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Mixture_Word_Problems/681775: An airplane, flying with a tail wind, travels 1380 miles in 2 hours. The return trip, against the wind, takes 2.5 hours.
Find the cruising speed of the plane and the speed of the wind (assume that both rates are constant).
1 solutions
Answer 422778 by mananth(12270)   on 2012-11-16 20:02:19 (Show Source):
You can put this solution on YOUR website!Plane speed =x mph
wind speed =y mph
Against windx-y 2.5 hours
with wind x+y 2 hours
Distance = 1380 miles distance= 1380
t=d/r against wind
1380.00 / ( x - y )= 2.50
2.50 x - -2.50 y = 1380.00 ....................1
with wind x+y
1380.00 / ( x + y )= 2.00
2.00 ( x + y ) = 1380.00
2.00 x + 2.00 y = 1380.00 ...............2
Eliminate y in the linear system
Multiply (1) by 2.00
Multiply (2) by 2.50
we get y
5.00 x + -5.00 y = 2760.00
5.00 x + 5.00 = 3450.00
10.00 x = 6210.00
/ 10.00
x = 621 mph
plug value of x in (1) y
2.5 x -2.5 y = 1380
1552.5 -2.5 -1552.5 = 1380
-2.5 y = 1380
-2.5 y = -172.5 mph
y = 69
Plane 621 mph
wind 69 mph
CHECK
x+y= 690
X-y= 552 +
1380.00 / ( 690.00 )= 2
1380 / ( 552 ) = 2.5
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Polynomials-and-rational-expressions/681763: A right angled triangle has a height of 2x + 3 centimeters, and a hypotenuse of length 4x - 1 centimeters. Find and expression for the base of the triangle.
1 solutions
Answer 422776 by mananth(12270) on 2012-11-16 19:54:10 (Show Source):
You can put this solution on YOUR website!height of 2x + 3 centimeters, and a hypotenuse of length 4x - 1
Pythagoras theorem
hypotenuse^2= base^2+height^2
base^2= hypotenuse^2-height^2
=(4x-1)^2-(2x+3)^2
=16x^2-8x+1-(4x^2+12x+9)
=16x^2-8x+1-4x^2-12x-9
=12x^2-20x-8
=4(3x^2-5x-2)
=4(3x^2-6x+x-2)
=4(3x(x-2)+1(x-2))
=4(3x+1)(x-2)
base =  cm
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Travel_Word_Problems/681759: A silversmith has two alloys, one containing 60% silver and the other 40% silver. How much of each should be melted and combined to obtain 800 grams of an alloy containing 54% silver?
1 solutions
Answer 422774 by mananth(12270) on 2012-11-16 19:36:50 (Show Source):
You can put this solution on YOUR website! Silver percent ---------------- quantity
Metal alloy I 60 ---------------- x grams
Metal alloy II 40 ------ 800 - x grams
Mixture 54 ---------------- 800
60x+ 40(800 -x)=54 * 800
6000x +4000(800-x) = 4320000
6000x+ 3200000 -4000x = 4320000
6000x- 4000x= 4320000 - -3200000
2000 x = 1120000
/ 2000
x = 560 grams 60.00% Metal alloy I
240 grams 40.00% Metal alloy II
m.ananth@hotmail.ca
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Percentage-and-ratio-word-problems/681755: A large corporation wants to invest 1,200000.00. Part of this amount is invested at 12.5 percent and part at 15%. If the total interest earnings should be 155 000.00 per year, how much should be invested at 15% and how much as 12.5%
1 solutions
Answer 422773 by mananth(12270) on 2012-11-16 19:31:21 (Show Source):
You can put this solution on YOUR website!Part I 15.00% per annum ------------- Amount invested =x
Part II 12.50% per annum ------------ Amount invested = y
1200000
Interest----- 155000
Part I 15.00% per annum ---x
Part II 12.50% per annum ---y
Total investment
x + 1 y= 1200000 -------------1
Interest on both investments
15.00% x + 12.50% y= 155000
Multiply by 100
15 x + 12.5 y= 15500000.00 --------2
Multiply (1) by -15
we get
-15 x -15 y= -18000000.00
Add this to (2)
0 x -2.5 y= -2500000
divide by -2.5
y = 1000000
Part I 15.00% $ 200000
Part II 12.50% $ 1000000
CHECK
200000 --------- 15.00% ------- 30000.00
1000000 ------------- 12.50% ------- 125000.00
Total -------------------- 155000.00
m.ananth@hotmail.ca
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Linear-equations/681403: My math problem is this: Tell whether the graphs of the two equations are parallel lines. Explain your reasoning.
y=5x-7, 5x+y=7
1 solutions
Answer 422666 by mananth(12270) on 2012-11-15 22:17:06 (Show Source):
You can put this solution on YOUR website!y=5x-7,
.
.
5x+y=7
re write in slope intercept form
y=-5x+7
compare the equations with the equation y=mx+b where m is the slope.
The slopes of the two lines are 5 & -5.
They are not equal.
Hence the lines are not parallel.
Parallel lines have equal slopes.
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Money_Word_Problems/681439: Fres Calibig invests a part of $17000 at 8% and the rest 9%. If the annual incomes from the two investments are equal, how much has he invested at each rate?
1 solutions
Answer 422665 by mananth(12270) on 2012-11-15 22:11:51 (Show Source):
You can put this solution on YOUR website!Part I 8.00% per annum ------------- Amount invested =x
Part II 9.00% per annum ------------ Amount invested = y
Total= 17000
Part I 8.00% per annum ---x
Part II 9.00% per annum ---y
Total investment
x+y= 17000 -------------1
Interest on both investments
8.00% x = 9.00%
Multiply by 100
8 x = 9 y
8x-9y=0 --------2
1 x + 1 y = 17000 .............1
8 x -9 y = 0 .............2
Eliminate y
multiply (1)by 9
Multiply (2) by 1
9 x 9 y = 153000
8 x -9 y = 0
Add the two equations
17 x = 153000
/ 17
x = 9000
plug value of x in (1)
1 x + 1 y = 17000
9000 + y = 17000
y = 17000 -9000
y = 8000
y = 8000
x= 9000 Part I
y= 8000 Part II
m.ananth@hotmail.ca
|
test/681449: write an equation of the line that is perpendicular to the given line and passes through the given point. y=x-7(0,-5)
1 solutions
Answer 422662 by mananth(12270) on 2012-11-15 22:02:14 (Show Source):
You can put this solution on YOUR website!y=x-7 and (0,-5)
y=x-7
compare with the equation y = mx+b
m=1
so the slope is 1
the slope of line perpendicular to this line will be -1 (negative reciprocal)
using the equation
y-y1=m(x-x1) where m is the slope and (x1,y1) are the co ordibnates of the point on the line.
y-(-5)=-1(x-0)
y+5=-x
y=-x-5 is the equation
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logarithm/681441: The formula below can be used to find the number of milligrams D of a certain drug that is in a patients bloodstream h hours after the drug has been administered.
D = 5e-0.38h
When the number of milligrams reaches 2, the drug is to be administered again. What is the time between injections?
1 solutions
Answer 422659 by mananth(12270) on 2012-11-15 21:53:40 (Show Source):
You can put this solution on YOUR website!Generally it is an exponential function.
It may be D= 5e^(-0.37h)
I assume the above
here D = 2
2= 5e^(-0.37h)
/5
0.4=e^(-0.37h)
taking the natural log
ln(0.4)=-0.37h
(ln(0.4))/(-0.37)=h
h is the time in hours
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Radicals/681437: x + 2y = 3
3x - 2y = 5
What is the solution to the system of equations?
1 solutions
Answer 422650 by mananth(12270) on 2012-11-15 21:39:18 (Show Source):
You can put this solution on YOUR website!1 x + 2 y = 3................(1)
3 x + 2 y = 5................(2)
Eliminate y
multiply (1)by -1
Multiply (2) by 1
-1 x -2 y = -3
3 x + 2 y = 5
Add the two equations
2 x = 2
/ 2
x = 1
plug value of x in (1)
1 x + 2 y = 3
1 + 2 y = 3
2 y = 3
2 y = 2
y = 1
x= 1
y= 1
The solution (1,1)
m.ananth@hotmail.ca
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Travel_Word_Problems/680833: Walter and John leave in their cars at the same time. Walter drives 252 miles. John drives 10 miles per hours faster than Walter and travels 312 miles. If Walter and John arrive at their destinations at the same time, determine how fast Walter is driving.
1 solutions
Answer 422479 by mananth(12270) on 2012-11-14 21:55:17 (Show Source):
You can put this solution on YOUR website!Walter x mph
John 10 faster x + 10 mph
Walter 252 miles
John 312 miles
Walter time = John time
t=d/r
252 / x = 312 /( x + 10 )
cross multiply
252 ( x + 10 ) = 312 x
252 x + 2520 = 312 x
252 x - 312 x = -2520
-60 x = -2520
/ -60
x = 42 mph
Walter speed = 42 mph
John speed = 52 mph
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Linear_Equations_And_Systems_Word_Problems/680775: A man has Rs.8000 which he wishes to invest in two enterprises so that his total income per year will be Rs.425. if one enterprise pays 5.5% annually and the other 5% annually, how much must be invested in each.
1 solutions
Answer 422473 by mananth(12270) on 2012-11-14 21:46:52 (Show Source):
You can put this solution on YOUR website!Part I 5.50% per annum ------------- Amount invested =x
Part II 5.00% per annum ------------ Amount invested = y
8000
Interest----- 425
Part I 5.50% per annum ---x
Part II 5.00% per annum ---y
Total investment
x + 1 y= 8000 -------------1
Interest on both investments
5.50% x + 5.00% y= 425
Multiply by 100
5.5 x + 5 y= 42500.00 --------2
Multiply (1) by -5.5
we get
-5.5 x -5.5 y= -44000.00
Add this to (2)
0 x -0.5 y= -1500
divide by -0.5
y = 3000
Part I 5.50% $ 5000
Part II 5.00% $ 3000
CHECK
5000 --------- 5.50% ------- 275.00
3000 ------------- 5.00% ------- 150.00
Total -------------------- 425.00
m.ananth@hotmail.ca
|
test/680809: Identify the slope and y- intercept of the line with the equation.
2x-3y=0
1 solutions
Answer 422471 by mananth(12270) on 2012-11-14 21:42:16 (Show Source):
You can put this solution on YOUR website!2x-3y=0
2x=3y
y=2x/3
y/x= 2/3
slope = 2/3
Here b = 0
in the equation y=2x/3 when comparing with y= mx+b
the line passes through the origin. No intercept
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Money_Word_Problems/680811: you inherit $16,000 and invest it in two bonds that pay 6% and 8% annual interest. At the end of one year the interest from the 8% bond is $580 greater than the interest from the 6% bond. How much was invested in each bond?
1 solutions
Answer 422470 by mananth(12270) on 2012-11-14 21:38:38 (Show Source):
You can put this solution on YOUR website!6% bond investment be x
8% bond investment be y
x+y = 16000.................(1)
6%x+580=8%y
multiply by 100
6x+58000=8y
6x-8y=-58000................(2)
solve simultaneously
1 x + 1 y = 16000 .............1
6 x -8 y = -58000 .............2
Eliminate y
multiply (1)by 8
Multiply (2) by 1
8 x 8 y = 128000
6 x -8 y = -58000
Add the two equations
14 x = 70000
/ 14
x = 5000
plug value of x in (1)
1 x + 1 y = 16000
5000 + y = 16000
y = 16000 -5000
y = 11000
y = 11000
x= 5000
y= 11000
$ 5000 @ 6%
$ 11000 @8%
m.ananth@hotmail.ca
|
Equations/680818: I have to write out the answer for 72/n=9. How do I go about this.
1 solutions
Answer 422468 by mananth(12270) on 2012-11-14 21:30:57 (Show Source):
You can put this solution on YOUR website!72/n=9.
In all fractions in equations first you have to eliminate the denominator
we can eliminate the denominator by multiplying by n
multiply equation by n
72=9n
/9
72/9 = 9n/9
n=8
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Equations/680803: find the vertex, any intercepts &the symmetric line?
1. f(x)=x^2+10x+9
1 solutions
Answer 422467 by mananth(12270) on 2012-11-14 21:28:03 (Show Source):
You can put this solution on YOUR website!f(x)=x^2+10x+9
y= x^2+10x+9
x coordinate of vertex = -b/2a= -10/2= -5
plug x= 5 in the equation
x^2+10x+9=y
(-5)^2+10(-5)+9=y
y=-16
Vertex(-5,-16)
The x intercept occurs when y=0, make the equation = 0 and solve for x
x^2 +10x+9 = 0
Factor
(x+9)(x+1) = 0
x = -9 and x = -1, these are the x intercepts
:
y intercept occurs when x=0, substitute 0 for x in the equation, and find y
y = 0^2 - 10(0) + 9
y = 9; :
Axis of symmetry x = -b/2a= -10/2=-5
x=-5 is the axis of symmetry.
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Quadratic_Equations/680795: use the quadratic formula for :
4x^2+4=17x
my answer:
4x^2+4=17x
4x^2+4-17=0
(-17)^2-4(4)(4)=225
___
17(+/-) /225
___________ = 17(+/-)15 /8
8
root: 4, (1/4)
is this right?
1 solutions
Answer 422462 by mananth(12270) on 2012-11-14 21:00:35 (Show Source):
You can put this solution on YOUR website!yes you are right.
a= 4 b= -17 c= 4
b^2-4ac= 289 - 64
b^2-4ac= 225  = 15
x1=( 17 + 15 )/ 8
x1= 4
x2=( 17 -15 ) / 8
x2= 0.25
(4,0.25)
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Percentage-and-ratio-word-problems/680793: Anne and Nancy use a metal alloy that is 15.6% copper to make jewelry. How many ounces of an alloy that is 14% copper must be mixed with an alloy that is 16% copper to form 100 ounces of the desired alloy?
1 solutions
Answer 422460 by mananth(12270) on 2012-11-14 20:57:07 (Show Source):
You can put this solution on YOUR website! percent ---------------- quantity
Metal alloy I 14 ---------------- x ounces
Metal alloy II 16 ------ 100 - x ounces
Mixture 16 ---------------- 100
14x+16(100-x)=15.6*100
1400x+1600(100- x)=156000
1400x+160000-1600x=156000
1400x-1600x= 156000 -160000
-200 x = -4000
/ -200
x=20ounces 14.00% Metal alloy I
80 ounces 16.00% Metal alloy II
m.ananth@hotmail.ca
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Linear-systems/680783: The question is: Solve each system algebraically. Write the solution as an ordered pair.
Problem: {x+ y= 7
{y = 2x -2
I have to find the solution but I am confused on where to begin.
Thanks for the help
1 solutions
Answer 422457 by mananth(12270) on 2012-11-14 20:47:57 (Show Source):
You can put this solution on YOUR website!1 x + 1 y = 7 .............1
y=2x-2
2x-y=2
2 x - y = 2 .............2
Eliminate y
multiply (1)by 1
Multiply (2) by 1
1 x 1 y = 7
2 x -1 y = 2
Add the two equations
3 x = 9
/ 3
x = 3
plug value of x in (1)
1 x + 1 y = 7
3 + y = 7
y = 7 -3
y = 4
y = 4
x= 3
y= 4
(3,4) is the solution
m.ananth@hotmail.ca
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Linear_Equations_And_Systems_Word_Problems/680782: A father is six times as old
as the son. Four years ago
the father was ten times
as old as his son.
Find the
1. son's age
2. Father's age
3. Son's age in 3yrs times.
1 solutions
Answer 422456 by mananth(12270) on 2012-11-14 20:43:36 (Show Source):
You can put this solution on YOUR website!son's age =x
father's age =6x
4 years ago
son's age = x-4
father's age =6x-4
conditon
6x-4=10(x-4)
6x-4=10x-40
6x-10x=-40+4
-4x=-36
/-4
x=9
son's age = 9 years
father's age = 6x= 54
son's age 3 years later --> x+3= 9+3=12
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Linear_Algebra/680747: Solve Linear Systems Algebraically.
x+ 4y = 1
3x + 2y = -12
and
3x + 2y = 6
x-4y = -6
Pleas help, Clari
1 solutions
Answer 422453 by mananth(12270) on 2012-11-14 20:05:36 (Show Source):
You can put this solution on YOUR website!1 x + 4 y = 1 .............1
3 x + 2 y = -12 .............2
Eliminate y
multiply (1)by 1
Multiply (2) by -2
1 x 4 y = 1
-6 x -4 y = 24
Add the two equations
-5 x = 25
/ -5
x = -5
plug value of x in (1)
1 x + 4 y = 1
-5 + 4 y = 1
4 y = 1 + 5
4 y = 6
y = 2
x= -5
y= 2
---------------
3 x + 2 y = 6 .............1
1 x -4 y = -6 .............2
Eliminate y
multiply (1)by 2
Multiply (2) by 1
6 x 4 y = 12
1 x -4 y = -6
Add the two equations
7 x = 6
/ 7
x = 1
plug value of x in (1)
3 x + 2 y = 6
3 + 2 y = 6
2 y = 6 -3
2 y = 3
y = 2
x= 1
y= 2
m.ananth@hotmail.ca
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Rectangles/679545: The three dimensions of a rectangular box are height, length, and width. The us of the dimensions is 18 feet. The height equals four fifths the sum of the length and the width. It also equals four times the difference of the length and the width. What are the dimensions of the box?
1 solutions
Answer 421973 by mananth(12270) on 2012-11-12 21:23:06 (Show Source):
You can put this solution on YOUR website!sum of dimensions = 18 feet
l+w+h=18
(l+w)=18-h
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second condition
h= 4/5(l+w)
replace l+w by (18-h)
h=4/5(18-h)
multiply equation by 5
5h= 4(18-h)
5h=72-4h
5h+4h=72
9h=72
h=8
h=4(l-w)
8=l-w
l=8+w
l+w+h=18
8+w+w+8=18
2w+16=18
2w=18-16
2w=2
w=1
so Length =8+w= 9 feet (w=1)
the dimensions are 9 by 8 by 1 feet
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Angles/679542: Please help me to solve the following;
The complement of an angle measures 10(degrees) less than one-fifth of its supplement. Find the measure of the angle.
I started out by writing: 90-x = 10 -1/5(90 - x)
I"m not sure how to handle the fraction (one-fifth). The answer is x=80. Everything I've tried did not work. Your help is appreciated.
Thanks
Joshua
1 solutions
Answer 421969 by mananth(12270) on 2012-11-12 21:13:26 (Show Source):
You can put this solution on YOUR website!angle =x
complement= (90-x)
supplement = 180-x
(90-x)= 1/5(180-x)-10
multiply the equation by 5
5(90-x)= (180-x)-50
450-5x=180-x-50
5x-x= 450-180+50
4x=320
/4
x=80 deg
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Linear-systems/679515: 1.find the equation of a line that passes through the point (0,2)and (4,-1)
2.find the equation of a line that passes through the points (-2,0)and (0,1)
1 solutions
Answer 421968 by mananth(12270) on 2012-11-12 21:07:14 (Show Source):
You can put this solution on YOUR website!(x1,y1)(0,2)and (x2,y2)(4,-1)
The equation of line when coordinates of two pointsa are given
plug the values of (x1,y1)(0,2)and (x2,y2)(4,-1)
y-2=3(x-4)
y-2=3x-12
3x-y-10=0
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Linear-systems/679506: Solving Linear Systems of equations
The problem: one is 5% acid and one is 6.5% acid . You want to make 200ml of vinegar,with 6% acid. How many ml of each vinegar do you need to mix together?
My question: With percents I get confused, and I am not sure which variables you would use to set this up into two equations?
1 solutions
Answer 421967 by mananth(12270) on 2012-11-12 20:58:17 (Show Source):
You can put this solution on YOUR website!Let quantity of 5% acid required be x
Let quantity of 6.5% acid required be y
Mixture = 6%
Equate percentages
5%x+6.5%y=6%*200
multiply by 100
5x+6.5y=1200................(1)
Quantity
x+y=200.....................(2)
multiply equation (2) by -5
we get -5x-5y=-1000
Add this equation to (1)
we get
1.5y=200
y= 200/1.5
y=133.3 ml
x= balance amount= 66.67ml
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