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What is the rate of current of the river?
1 solutions
Answer 263893 by mananth(12270)   on 2010-11-12 20:07:57 (Show Source):
You can put this solution on YOUR website!The speed of the boat in still water is 28 mph. the boat traveled 70 miles per hour downstream in the same amount of time that it took to travel 42 miles upstream. What is the rate of current of the river?
..
let rate of current be x mph
rate of boat in still water = 28mph
..
Upstream rate = 28-x mph
downstream rate = 28+x
..
upstream distance = 42 miles
downstream distance = 70 miles
...
t= d/r
upstream time = downstream time
...
42/(28-x) = 70/x
42x=70(28-x)
42x=1960-70x
42x+70x=1960
112x=1960
/112
x= 1960/112
x= 17.5 mph. the rate of current
...
m.ananth@hotmail.ca
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Inequalities/370230: Florencia has at most $60 to spend on clothes. She wants to buy a pair of jeans for $22 dollars and spend the rest on t-shirts. Each t-shirt costs $8. Write an inequality for the number of t-shirts she can purchase and explain how you got that answer.
1 solutions
Answer 263891 by mananth(12270) on 2010-11-12 19:58:52 (Show Source):
You can put this solution on YOUR website!Florencia has at most $60 to spend on clothes. She wants to buy a pair of jeans for $22 dollars and spend the rest on t-shirts. Each t-shirt costs $8. Write an inequality for the number of t-shirts she can purchase and explain how you got that answer.
..
she has $60 at most so that will be<=60
..
she wants to buy a pair of jeans for $22.
she will spend 22 for sure.
..
let number of T shirts she buys be x
so the cost of x T shirts will be 6x
..
INEQUALITY
..
...
m.ananth@hotmail.ca
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Human-and-algebraic-language/370233: If 8/3 of a cetain number is subtracted from eight times the number the result is 128. Find the number.
One number is 20 more than a second number. Their sum is twenty six. What are the numbers?
If tem times the smaller of two consectuve integers is added to six times the larger, the result is 118. Find the integers.
Please help me write all three of them in equation form.
1 solutions
Answer 263881 by mananth(12270) on 2010-11-12 19:38:34 (Show Source):
You can put this solution on YOUR website!If 8/3 of a cetain number is subtracted from eight times the number the result is 128. Find the number.
8x - (8/3)x]= 128
One number is 20 more than a second number. Their sum is twenty six. What are the numbers?
lets second number be x
first number = x+20
x+x+20=26
2x+20 =26
If tem times the smaller of two consectuve integers is added to six times the larger, the result is 118. Find the integers.
..
x, x+1 be the integers
10 times smaller = 10x
6 times larger = =6(x+1)
10x+6(x+1)= 110
m.ananth@hotmail.ca
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Graphs/370074: for the data in the table tell whether y varies directly with x if it does write an equation for the direct variation
x y
0 0
1 -2.5
2 -5
3 -7.5
1 solutions
Answer 263725 by mananth(12270) on 2010-11-12 09:50:51 (Show Source):
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Graphs/370075: the table models the height of a plant as it grows
model the data with an equation
based on your model predict the height of the plant at 12months
time(months)plant height(cm)
3 15
5 25
7 35
9 45
1 solutions
Answer 263723 by mananth(12270) on 2010-11-12 09:48:34 (Show Source):
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Graphs/370077: giselle pays $190 in advanced oh her account at the athletic club each toim she uses the club $5 is deducted from the account the situation can be modled by the equation b=190-5x, where x is the number of visits and b is the total account balance.
graph the equation
find the account balance after 7 visits ($155)
1 solutions
Answer 263721 by mananth(12270) on 2010-11-12 09:46:05 (Show Source):
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Equations/370047: Helen has a rectangular garden that measures 65 meters by 20 meters. How long is the diagonal length of the garden? (An example of diagonal length is from the top left corner to the bottom right corner of the garden.)
1 solutions
Answer 263697 by mananth(12270) on 2010-11-12 08:34:59 (Show Source):
You can put this solution on YOUR website!dimensions of the garden are 65 by 20 meters
..
diagonal and thge sides form a right triangle.
so we have to use Pythagoras theorem
...
Diagonal ^2 = 65^2+20^2
=4225-400
=3825
= sqrt 3825
=61.8 meters
..
m.ananth@hotmail.ca
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Graphs/370044: I am trying to find the slope for the line. 20x-5y=1.2 y=mx+b I have to get the y by itself, so am i setting up the problem like this -5y+20x+1.2. I have to subtract 20 by both sides. i am lost can you help me out.
1 solutions
Answer 263688 by mananth(12270) on 2010-11-12 08:18:26 (Show Source):
You can put this solution on YOUR website!20x-5y=1.2
to simplify , since there is one decimal multiply equation by 10
200x-50y =12
50y = 200x-12
y = 200x/50 -12/50
y = 4x - 6/25
..
slope = 4
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m.ananth@hotmail.ca
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Travel_Word_Problems/370037: a tortoise makes a journey in two parts; it can either walk at 4cm/s or crawl at 3cm/s. if the tortoise walks the first part and crawls the second, it takes 110 seconds. If it crawls the first part and walks the second, it takes 100 seconds. find the lengths of the two parts of the journey.
1 solutions
Answer 263684 by mananth(12270) on 2010-11-12 08:14:33 (Show Source):
You can put this solution on YOUR website!let it walk x cm
let it crawl y cm
..
x/4 + y/3 = 110
3x+4y /12= 110
3x+4y = 1320.....................1
...
x/3 + y/4 = 100
4x+3y / 12 = 100
4x+3y= 1200......................2
...
multiply equation 1 by -4 & equation 2 by 3
-12x-16y= -5280
12x+9y = 3600
...
add the two equations
...
-7 y = -5280+3600
-7y = -1680
y = -1680/-7
y = 240 cm crawl
plug value of y in equation 1
3x+4y=12*110
3x+960=1320
3x=1320-960
3x=360
x = 120 cm walking
m.ananth@hotmail.ca
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Travel_Word_Problems/370035: Andrea purchased two house plants for a total of $65.oo. If the orchard cost $19 more than the Fern, how much did the fern cost?
1 solutions
Answer 263678 by mananth(12270) on 2010-11-12 07:38:54 (Show Source):
You can put this solution on YOUR website!let the price of fern be $x
the orchard will cost x+19
..
she paid $65 for both of them
..
x+x+19 = 65
2x+19=65
add -19
2x+19-19 = 65-19
2x=46
/2
x= $ 23 The price of fern.
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m.ananth@hotmail.ca
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Travel_Word_Problems/370034: Ron and Doug leave the same spot at the same time going in opposite directions. Ron travels at 40mph while doug travels at 60mph. In how many hours will they be 350 miles apart?
1 solutions
Answer 263676 by mananth(12270) on 2010-11-12 07:33:58 (Show Source):
You can put this solution on YOUR website!Ron 40 mph
Doug 60 mph
..
they are moving away from each other
their combined speed = 100 mph
..
distance = 350 miles
..
t = d/r
..
t = 350/100
t=3.5 hours
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m.ananth@hotmail.ca
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Metalworking/369900: there are five people standing in a room. Antonio is 5 time the age of Patrick who is half the age of Merlyn. Ed is 30 years younger than double Merlyn and Patrick's combined ages. Precious is 79 years younger than Antonio. The sum of their ages is 271. How old is Precious?
1 solutions
Answer 263674 by mananth(12270) on 2010-11-12 06:27:21 (Show Source):
You can put this solution on YOUR website!there are five people standing in a room. Antonio is 5 time the age of Patrick who is half the age of Merlyn. Ed is 30 years younger than double Merlyn and Patrick's combined ages. Precious is 79 years younger than Antonio. The sum of their ages is 271. How old is Precious?
..
let Antonio = x years
Precious = x-79
Antonio = x= 5* age of patrick
Patrick = x/5
..
Patrick = 1/2 age of Merlyn
2*patrick = Merlyn
2x/5= Merlyn
..
Ed = 2*(2x/5 + x/5)-30
Ed = 2*(3x/5)-30
Ed= 6x/5-30
...
now you have all their ages in variables
add them up
x+x-79+x/5 +2x/5 +6x/5-30 =271
2x+x/5 +2x/5+6x/5 = 271+79+30
(10x+x+2x+6x)/5 =380
19x=5*380
x= 5*380/19
x = 100 Antonio's age
Precious = Antonio's age -79
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100-79 = 21
Precious is 21 years
..
m.ananth@hotmail.ca
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Linear-systems/369875: Carla has already written 10 pages of a novel. She plans to write 15 additional pages per month until she is finished.
Write an equation to find the total number of pages P written after any number of months m.
1 solutions
Answer 263673 by mananth(12270) on 2010-11-12 05:58:36 (Show Source):
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Geometry_Word_Problems/369880: A tree casts a shadow 180 feet long. Find the height of the tree if the angle of elevation of the sun is 30°.
1 solutions
Answer 263669 by mananth(12270) on 2010-11-12 05:33:47 (Show Source):
You can put this solution on YOUR website!Height of tree = x feet
length of shadow = 180 feet
angle of elevation = 30 deg.
..
Tan  = height/shadow
Tan (30)* 180 = height of tree
height of tree = 104 feet ( rounded off)
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m.ananth@hotmail.ca
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Geometry_Word_Problems/369984: The length of a room exceeds the width by 5 feet, and the height is 3 feet less than the width. The area of the four walls exceeds the sum fo the areas of ceiling and floor by 240 square feet. Find the dimensions of the room.
1 solutions
Answer 263663 by mananth(12270) on 2010-11-12 05:20:34 (Show Source):
You can put this solution on YOUR website!let width be x
length = x+5
height = x-3
..
Area of 4 walls = 2*LH + 2*WH
= 2*(x-3)(x+5)+2*x*(x-3)
=2(x^2+2x-15)+2x^2-6x
=2x^2+4x-30+2x^2-6x
=4x^2-2x-30
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Area of ceiling & floor
Area = 2 * LW
Area = 2*x*(x+5)
Area = 2x^2+10x
..
4x^2-2x-30 =2x^2+10x+240
2x^2-12x-270=0
/2
x^2-6x-135=0
x^2-15x+9x-135=0
x(x-15)+9(x-15)=0
(x-15)(x+9)=0
x= 15 feet the width
length = x+5 = 15 +5 = 20 feet
height = x-3 = 15-3 = 12 feet
...
m.ananth@hotmail.ca
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Travel_Word_Problems/370005: There is a race to a point 3miles away and back. Person A goes 20 mph, Person B goes 16mph. Where do they meet (in feet).
I figured that it took person A .15 hours to the turning point and the Person B had traveled 2.4 miles in that time.
I don't know how to go the rest of the answer....! Help!
1 solutions
Answer 263659 by mananth(12270) on 2010-11-12 05:01:23 (Show Source):
You can put this solution on YOUR website! race distance = 3 & back
A = 20 mph
B= 16 mph
..
A takes 3/20 hour to reach other end
..
By then
B has reached 16*3/20 miles
=12/5 miles
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at this point of time they are 3-(12/5) miles apart facing each other.
=3/5 miles.
..
Now they are running towards each other
their speeds when added up is 36 mph
..
distance = 3/5 miles
speed = 36 mph
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time they meet = (3/5) /36
3/5 *1/36
=3/180 hours.
..
in 3/180 hours B will run ( d= rt)
3/180 * 20
=1/3 mile
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1/3 * 5280 = 1760 feet from the returning end.
...
m.ananth@hotmail.ca
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Equations/370015: Hi,
I don't understand how to do the below problem, can someone explain please?
(1 1/3)(-1/3)(3/4)
Thank you!!
1 solutions
Answer 263655 by mananth(12270) on 2010-11-12 04:26:17 (Show Source):
You can put this solution on YOUR website!1 1/3 = 4/3
..
4/3 * -1/3 *3/4
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since all are to be multiplied group them in the numerator & denominator
(4*-1*3)/(3*3*4)
-12/36
-1/4
..
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Average/370018: If i score 99 on my first test and 85 on my second, what do I need to get on my third test in order to get an overall average of 90?
1 solutions
Answer 263653 by mananth(12270) on 2010-11-12 04:22:27 (Show Source):
You can put this solution on YOUR website!99 on first
85 on second
total of two tests = 184
..
you need average 90 from 3 tests
so total score will be 90*3 = 270
..
you have 184
you require 270 -184 = 86 in the third test
...
m.ananth@hotmail.ca
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Angles/369970: two angles are supplementary if their sum is 180degrees. the larger angle measures eight degrees more than three times the smaller angle. if x represents the measure of the smaller angle and these two angles are supplementary, find the measure of each angle.
1 solutions
Answer 263601 by mananth(12270) on 2010-11-11 22:10:17 (Show Source):
You can put this solution on YOUR website!smaller angle x
larger angle = 3x+8
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their sum =180
x+3x+8=180
4x+8=180
-8
4x= 172
/4
x=43 degrees
the other angle will be 180 -43=137 degrees
...
m.ananth@hotmail.ca
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Surface-area/369955: Please help me solve this word problem:
There is a 30-60-90 triangle with an area of 24 radical 3. What is the perimeter of this triangle, and what are the side lengths? (All in terms of X)
Thanks so much for the help.
1 solutions
Answer 263591 by mananth(12270) on 2010-11-11 21:51:45 (Show Source):
You can put this solution on YOUR website!in a 30-60-90 triangle the legs are x & xsqrt3
the hypotenuse = 2x
..
Area = !/2 * base * height
multiply by 2
divide by sqrt3
x^2= 48
x = 6.92
hypotenuse = 2*6.92= 13.84
second leg = x sqrt*(3)
=6.92*sqrt*(3)
= 11.98
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perimeter = 11.98+6.92+13.84= 32.74
m.ananth@hotmail.ca
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Travel_Word_Problems/369904: an artic tern flew 11,000 miles in 115 days. How many feet per minute did the bird average?
A sneeze can travel up to 100 mi/h. how many feet per second is this?
1 solutions
Answer 263566 by mananth(12270) on 2010-11-11 20:36:30 (Show Source):
You can put this solution on YOUR website!11,000 miles in 115 days.
..
1 mile = 5280 feet
11000 miles =
11000* 5280 feet
=58080000 feet
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115 days
115 * 24 = 2760 hours
2760 * 60 = 165,600 minutes
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feet /min = 58,080,000/165,600
= 350.72 feet/minute
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sneeze speed = 110 mph
110 miles = 110 * 5280 =580,800 feet
1hour = 3600 seconds
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feet/second = 580,800/3600
= 161.33 feet/second
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m.ananth@hotmail.ca
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Numeric_Fractions/369882: Find the least common denominator (LCD) for fractions with the given denominators.
1. 14 and 21
2. 3, 4, and 5
1 solutions
Answer 263562 by mananth(12270) on 2010-11-11 20:27:32 (Show Source):
You can put this solution on YOUR website!1. 14 and 21
14= 2*7
21=3*7
common factor = 7
LCD = common factor * non common factors
LCD = 7 * 3*2
LCD= 42
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2. 3, 4, and 5
60
...
m.ananth@hotmail.ca
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Linear_Equations_And_Systems_Word_Problems/369883: Giselle pays $190 in advance on her account at the athletic club.Each time she uses the club,$5 is deducted from the account.The situation can be moldeled by the equation b=190-5x,where x is the number of visits and b is the total account balance
graph the equation and find the account balance after 7 visits
1 solutions
Answer 263559 by mananth(12270) on 2010-11-11 20:23:25 (Show Source):
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