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Travel_Word_Problems/330466: please answer this question:
a car is travelling at the rate of 60 km. per hour while another car is travelling at the rate of 7 km per hour.in how many hours will the two cars be when they are 260km. apart?
1 solutions
Answer 236873 by mananth(12270)   on 2010-08-10 05:34:58 (Show Source):
You can put this solution on YOUR website!
I have assumed Car B rate as 70 km/hour instead of 7 which looks practical. If not then replace 70 with 7 and you will get the desired answer.
Car A 60 km/hour
car B 70 km/hour
..
Let Car A travel x km in the time car b travels 260-x
x/60 = 260-x/70
70x=60(260-x)
70x=15600-60x
70x+60x=15600
130x= 15600
x= 120 km
speed of car A = 60 km/hour
120/60 = time
=2 hours.
They will be 260 km apart after 2 hours
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Inequalities/330452: please help me solve this problem.
graph this inequality
1. y<-2x+1
1 solutions
Answer 236872 by mananth(12270) on 2010-08-10 05:24:33 (Show Source):
You can put this solution on YOUR website!y<-2x+1
take 3 values for x and find the corresponding y value. (x,1)(2-3)(-2 5)
draw the line.
Since y < -2x+1 draw the line dotted and shade the portion below the line which is is the area of our solution.
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Miscellaneous_Word_Problems/330465: The difference between 2 numbers, a and b, is 24.
When 4 is added to both a and b, the larger of these new numbers is 5 times the smaller of these new numbers.
What is the value of the smaller of the 2 numbers, a and b?
P.S. I know the answer is 2, but I don't know how to show the equation, as I'm confused with a and b!!! Thank you
1 solutions
Answer 236871 by mananth(12270) on 2010-08-10 05:18:30 (Show Source):
You can put this solution on YOUR website!let smaller number be b
bigger number be a
a-b=24...............1
..
a+4 = 5(b+4)
a+4=5b+20
a-5b=20-4
a-5b=16...............2
subtract equation 2 from 1
a-b-a+5b=24-16
4b=8
b=2 the smaller number
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Inequalities/330455: Please help me solve this equation.
Use substitution, addition/subtraction, or linear combination to solve the linear system.
10r-9s=18
6s+2r=1
1 solutions
Answer 236862 by mananth(12270) on 2010-08-10 02:28:45 (Show Source):
You can put this solution on YOUR website!10r-9s=18.....................1
6s+2r=1.......................2
multiply equation 2 by -5 and it to equation 1
-30s-10r+10r-9s=-5+18
-39s=+13
s= 13/-39
s=-1/3
..
plug the value of r in equation 1
10r-9*-1/3= 18
10r+3=18
10r=15
r=15/10
r=3/2
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Numbers_Word_Problems/330456: 600 people attended the premiere of a movie. Adult tickets $500 and children$200. Box office receipts totalled $2400,000, how many children attended the premiere?
1 solutions
Answer 236860 by mananth(12270) on 2010-08-10 02:03:53 (Show Source):
You can put this solution on YOUR website!let number of children be x
number of adults will be 600-x
..
child ticket = 200
adult ticket = 500
..
200x+500(600-x)=240,000
200x+300000-500x= 240,000
-300x=240000-300000
-300x=-60000
x= 200 children
I think the receipts should be 240, 000. I have worked on that basis
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Graphs/330449: Hello, I was hoping you'd please help me out with a math problem.
I have to find an equation in standard form of the line:
a. through (2,-2) and (4,4)
b. perpendicular to y= x + 5 and through (0, -8)
Can you please show me how to solve this problem?
Thank you so much for your help!
1 solutions
Answer 236858 by mananth(12270) on 2010-08-10 01:42:17 (Show Source):
You can put this solution on YOUR website!I have to find an equation in standard form of the line:
a. through (2,-2) and (4,4)
slope between points = y2-y1 / x2-x1
=4-(-2)/4-2
=6/2
=3 = slope
the general equation with slope 3 , y= 3x+b
(2-2) is on the line
-2=2*3+b
-2=6+b
-2-6=b
b=-8
So the equation will be y = 3x-8
b. perpendicular to y= x + 5 and through (0, -8)
y= x+5
compare with y = mx+b
m=1 slope
the line passes through (0,-8)& perpendicular to y =x+5
so the slope of this line will be -1
to find b plug the value of (0,8) & m
8=0+b
b=8
The equation of this line with slope -1 and b = 8 will be
y=-x+8
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Miscellaneous_Word_Problems/330426: if the sides of a square are lengthened by 8 cm, the area becomes 225 cm^2. Find the length of a side of the original square.
The length of a side of the original square is?
1 solutions
Answer 236856 by mananth(12270) on 2010-08-10 01:01:29 (Show Source):
You can put this solution on YOUR website!let side =x
..
the increased length = x+8
Area = (x+8)(x+8)=225
x^2+16x+64=225
x^2+16x-159=0
find the roots of the equation by the quadratic formula
a=1,b=16,c-159
x1=6.933 the original length of square
similarly x2 = -22.9 ignore
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Angles/330430: a car travels from one town to another at a speed of 18mph. if it had gone 18 mph faster, it could of made the trip in a half hour less time. how far apart are the towns?
1 solutions
Answer 236850 by mananth(12270) on 2010-08-10 00:44:04 (Show Source):
You can put this solution on YOUR website!let the distance between towns be x miles
initial speed = 18 mph
time taken = x/18
..
if speed is increased by 18
then speed will be 36 mph
distance =x
time = x/36
x/8- x/36=1/2
LCD= 72
9x-2x / 72=1/2
7x/72=1/2
7x= 72/2
x=72/2*7
x=5.14 miles
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expressions/330444: Solve the system by the elimination method
5x+2y=-7
7x-3y=13
What is the solution of the system?
(___,____) (Type the order pair. Use integers or fractions for any numbers in the expression)
1 solutions
Answer 236849 by mananth(12270) on 2010-08-10 00:33:29 (Show Source):
You can put this solution on YOUR website!5x+2y=-7 ................1
7x-3y=13 ................2
..
multiply equation 1 by 3 and equation 2 by 2 and add them
15x+6y+14x-6y=-21+26
29x=5
divide by 29
x=5/29
plug the value of x in equation 1
5*5/29 +2y=-7
25/29 +2y=-7
Add -25/29
2y=-7-25/29
2y=(-213-25)/29
2y=-228/29
y= -228/29*2
y= -114/29
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Geometry_Word_Problems/330442: My daughter needs help on this problem and I am terrible with word problems. Can you help me step by step on this problem so I can show her how to do it.
snookers lumber can convert logs into either lumber or plywood. In a given day, the mill turns out twice as many units of plywood as lumber. it makes a profit of $20 on a unit of lumber and $45 on a unit of plywood How many of each unit must be produced and sold in order to make a profit of $11440?
Snookers Lumber must produce and sell _____ units of lumber and ____ units of plywood to make a profit of $11440.
1 solutions
Answer 236847 by mananth(12270) on 2010-08-10 00:26:47 (Show Source):
You can put this solution on YOUR website!let them make x numbers of lumber
they will make 2x numbers of plywood. ( double)
Profit on lumber $20
Profit on plywood = $45
..
Total profit earned = $11440
..
Profit on selling lumber + profit on plywood = Total profit.
20x+(45*2x)=11440
20x+90x=11440
110x=11440
divide by 110
115x/110= 11440/110
x= 11440/110
lumber = 104 numbers
..
plywood is double of lumber.
104*2= 208 numbers
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Rectangles/330412: the question was use point-slope form to write the equation of the line with the gien properties. Write equation instandard form. it was "m = -3 passing through P(3,5)
1 solutions
Answer 236821 by mananth(12270) on 2010-08-09 22:04:18 (Show Source):
You can put this solution on YOUR website!"m = -3 passing through P(3,5)
y = mx+b ( plug the value of (x,y) to determine the intercept.
5=-3*3+b
5=-9+b
13=b
the equation will be y = -3x+13
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Rectangles/330407: the question was find the slope of the line passing through each pair of points, if possble. I got both questions wrong on my test. It was P(3,7);Q(6,16) and the other was P(5,17);Q(17,17) the sample they gave for these did not prepare me for that test.
1 solutions
Answer 236805 by mananth(12270) on 2010-08-09 21:34:46 (Show Source):
You can put this solution on YOUR website!P(3,7);Q(6,16)
slope of a line m = y2-y1/ x2-x1 for points (x1,y1) & (x2,y2)
use the formula for the above points
16-7 / 6-3
=9/3
=3
and the other was P(5,17);Q(17,17)
17-17/ 17-5
=0
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Rectangles/330403: the problem was "find the midpoint of the line segment PQ, then the question was P(0,3);Q(-10,-13). I really had problems with this one.
1 solutions
Answer 236801 by mananth(12270) on 2010-08-09 21:28:21 (Show Source):
You can put this solution on YOUR website!the mid point formula between two points (x1,y1) & (x2,y2) is
 
..
P(0,3);Q(-10,-13)
x,y= {0+(-10) / 2 , 3+(-13)/2}
=(-10/2,-10/2}
=-5,-5
..
The mid point is (-5,-5)
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Human-and-algebraic-language/330404: a canoe can travel 12 miles upstream in the same amount of time it takes to travel 30 miles downstream. if the speed of the current is 6 miles per hour, what was the speed of the canoe in still water?
1 solutions
Answer 236798 by mananth(12270) on 2010-08-09 21:21:49 (Show Source):
You can put this solution on YOUR website!let speed of canoe in still water be x
speed of current = 6mph
..
speed with current = x+6 mph
speed against current = x-6 mph
..
time = distance /rate
12/x-6 = 30/x+6 (upstream / down stream times are same )
12(x+6)=30(x-6)
12x+72=30x-180
-18x=-252
x=14 mph
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Numbers_Word_Problems/330178: A friend takes you out to dinner, and you notice that they left a $4.50 tip. The friend tells you they left a 15% tip, so how much was the dinner? Construct an algebra equation where “x” represents the cost of the meal, and solve for x.
1 solutions
Answer 236618 by mananth(12270) on 2010-08-09 10:46:29 (Show Source):
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Quadratic_Equations/330143: I'm on college and math is not my subject. I have tried to work these problems, but I just can't get them. Please help me solve the Quadratic equation x2-2x-13=0 and 4x2-4x+3=0 Thanks so much.
1 solutions
Answer 236600 by mananth(12270) on 2010-08-09 10:14:57 (Show Source):
You can put this solution on YOUR website!x2-2x-13=0
compare it with the general equation
ax^2 +bx +c
a=1, b=-2, c=-13
x1,x2 the roots of the equation are
.
plug the values of a,b,c in the equation.
..
..
and 4x2-4x+3=0
compare it with the general equation
ax^2 +bx +c
a=4, b=-4, c=3
x1,x2 the roots of the equation are
.
plug the values of a,b,c in the equation.
Thanks so much.
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Average/330099: A student’s test scores are 88, 87, 82, 95, and 89. If the student needs an average test score of 90 to obtain a grade of A, what must the score be
on the last test of the semester?
1 solutions
Answer 236548 by mananth(12270) on 2010-08-09 07:28:34 (Show Source):
You can put this solution on YOUR website!
88, 87, 82, 95, and 89.
The total of these scores = 441
If he needs an average of 90 from 6 tests he has to score 90*= 540
..
540-441= 99
..
He has to score 99 to get an average of 90 in the last test
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Linear_Algebra/330055: *You want to get rid of the x by elimination in the system below.
3x + 4y = 7
4x – 2y = 24
If you multiply the top equation by 4, by which number will you multiply the bottom equation?
*Which expression can be substituted for x in the top equation of the system below to solve the system by substitution?
2x + 10y = 1
x – 4y = –4
1 solutions
Answer 236546 by mananth(12270) on 2010-08-09 07:17:02 (Show Source):
You can put this solution on YOUR website!3x + 4y = 7....................1
4x – 2y = 24 ..................2
Multiply equation 1 by -4 and equation 2 by 3 to eliminate x
-12x-16y+12x-6y=-28+72
-22y=44
y=44/-22
y=-2
..
plug the value of y in equation 1
3x+4*-2=7
3x-8=7
3x=7+8
3x=15
x= 15/3
x=5
......
2x + 10y = 1
x – 4y = –4
x= (-4+4y)
2(-4+4y)+10y=1
-8+8y+10y=1
18y=8+1
18y=9
y=1/2
lug the value of y to get value of x
2x+10*1/2 =1
2x+5=1
2x=-4
x=-2
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Numbers_Word_Problems/330091: Give that (6,p) is the midpoint of the line joining the points (q,4) and (8,6), find the values of p and q
1 solutions
Answer 236543 by mananth(12270) on 2010-08-09 06:49:58 (Show Source):
You can put this solution on YOUR website!the midpoint between (x1,y1)&(x2,y2) =  , 
..
the points are (q,4) (8,6)
mid point = (6,p)
(q+8)/2 =6
q+8=12
q=12-8
q=4
..
4+6 /2 =p
10/2=p
p=5
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Mixture_Word_Problems/330094: in high school auditorium the number of rows of seats is double the number of seats in each row. if there are the same number of seats in each row and 1352 seats in total, how many rows are there?
1 solutions
Answer 236541 by mananth(12270) on 2010-08-09 06:38:58 (Show Source):
You can put this solution on YOUR website!let there be x seats in each row.
total seats = 1352
number of rows = 1352/x
number of rows = 2times the number of seats in each row
1352/x = 2x
1352/2=x^2
676=x^2
x= 26 seats in each row.
number of rows = 2*26=52
..
CHECK
52*26=1352
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