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write the equation of a line that is perpendicular to the given line and that passes through the given point
1 solutions
Answer 262703 by mananth(12270)   on 2010-11-09 20:00:37 (Show Source):
You can put this solution on YOUR website!4x-12y=2
12y=4x-2
/12
y= (1/3)X -1/6
slope = 1/3
..
the line perpendicular will have a slope of -3
equation of line passing through (10,-1) & slope -3
(y-10)=-3(x+1)
y-10 = -3x-3
y=-3x+7
...
...
m.ananth@hotmail.ca
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Linear-systems/368733: y=5x+6
-18x+3y=-54
Are the graphs of the lines in the pair parallel? Explain.
Solution:
In the second equation, divide everything by 3: -6x+y=-54
Then, add 54 to each side: 54-6x+y=0
Next, subtract y from each side: -6x+54=-y
Now, add the two equations together: 0=-x+60
Finally, add x to both sides: x=60
The equation "x=60" denotes a vertical line, but the equation "y=5x+6" denotes a line with a slope of 5, so the lines are not parallel.
1 solutions
Answer 262699 by mananth(12270) on 2010-11-09 19:54:03 (Show Source):
You can put this solution on YOUR website!y=5x+6..............1
...
-18x+3y=-54
3y= 18x-54
/3
y = 6x -18 .......2
compare the slopes.
They are not the same. Hence they are not parallel lines.
..
...
m.ananth@hotmail.ca
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Exponential-and-logarithmic-functions/368721: A car dealership offers two ways to decrease the cost of a new car the dealer will offer a 10% discount off the sticker price for buying today, and there is a manfacturer rebate offered of $2000 if you buy a GMC vehicle. You decide to buy a GMC Yukon for $50,000. Does it matter what order the dealer applies the two deals to lower your price? Calculate the cost with the discount first and then rebate second. Calculate the cost with the rebate first and then the discount econd. Is there a difference
1 solutions
Answer 262698 by mananth(12270) on 2010-11-09 19:45:58 (Show Source):
You can put this solution on YOUR website!price of car $50,000
less rebate $ 2,000
selling price $48,000
..
10% discount on $48,000 = $4800
Final price of the car = 48,000 less $4,800
= $43,200.00
..
Option 2- discount first
price of car $ 50,000
less 10% discount= $5000
Price = $45,000.
less $2,000
= $ 43,000
Now you can decide.
..
m.ananth@hotmail.ca
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Graphs/368208: A fax machine costs $700, and depriciates at a rate of $25 a month.
Find the function F that can be used to determine the value of the fax machine t months after purchase?
Complete model F(t)=
1 solutions
Answer 262427 by mananth(12270) on 2010-11-09 05:13:03 (Show Source):
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Average/368238: One inch is equal to approximately 2.5 centimeters. Let x represent inches and y represent centimeters. Write an equation in standard form relating x and y. Give the values of A, B, and C.
1 solutions
Answer 262423 by mananth(12270) on 2010-11-09 05:08:55 (Show Source):
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Miscellaneous_Word_Problems/368293: Several people are standing in a straight line to buy concert tickets. Starting at one end of the line, Bill is counted as the 15th person, and starting at the other end, he is counted as the 37th person. How many people are in the line?
(A) 22 (B) 23 (C) 50 (D) 51 (E) 52
1 solutions
Answer 262421 by mananth(12270) on 2010-11-09 05:02:41 (Show Source):
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Equations/368263: Find the value of x:
x^-2 = 1/36
I took the reciprocal of the index -2...
(x^-2)-1/2 = (1/36)^-1/2
I am stuck right here. Can anyone provide me with step by step solutions? Thank you so much and have a nice day!
1 solutions
Answer 262418 by mananth(12270) on 2010-11-09 04:32:08 (Show Source):
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Travel_Word_Problems/368155: Char travels 3.6 hours on Saturday to visit.
On Sunday she travels the same distance in 4 hours. Her speed on Sunday is
5 mph slower. What was her speed on Sunday?
1 solutions
Answer 262392 by mananth(12270) on 2010-11-08 22:43:59 (Show Source):
You can put this solution on YOUR website!Char travels 3.6 hours on Saturday to visit.
On Sunday she travels the same distance in 4 hours. Her speed on Sunday is
5 mph slower. What was her speed on Sunday?
let speed on saturday be x mph
..
on sunday speed = x-4 mph
3.6x = 4(x-4)
3.6x = 4x-16
0.4x= 16
x= 16/0.4
x= 40 mph. speed on saturday
..
speed on sunday = 35 mph
,,,
m.ananth@hotmail.ca
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test/368207: What is a cofficient? What is a constant?
1 solutions
Answer 262391 by mananth(12270) on 2010-11-08 22:39:01 (Show Source):
You can put this solution on YOUR website!co-efficients are numbers multiplied by a variable
3x, 4ab,6t^2 12abc,16a^b^2c^2
the numbers before the variables are all coefficients. The value of the whole term depenmds on the value of the variable.
..
constants are numbers. They have a fixed value.
...
m.ananth@hotmail.ca
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Geometry_Word_Problems/368224: the base of a triangle exceeds the height by 9 yards, if the area is 221 square yards, find the length of the base and the height of the triangle
1 solutions
Answer 262389 by mananth(12270) on 2010-11-08 22:34:15 (Show Source):
You can put this solution on YOUR website!let height be h
base = h+9
area = 1/2 * h * (h+9)
221= 1/2 (h^2+9h)
442= h^2 +9h
h^2+9h-442=0
h^2+26h-17h-442=0
h(h+26)-17(h+26)=0
(h-17)(h+26)=0
So h = 17 yards the height
base = 26 yards
...
m.ananth@hotmail.ca
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Linear_Equations_And_Systems_Word_Problems/368233: Martina is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
Company A charges $117 and allows unlimited mileage.
Company B has an initial fee of $75 and charges an additional $0.70 for every mile driven.
For what mileages will Company A charge at least as much as Company B? Use m for the number of miles driven, and solve your inequality for m.
1 solutions
Answer 262387 by mananth(12270) on 2010-11-08 22:27:44 (Show Source):
You can put this solution on YOUR website!Company A charges $117 and allows unlimited mileage.
Company B has an initial fee of $75 and charges an additional $0.70 for every mile
..
let number of miles = m
75+0.7m = 117
0.7m = 117-75
0.7m = 42
/0.7
m= 42/0.7
m = 60 miles they will be costing same
...
m.ananth@hotmail.ca
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Mixture_Word_Problems/368228: a chemist mixes a 20% acid solution with a 60%acid solution to make 40 gallons of a 50%acid solution and how much of the 20% soloion and how much of the 60% solution was used
1 solutions
Answer 262386 by mananth(12270) on 2010-11-08 22:24:29 (Show Source):
You can put this solution on YOUR website!a chemist mixes a 20% acid solution with a 60%acid solution to make 40 gallons of a 50%acid solution and how much of the 20% soloion and how much of the 60% solution was used
..
20% acid solution : x gallons
60%acid solution : 40-x
50%acid solution 40 gallons
..
0.2x+0.6(40-x)= 0.5*40
0.2x+24x-0.6x=20
-0.4x= -4
/-0.4
x= 10 gallons---- 20%
...
30 gallons 60% solution
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m.ananth@hotmail.ca
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Linear_Equations_And_Systems_Word_Problems/368223: the dimensions of a rectangle are such that its lenght is 7in more than its width. if the length were doubled and the width were decreased by 3in. the area would be increased by 68in^2. what are the length and width of the rectangle
1 solutions
Answer 262385 by mananth(12270) on 2010-11-08 22:20:32 (Show Source):
You can put this solution on YOUR website!the dimensions of a rectangle are such that its lenght is 7in more than its width. if the length were doubled and the width were decreased by 3in. the area would be increased by 68in^2. what are the length and width of the rectangle
..
let width be x
length = x+7
..
length doubled 2(x+7)
width decreased = (x-3)
..
2(x+7)(x-3)-x(x+7)=68
2(x^2+4x-21)-(x^2+7x)=68
(2x^2+8x-42-x^2-7x)=68
x^2+x-42-68=0
x^2+x-110=0
x^2+11x-10x-110=0
x(x+11)-10(x+11)=0
(x+11)(x-10)=0
So x = 10 in the width
length = 17 in.
..
m.ananth@hotmail.ca
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Rectangles/368221: What is the perimeter P of a rectangle whose length is 7 ft more than its width x
I have already tried to put in 2l(7)+2w
1 solutions
Answer 262382 by mananth(12270) on 2010-11-08 22:04:45 (Show Source):
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Average/368219: Tell whether the equation is linear. If so, write the equation in standard form and give the values of A, B, and C.
2x = y/3 - 4
1 solutions
Answer 262381 by mananth(12270) on 2010-11-08 22:02:19 (Show Source):
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Rectangles/367691: A rectangle has an area of 180 centimeters squared and a perimeter of 54 centimeters. What are its dminesions?
1 solutions
Answer 262099 by mananth(12270) on 2010-11-08 10:07:29 (Show Source):
You can put this solution on YOUR website!let length be L & width be W
2(L+W) = 54
L+W = 27
LW = 180
L= 180/W
..
180/W + W = 27
(180+W^2)/W = 27
180+W^2 = 27W
W^2-27W+180=0
W^2-15W-12W+180=0
W(W-15)-12(W-15)=0
(W-15)(W-12)=0
W= 15 OR 12
The dimensions are 15cm by 12 cm
..
m.ananth@hotmail.ca
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Travel_Word_Problems/367680: Rowing with the current of a river, a rowing team can row 25 mi. in the same amount of time it takes to row 15 mi. against the current. The rate of the rowing team in calm water is 20 mph. Find the rate of the current.
1 solutions
Answer 262096 by mananth(12270) on 2010-11-08 10:00:33 (Show Source):
You can put this solution on YOUR website!Rowing with the current of a river, a rowing team can row 25 mi. in the same amount of time it takes to row 15 mi. against the current. The rate of the rowing team in calm water is 20 mph. Find the rate of the current.
..
rate of current be x mph
with current rate = x+20 mph
distance = 25 miles
..
time = 25/(20-x)
...
against current speed = x-20 mph
distance = 15
time = 15/(20-x)
..
25/(x+20)= 15/(20-x)
25(20-x)= 15(x+20)
-25x+500= 15x+300
-25x-15x= -500+300
-40x = -200
x= 5 mph
...
m.ananth@hotmail.ca
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Evaluation_Word_Problems/367652: a store mixes kenyan coffee worth $11 per kilogram and venezuelan coffee worth $13 per kilogram. The mixture is to sell for $12 per kilogram. Find how much of each should be used to make a 252-kilogram mixture.
1 solutions
Answer 262068 by mananth(12270) on 2010-11-08 08:57:13 (Show Source):
You can put this solution on YOUR website!a store mixes kenyan coffee worth $11 per kilogram and venezuelan coffee worth $13 per kilogram. The mixture is to sell for $12 per kilogram. Find how much of each should be used to make a 252-kilogram mixture.
kenyan coffee worth $11 per kilogram : let this be x kg
venezuelan coffee worth $13 per kilogram. : 252-x kg
mixture is to sell for $12 per kilogram. 252-kilogram mixture.
...
11x + 13(252-x)= 12*252
11x+3276-13x = 3024
-2x=-252
x = 171 kg ----------- kenyan coffee
171 kg venezuela coffee
...
m.ananth@hotmail.ca
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test/367647: Joel spent 15hrs watching movies. The space adventures were 1.5hrs long and the mysteries were 2hrs long. He watched twice as many space adventures as mysteries. How much time did he spend watching space adventures?
1 solutions
Answer 262058 by mananth(12270) on 2010-11-08 08:36:06 (Show Source):
You can put this solution on YOUR website!let mysteries movies watched be x
space adventures movies watched will be 2x
..
mysteries = 2hours long
space adventures = 1.5 hours
..
2x+1.5*2x =15
2x+3x=15
5x=15
/5
x= 3 movies mysteries
6 movies space adventure
6*1.5 = 9 hours of space adventure
...
m.ananth@hotmail.ca
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Numbers_Word_Problems/367646: Consecutive problem:
If three times the smaller of two consecutive even integers is added to the larger, the result is 4 more than three times the larger. Find the two numbers (solve algebraically).
This is what I have:
3x+x=4x+3x
1 solutions
Answer 262044 by mananth(12270) on 2010-11-08 08:19:00 (Show Source):
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Functions/367621: Once again, I am not sure that I got the topic correct.
Here is the question: 9(2x+1)^3+6(2x+1)^2-15(2x+1)
the answer is: 12(2x+1)(3x+4)
I get the whole answer except the latter 4! I am just not sure!
1 solutions
Answer 262033 by mananth(12270) on 2010-11-08 06:11:11 (Show Source):
You can put this solution on YOUR website!9(2x+1)^3+6(2x+1)^2-15(2x+1)
...
(2x+1)(9(2x+1)^2+6(2x+1)-15)
..
(2x+1)(9(2x+1)^2+9(2x+1)-3(2x+1)-15))
let (2x+1)=a
a(9a^2+6a-15)
3a(3a^2+2a-5)
3a(3a^2+5a-3a-5)
3a((a(3a+5)-1(3a+5))
3a(3a+5)(a-1)
resubstitute the value of a
3a(3(2x+1)+5)(2x+1-1)
3(2x+1)(6x+3+5)(2x)
6x(2x+1)(6x+8)
12x(2x+1)(3x+4)
...
m.ananth@hotmail.ca
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Quadratic_Equations/367596: Dal and Kim can assemble a swing set in 1 1/2 hr. Working alone, it takes Kim 4 hr longer than Dal to assemble the swing set. How long would it take Dal, working alone, to assemble the swing set? I do not have a clue how to set this up Please help!!!
1 solutions
Answer 262018 by mananth(12270) on 2010-11-08 05:45:59 (Show Source):
You can put this solution on YOUR website!Dal and Kim can assemble a swing set in 1 1/2 hr. Working alone, it takes Kim 4 hr longer than Dal to assemble the swing set. How long would it take Dal, working alone, to assemble the swing set?
..
let Dal assemble in x hours
so he does 1/x of the job in 1 hour
..
kim takes (x+4) hours
so he does 1/(x+4) of the job in 1 hour.
..
Together they assemble in 3/2 hours
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1/x + 1/(x+4) = 3/2
(x+4+x)/x(x+4)= 3/2
2x+4 /x(x+4)= 3/2
2(2x+4)=3x(x+4)
4x+8 = 3x^2+12x
3x^2-4x+12x-8 =0
3x^2+8x-8=0
..
find the roots by quadratic equation
discriminant = 160
x1= (-8+sqrt(160))/6
0.77 hours
Dal takes 0.77 hours to complete the job alone
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m.ananth@hotmail.ca
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