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mananth answered: 12270 problems
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Write in Slope-Intercept form:
So far I have
x+3y-3y-4=4-3y-4
x-4=-3y
then divide each side by -3
-1x/3-(-4/3)=y or y=-1x/3+3/4
-5=-1(0)/3+3/4 it gets mixed up from here, am I even doing this correctly? Thanks
1 solutions
Answer 446757 by mananth(12270)   on 2013-03-26 07:03:19 (Show Source):
You can put this solution on YOUR website!good job
slope = -1/3
the line perpendicular will have a slope of 3 ( negative reciprocal)
point (0,-5)
equation will be
(y-(-5))=3(x-0)
y+5=3x
y=3x-5 is the equation
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Age_Word_Problems/730624: a man is ten times as old as his daughter, in 5 years time he will be 5 times as old as his daughter. how old are each of them now ?
Please send breakdown of solution
a father is 48 years old and his son 14 years old ,in how many years will the father be three times older than the son?
Please send break down and solution
1 solutions
Answer 446756 by mananth(12270) on 2013-03-26 06:58:28 (Show Source):
You can put this solution on YOUR website!daughter 's age =x
father's age = 10x
5 years later
daughter's age = x+5
father's age = 10x+5
10x+5 = 5(x+5)
10x+5=5x+25
10x-5x=25-5
5x=20
x=4
daughter 4 years
Father 40 years
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Travel_Word_Problems/730627: A motor boat went downstream for 120 km and immediately returned. It took the boat 15 hours to complete the round trip. If the speed of the river was twice as high, the trip downstream and back would have taken 24 hours. What is the speed of the boat in still water?
1 solutions
Answer 446755 by mananth(12270) on 2013-03-26 06:54:18 (Show Source):
You can put this solution on YOUR website!speed of boat = x
speed of current = y
 ...................(1)
 ....................(2)
x/y =3,
x=3y
substitute x=3y
120+240=60y
360=60y
y=6 kphthe speed of current
x= 3y
x= 18kph speed of boat
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Travel_Word_Problems/730555: A Train leaves Boston at 2:00pm. A second train leaves the same city in the same direction at 8:00pm. The second train travels 150mph faster than the first. If the second overtakes the first at 10pm, what is the speed of each of the two trains.
1 solutions
Answer 446729 by mananth(12270) on 2013-03-26 00:29:08 (Show Source):
You can put this solution on YOUR website!Speed of first train ---------------x
speed of train II-----------------x+150
Second train leaves after 6 hours
the first train has traveled 6x miles before train II starts
catch up speed = 150
catch up distance = 6x
catch up time =8 hours
8=6x/150
x=200 mph speed of first train
200+150 = 350 mph is the speed of train II
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Geometry_Word_Problems/730512: A stained glass window is being designed in the shape of a rectangle surmounted by a semicircle. thw width of the window is to be 3 feet, but the height h. if 24 square feet of glass is to be used, find the hight h.
1 solutions
Answer 446711 by mananth(12270) on 2013-03-25 20:52:53 (Show Source):
You can put this solution on YOUR website!Total area = area of rectangle + area of semi circle
24=h*3 + pi*1.5^2
24=3h +1/2(3.14*2.25)
24= 3h+3.53
3h= 20.47
h=6.82 feet the height of the rectangular portion
if you need total height
then add the radius to it
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Expressions-with-variables/730200: 2x - y =4 (1)
3x - 2y=7 (2)
1 solutions
Answer 446548 by mananth(12270) on 2013-03-25 05:43:58 (Show Source):
You can put this solution on YOUR website!2 x -1 y = 4 .............1
3 x -2 y = 7 .............2
Eliminate y
multiply (1)by -2
Multiply (2) by 1
-4 x 2 y = -8
3 x -2 y = 7
Add the two equations
-1 x = -1
/ -1
x = 1
plug value of x in (1)
2 x -1 y = 4
2 -1 y = 4
-1 y = 4 -2
-1 y = 2
y = -2
x= 1
y= -2
m.ananth@hotmail.ca
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Travel_Word_Problems/730190: system of equations
2 cars start from points 92 miles apart and travel directly towards each other. one car starts at 11am and travels slower and the other starts at 11:15am and goes faster to make up for lost time. they meet at 12pm find the average speed of each car, if the slower car travels 6 mph slower than the faster one.
1 solutions
Answer 446546 by mananth(12270) on 2013-03-25 05:26:48 (Show Source):
You can put this solution on YOUR website!let the speed of slower car be x
the speed of car II = x+6
They meet after 1 hour after car I starts
distance by car I = x
distance by car II = (x+6)*3/4........... ( speed * time)
x+3/4(x+6)=92
multiply by 4
4x+3(x+6)=368
4x+3x+18=350
7x=350
x=50
50 & 56mph
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Sequences-and-series/730193: The fifth term of a geometric sequence is 15 and the eighth term is -15/8. Find the first term, common ratio and the third term.
1 solutions
Answer 446544 by mananth(12270) on 2013-03-25 04:50:08 (Show Source):
You can put this solution on YOUR website!t5 = a*r^4=15
t8 = ar^7= -15/8
r=-1/2
ar^4 = 15
a*(-1/2)^4=16
a*(1/16)=15
a= 240
T3 = 240*(1/4)
T3= 60
CHECK
t8= 240 * (-1/2)^7
= 240*(-1/128)
=-15/8
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Money_Word_Problems/730175: interest received on one account at 8% and the second account at 9.5% first account is 3000 more than second what is total amount of interest earned
1 solutions
Answer 446519 by mananth(12270) on 2013-03-25 00:19:02 (Show Source):
You can put this solution on YOUR website!Account II--------------------x--------------------9.5%
Account I------------------x+3000------------------8%
Total interest earned = 9.5%x+8%(x+3000)
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test/729945: (6,-6); 9x+7y=8 write an equations of the line containing the given point and perpendicular to the line
1 solutions
Answer 446500 by mananth(12270) on 2013-03-24 22:12:11 (Show Source):
You can put this solution on YOUR website!9 x + 7 y = 8
Find the slope of this line
7 y = -9 x + 8
Divide by 7
y = -9/ 7 x + 8/7
Compare this equation with y=mx+b, m= slope & b= y intercept
slope m = -9/7
The slope of a line perpendicular to the above line will be the negative reciprocal 7/9
Because m1*m2 =-1
The slope of the required line will be 7/9
m= 7/9 ,point ( 6 , -6 )
Find b by plugging the values of m & the point in
y=mx+b
-6 = 14/ 3 + b
b= -32/3
m= 7/9
The required equation is y = 7/ 9 x -32/ 3
m.ananth@hotmail.ca
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Linear_Equations_And_Systems_Word_Problems/730123: An investor invested a total of $2,500.00 in two mutual funds. one fund earned 9% of the profit while the other earned a 6% profit. If the investors total profit was $165.00 how much was invested in each mutual fund?
1 solutions
Answer 446495 by mananth(12270) on 2013-03-24 22:01:31 (Show Source):
You can put this solution on YOUR website!Part I 9.00% per annum ------------- Amount invested =x
Part II 6.00% per annum ------------ Amount invested = y
2500
Interest----- 165.00
Part I 9.00% per annum ---x *
Part II 6.00% per annum ---y
Total investment
x + 1 y= 2500 -------------1
Interest on both investments
9.00% x + 6.00% y= 165
Multiply by 100
9 x + 6 y= 16500.00 --------2
Multiply (1) by -9
we get
-9 x -9 y= -22500.00
Add this to (2)
0 x -3 y= -6000
divide by -3
y = 2000 - x)
Part I 9.00% $ 500
Part II 6.00% $ 2000
CHECK
500 --------- 9.00% ------- 45.00
2000 ------------- 6.00% ------- 120.00
Total -------------------- 165.00
11.6
m.ananth@hotmail.ca 1520
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Linear-systems/730132: use the method of substitution to solve the system of linear equation
a. 2x-y=2
b. 7x-3y=10
1 solutions
Answer 446493 by mananth(12270) on 2013-03-24 21:59:06 (Show Source):
You can put this solution on YOUR website!2 x + - y = 2 .............1
- y = 2 + -2 x
/ -1 =
y = -2 + 2 x
7 x + -3 y = 10 .....................2
Substitute y in (2)
7 x -3 ( -2 + 2 x ) = 10
7 x + 6 + -6 x = 10
7 x -6 x = 4
1 x = 4
/ 1
x= 4
Plug the value of x in (1)
2 x - y = 2
2 * 4 - y = 2
8 + - y = 2
-1 y = -6
/ -1
y= 6
m.ananth@hotmail.ca
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Travel_Word_Problems/730127: A woman rows a boat upstream form one point on a river to another point 12km away in 1 and half hours. The return trip with the current takes only 40 minutes. How fast would she be rowing if she were rowing in still water (as if there is no current), and what speed is the current flowing ?
1 solutions
Answer 446491 by mananth(12270) on 2013-03-24 21:54:08 (Show Source):
You can put this solution on YOUR website!Boat speed speed =x mph
current speed =y mph
against current 1.5 hours
with current 2/ 3 hours
Distance with current 12 miles distance against current 12
t=d/r against current (x-y)
12.00 / ( x - y )= 1.50
1.50 x - -1.50 y = 12.00 ....................1
with current (x+y)
12.00 / ( x + y )= 2/3
2/3 ( x + y ) = 12.00
2/3 x + 2/3 y = 12.00
2x+2y=36
x+y=18........................(2)
multiply equation (1) by 2
we get3x-3y=24
multiply equation (2) by 3
3x+3y=54
add up the equations
6x=78
x=13 km/h the speed of boat in stll water
plug x in the equation x+y=18
y=5km/h the current speed
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Linear_Equations_And_Systems_Word_Problems/730125: a+6b=5
a+2b=-3
solve using the elimination method, the answer is an ordered pair
1 solutions
Answer 446486 by mananth(12270) on 2013-03-24 21:43:21 (Show Source):
You can put this solution on YOUR website!1 a + 6 b = 5 .............1
1 a + 2 b = -3 .............2
Eliminate y
multiply (1)by 1
Multiply (2) by -3
1 a 6 b = 5
-3 a -6 b = 9
Add the two equations
-2 a = 14
/ -2
a = -7
plug value of a in (1)
1 a + 6 b = 5
-7 + 6 b = 5
6 b = 5 + 7
6 b = 12
b = 2
a= -7
b= 2
(-7,2) is the solution
m.ananth@hotmail.ca
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Mixture_Word_Problems/730110: ellen wants to mix candy worth 1.09$ per pound with candy worth $3.32 per pound to form 25 pounds of a mixture worth $2.43 per pound. how many pounds of the expensive candy should she use?
1 solutions
Answer 446476 by mananth(12270) on 2013-03-24 21:18:16 (Show Source):
You can put this solution on YOUR website! price ---------------- quantity
Candy type I 3.32 ---------------- x pounds
Candy type II 1.09 ------ 25 - x pounds
Mixture 2.43 ---------------- 25
25
3.32 x + 1.09 ( 25 - x ) = 60.75
3.32 x + 27.25 - 1.09 x = 60.75
3.32 x - 1.09 x = 60.75 - -27.25
2.23 x = 33.5
/ 2.23
x = 15.02 pounds 3.32 Candy type I
9.98 pounds 2.43 Candy type II
m.ananth@hotmail.ca
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Equations/730084: Mrs. Crews bought 4 pencils and 3 pens for $5.60... Mrs Henderson bought 2 pencils and 3 pens for $4.60 of the same kind... What is the price for each pen and pencil?
1 solutions
Answer 446473 by mananth(12270) on 2013-03-24 21:12:45 (Show Source):
You can put this solution on YOUR website!x= price of pencil
y= price of pen
4.00 x + 3.00 y = 5.60 .............1
2.00 x + 3.00 y = 4.60 .............2
Eliminate y
multiply (1)by -1.00
Multiply (2) by 1.00
-4.00 x -3.00 y = -5.60
2.00 x + 3.00 y = 4.60
Add the two equations
-2.00 x = -1.00
/ -2.00
x = .50
plug value of x in (1)
4.00 x + 3.00 y = 5.60
2.00 + 3.00 y = 5.60
3.00 y = 5.60 -2.00
3.00 y = 3.60
y = 1.20
x= 0.50 price of pencil
y= 1.20 price of pen
m.ananth@hotmail.ca
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Travel_Word_Problems/729798: An aeroplane takes off from the ground at an angle of 27 degrees and its average speed in the first 10 seconds is 200 km h-1 . What is the altitude of the plane at the end of this time?
1 solutions
Answer 446256 by mananth(12270) on 2013-03-24 06:19:40 (Show Source):
You can put this solution on YOUR website!from the given condition
sin theta = opposite side / hypotenuse
Sin 27 = altitude/ the distance traveled in 10 seconds
200 km/h
200*1000/3600 m /s
=55.56
sin 27 = altitude / 55.56
0.45= altitude/55.56
altitude = 25 meters
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Linear-systems/729818: Three numbers are in the ratio of 4 : 5 : 6. If the sum of the largest and the smallest equals the sum of the third and 55, find the numbers.
1 solutions
Answer 446255 by mananth(12270) on 2013-03-24 06:08:07 (Show Source):
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test/729826: THE DIAMETER OF THE WHEEL OF A CAR IS 5OCM.THE CAR TRAVELLS 72KM/HR,THEN WHAT IS THE DISTANCE COVERED BY CAR IN 1SEC,AND HOW MANY TIMES THE WHEEL RPTATES WITHIN 1 SECOND??
1 solutions
Answer 446254 by mananth(12270) on 2013-03-24 06:02:02 (Show Source):
You can put this solution on YOUR website!72 km/h = (72000/3600) m/s
= 20 m/s
it travels 20 m in 1 sec
=2000 cm
circumference of wheel = pi *d
=3.14*50
=157 cm
Number of rotations = 2000/157
= 12.74 rev
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Equations/729830: a rectangle has a perimeter of 36cm. the square of the length of its diagonal is 164 square metres. find the dimensions of the rectangle.
1 solutions
Answer 446253 by mananth(12270) on 2013-03-24 05:53:45 (Show Source):
You can put this solution on YOUR website!Perimeter
2(l+w)=36
l+w=18
l^2+w^2= 164
(l+w)^2-2lw=164
18^2-2lw=164
324-21w=164
21w=160
lw=80
l=80/w
substitute l
in l+w=18
80/w + w = 18
multiply by w
80+w^2=18w
w^2-18w+80=0
(w-10)(w-8)=0
w=8 OR 10
so dimensions are 10cm & 8 cm
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Travel_Word_Problems/729729: Hi, could you help me solve this word problem:
Ahmed and Bryan are on two different boats that are 60km apart. Byran starts sailing west at 10km/h. Two hours later, Ahmed starts sailing south at 30km/h. They both arrive at the port, P at exactly the same time. How long does it take Bryan to get to the port?
I set up a digram, and I started to set up a table that has time, speed, and distance. Ahmed's time was x-2 his speed x and distance 30. Bryan's time was x his speed x and distance 10. That's as far as I got before I became unsure if this was the right approach. Thanks.
1 solutions
Answer 446233 by mananth(12270) on 2013-03-23 22:20:35 (Show Source):
You can put this solution on YOUR website!Ahmad boat A
Bryan boat B
They meet at P
BPA is right angled
Let Bryan take time t
Ahmad takes t-2
in time t Bryan goes 10 t km
in time (t-2) Ahmad goes 30 (t-2) km
(10t)^2 +(30(t-2))^2=60^2
100t^2+900t^2-3600t+3600=3600
1000t^2_3600t=0
1000t^2=3600t
1000t=3600
t=3.6 hours
Check
10*3.6 = 36 km
30*1.6 = 48 km
36^2+48^2=3600
60^2=3600
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Quadratic_Equations/729742: Solve the following system of equation,graphically:y=3x+6
y= -x-2
X. /. Y. X. / Y.
1 solutions
Answer 446222 by mananth(12270) on 2013-03-23 21:47:32 (Show Source):
You can put this solution on YOUR website!Find the x & y intercept points by plugging x=0,y=0 in both equations.
y=3x+6.........................(1)
y=-x-2..........................(2)
equation I
when x= 0 y= 6 ,( 0 , 6 )
when y = 0 x= 6 ,( -2 , 0 )
Equation 2
when x= 0 y= -2 ( 0 , -2 )
when y = 0 x= -2 ( -2 , -0 )
You will observe that the point of intersection is -2,0
The solution of the system is ( -2 , 0 )
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Volume/729582: water flows through a circular pipe of diameter 2cm at 7m/sec into a cylindrical vessel of base radius 40cm. by how much the level of water in it rise in 30 min?
1 solutions
Answer 446049 by mananth(12270) on 2013-03-23 08:32:46 (Show Source):
You can put this solution on YOUR website!water flows through a circular pipe of diameter 2cm at 7m/sec into a cylindrical vessel of base radius 40cm. by how much the level of water in it rise in 30 min?
the volume flowing in 1 sec is its volume
pi*r^2h
r=1cm
h=700cm
V= pi*1^2*700
=22/7 *1*700
=2200 cm^3
2200cm^3 in 1 sec
in 30 * 60 = 1800 sec
2200*1800 cm^3
3960000 cm^3 in 30 min
radius = 40 cm
V= pi*r^2 *h
=22/7 * 40*40*h
3960000=(22/7) *40*40*h
h=7*3960000/40*40*22
787.5 cm in 30 minutes
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Travel_Word_Problems/729600: car A left dagupan at 9:00 am going to manila with a velocity of 40km/hr.
after 1hr,car B left from the same location and taken the same route as car A going to manila. if car B has a velocity of 90km/hr, what time does car B over take car A?
1 solutions
Answer 446048 by mananth(12270) on 2013-03-23 08:17:28 (Show Source):
You can put this solution on YOUR website!First car 40 mph
Car II 90 mph
First car 09:00
Car II 10:00
Difference in time= 01:00 => 1.00 hours
First car will have covered 40.00 miles Car II starts
catch up distance= 40.00 miles
catch up speed = 90 -40
catch up speed = 50 mph
Catchup time = catchup distance/catch up speed
catch up time= 0.8
catch up time= 0.80 hours =48 minutes
They will meet at 10:48 pm
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Travel_Word_Problems/729588: a plane flies to Sydney airport and back,It took one hour less time to get there than it did to get back.The average speed on the trip there wsa 220 km/h.The average speed on the way back was 200km/h.How many hours did the trip there take?
1 solutions
Answer 446047 by mananth(12270) on 2013-03-23 08:13:31 (Show Source):
You can put this solution on YOUR website!let speed of plane be x kmph
time there - time return = 1
x/200 - x/220 = 1
220x-200x=220*200
20x= 220*200
x= 220*200/20
x= 2200 km
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Linear-equations/729602: 1)if the line passing through the points (2,a) and (5,-3) is parallel to the line passing through the points (4,8) and (-5,a+1), what is the value of a?
2) determine the value of k for which the system of linear equations has no solution
2x-y=3
4x+ky=5
1 solutions
Answer 446046 by mananth(12270) on 2013-03-23 08:08:55 (Show Source):
You can put this solution on YOUR website!(2,a) and (5,-3)
slope 
=(-3-a)/2
is parallel to the line passing through the points
(4,8) and (-5,a+1)
slope 
= 
the lines are parallel so the slopes are equal
-9(-3-a)=2(a-7)
27+9a=2a-14
7a=-41
a=-41/7
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