: The combine resistanc of two resistors R1 and R2 in a parellel circuit is given by the formula
Rt = 1/ 1/R1 + 1/R2
Simplify the formula
1 solutions
Answer 68918 by ankor@dixie-net.com(15639) on 2007-08-27 13:59:21 (Show Source):
You can put this solution on YOUR website!The combine resistanc of two resistors R1 and R2 in a parellel circuit is given by the formula
Rt = 1/ 1/R1 + 1/R2
Simplify the formula
:
Rt =  =  = 1 *  ; or just:
:
The steps:
1. Put the denominator fraction over a single denominator
2. Invert the dividing fraction and multiply
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Quadratic_Equations/94565: An art dealer sold two artworks for $1520 thereby making a profit of 25% on the first work and 10% on the other, whereas if he had approached any exhibition he would have sold them together for $1535 with a profit of 10% on the first and 25% on the other artwork. Find the actual cost of each artwork.
1 solutions
Answer 68914 by ankor@dixie-net.com(15639) on 2007-08-27 13:21:41 (Show Source):
You can put this solution on YOUR website!An art dealer sold two artworks for $1520 thereby making a profit of 25% on the first work and 10% on the other, whereas if he had approached any exhibition he would have sold them together for $1535 with a profit of 10% on the first and 25% on the other artwork. Find the actual cost of each artwork.
:
Let x = cost of the 1st artwork, Let y = cost of 2nd artwork
:
Art dealer: Retail price 1st piece = 1.25(x); Retail price of 2nd = 1.10(y)
1.25x + 1.10y = 1520
:
Exhibition: Retail price 1st piece = 1.10(x); Retain price of 2nd = 1.25(y)
1.10x + 1.25y = 1535
:
Use two equation in the elimination method:
multiply the 1st equation by 100, and the 2nd equation by 88,resulting in:
125x + 110y = 152000
96.8x +110y = 135080
----------------------subtracting eliminates y
28.2x + 0y = 16920
x = 16920/28.2
x = $600 is the cost of the 1st piece
:
2nd piece cost using the 1st equation:
1.25(600) + 1.1y = 1520
750 + 1.1y - 1520
1.1y = 1520 - 750
1.1y = 770
y = 770/1.1
y = $700 is the cost of the 2nd equation:
:
:
Check our solutions in the 2nd equation:
1.1(600) + 1.25(700) =
660 + 875 = 1535 as given
:
Did this make sense to you? In case you wondered how I came up 88 as multiplier
in the 2nd equation. I multiplied the 1st equation by 100 to get rid of the
decimal. Then divided 1.25 into 110 and saw it came out to an even 88.
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Average/94509: I am just lost on this one
HElp
A small company produces both doll houses and sets of doll furniture. The doll houses take 3 hours of labor to produce, and the furniture sets take 8 hours. The labor available is limited to 400 hours per week, and the total production capacity is 100 items per week. Existing orders requare that at least 20 doll houses and 10 sets of furniture be produced per week. Write a system of inequalities representing this situation, where x is the number of doll houses and y is the number of furniture sets. Then graph the system of inequalities.
1 solutions
Answer 68870 by ankor@dixie-net.com(15639) on 2007-08-26 21:32:22 (Show Source):
You can put this solution on YOUR website!This same problem came up a few months ago. This is what I submitted then.
Perhaps it will help you.
:
:
A small company produces both doll houses and sets of doll furniture. The doll houses take 3 hours of labor to produce, and the furniture sets take 8 hours. The labor available is limited to 400 hours per week, and the total production capacity is 100 items per week. Existing orders require that at least 20 doll houses and 10 sets of furniture be produced per week. Write a system of inequalities representing this situation, where x is the number of doll houses and y is the number of furniture sets. Then graph the system of inequalities.
:
x = number of doll houses; y = furniture sets
:
The labor constraint:
3x + 8y =< 400
Arrange in the general (y=) form so we can plot the graph
8y =< 400 - 3x
y =< (400/8) - (3/8)x
y =< 50 - (3/8)x
:
The production constraint:
x + y =< 100
y =< 100 - x
:
Min house constraint:
x => 20
:
Min furniture constraint
y => 10
:
Plot the Labor equation; I assume you know how to substitute for x and find y
x | y
-------
0 | 50
8 | 47
32 | 38
:
Plot the production restraint
x | y
------
0 |100
20 | 80
50 | 50
:
x => 20 is at or to the right of a vertical line going thru x=20
:
y => 10 is at or above a horizontal line going thru y = 10
:
Look something like this: You have to draw in the vertical line at x = 20
:
Area of feasibility:
1. At or below the green or purple lines which ever is lowest
2. At or above the horizontal line
3. At or to the right of vertical line at x=20 which you have to draw in
:
Any question about this?
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Travel_Word_Problems/94481: A Monorail car traves 100 miles in 50 minutes less time than it takes and automobile to travel the same distance. Find the speeds of the two vehicles if the monorail goes 20 mph faster than the automobiles.
1 solutions
Answer 68818 by ankor@dixie-net.com(15639) on 2007-08-26 18:13:38 (Show Source):
You can put this solution on YOUR website!A Monorail car travels 100 miles, in 50 minutes less time than it takes and automobile to travel the same distance. Find the speeds of the two vehicles if the monorail goes 20 mph faster than the automobiles.
:
Let s = speed of the auto
Then
(s+20) = speed of the monorail
:
Change 50 min to hr: 50/60 = 5/6 hr
:
Write a time equation, time = dist/speed
:
Auto time - mono time =  hr
 -  =
:
Get rid of the denominators, multiply equation by 6s(s+20)
6(s+20)(100) - 6s(100) = s(s+20)(5)
:
(6s + 120)(100) - 600s = 5(s^2+ 20s)
:
600s + 12000 - 600s = 5s^2 + 100s
:
0 = 5s^2 + 100s - 12000
:
Simplify the quadratic equation, divide by 5
s^2 + 20s - 2400 = 0
:
Factors to:
(s + 60)(s - 40) = 0
:
s = +40; it's the positive solution we want here
:
Auto speed: 40 mph, monorail speed: 60 mph
:
:
Check our solutions
100/40 - 100/60 =
2.5 - 1.667 = .8333 which is 5/6
:
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