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mananth answered: 12270 problems
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Functions/367599: I am not sure that I chose the correct topic for the question. It is algebriac, but I am not sure of its specific topic. Anyway, here is the question:
(r+2t)^3+(r-7t)^3
The answer is (2r-5t)(r^2+5rt+67t^2)
I cannot figure out how they got the 67t^2!
1 solutions
Answer 262008 by mananth(12270)   on 2010-11-08 05:03:03 (Show Source):
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real-numbers/367602: Consider the equation x2 – 4x + 29 = 0.
(a) Compute the discriminant, b2 – 4ac and state whether there is one real-number solution, or two different real-number solutions, or two different imaginary-number solutions.
(b) Use the quadratic formula to find the exact solutions of the equation. Show work.
1 solutions
Answer 262007 by mananth(12270) on 2010-11-08 04:44:35 (Show Source):
You can put this solution on YOUR website!x2 – 4x + 29 = 0.
..
a=1, b = -4, c= 29
b^2-4ac= 16-116
b^2-4ac=-100
it is less than 0
so the roots are complex
...
x1= 
x1=2+5i
x2= 
...
x2=2-5i
...
m.ananth@hotmail.ca
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test/367603: How do I translate to an inequality: The average speed s, was between 100 and 110 mph?
1 solutions
Answer 262006 by mananth(12270) on 2010-11-08 04:37:10 (Show Source):
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Equations/367606: Find the slope if it exists
x+8y=16
need to know how to solve this problem and how to either write it out in integer or simplified fraction
1 solutions
Answer 262004 by mananth(12270) on 2010-11-08 04:26:03 (Show Source):
You can put this solution on YOUR website!x+8y=16
you have to rewrite the equation in the form y = mx+b
where m is the slope and b the y intercept.
x+8y=16
add -x
x-x+8y=-x+16
8y= -x+16
/8
y = -x/8 +2
the slope is -(1/8)
..
m.ananth@hotmail.ca
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Quadratic_Equations/367556: The denominator of a fraction exceeds the numerator by 2. If 5 be added to numerator the fraction increased by unity. The Fraction is?
1 solutions
Answer 261976 by mananth(12270) on 2010-11-07 23:41:18 (Show Source):
You can put this solution on YOUR website!numerator be x
denominator = x+2
fraction = x/(x+2)
..
(x+5)/(x+2) = x/(x+2) +1
..
(x+5)/(x+2) - x/(x+2) =1
(x+5 -x)/(x+2)= 1
5/(x+2) = 1
5 = x+2
5-2 = x
x=3
...
The fraction is 3/5
.
m.ananth@hotmail.ca
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Miscellaneous_Word_Problems/367553: You are moving to a new home. You decide to hire a moving company, but are unsure which company to choose. You search online and are interested in contacting two companies, Heavy Lifters and Quick Move, to discuss their rates. Heavy Lifting charges an $80 fee plus $35 per hour. Quick Move charges $55 per hour with no additional fees.
Which mover provides a better deal for 2 hours of work? How did you arrive at your answer?
Tips: We need to solve the charge from the two companies for two hours of work. We will multiply the hourly rate by the number of ours. Heavy Lifters have a fee we need to add.
1 solutions
Answer 261974 by mananth(12270) on 2010-11-07 23:36:34 (Show Source):
You can put this solution on YOUR website!Heavy Lifters and Quick Move, to discuss their rates. Heavy Lifting charges an $80 fee plus $35 per hour. Quick Move charges $55 per hour with no additional fees.
Which mover provides a better deal for 2 hours of work? How did you arrive at your answer?
heavy lifters $80 + $35/hour
For 2 hours
80+2*35
= $150
...
Quick Move
$55 /hour
for 2 hours
2*55 = 110
..
Quick Move is a better deal
..
m.ananth@hotmail.ca
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Miscellaneous_Word_Problems/367551: You are back on the HOA board. The time has come to buy more trees and bushes for the neighborhood park. The first order was for 24 bushes and 16 trees and the bill totaled $3960. The second order was 12 bushes and 32 trees and the bill totaled $5220.
Write an equation illustrating the first bill using b for the cost of the bushes and t for the cost of the trees.
Tips: This is writing a basic equation showing the bill. We know how many trees and bushes and the total bill. The unknowns are the cost of each.
Your Solution - Show your Work Below Worth 1 Point
1 solutions
Answer 261972 by mananth(12270) on 2010-11-07 23:32:38 (Show Source):
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Graphs/367482: Find equation of the lines containing the given pair of points..
m=2/3(5,-7)
1 solutions
Answer 261971 by mananth(12270) on 2010-11-07 23:28:48 (Show Source):
You can put this solution on YOUR website!m=2/3(5,-7)
..
the general equation is (y-y1)=m(x-x1)
y-(-7)=2/3(x-5)
y+7 = 2/3x -10/3
y = 2/3 *x -10/3 -7
y= 2/3*x -31/3
...
m.ananth@hotmail.ca
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Travel_Word_Problems/367527: A car is traveling 30 mph faster than a bus, in the time that it takes the bus to travel 105 miles the car travels 195 miles, what is the speed of the car?
Im having trouble ive tried utilizing the v=d/t equation but i keep getting confused in my chart. Your help would be appreciated.
1 solutions
Answer 261970 by mananth(12270) on 2010-11-07 23:21:54 (Show Source):
You can put this solution on YOUR website!A car is traveling 30 mph faster than a bus, in the time that it takes the bus to travel 105 miles the car travels 195 miles, what is the speed of the car?
bus speed be x mph
bus distance = 105
bus time = 105/x
car speed = x+30 mph
car distance = 195
car time = 195/(x+30)
..
car time = bus time
195/(x+30)= 105/x
195x=105(x+30)
195x=105x+3150
195x-105x= 3150
90x = 3150
/90
x= 35 mph speed of bus
speed of car = 30+35 = 65 mph
...
m.ananth@hotmail.ca
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Radicals/367531: sqrt(x+3)+1=sqrt(3x-2) Solve for x
1 solutions
Answer 261966 by mananth(12270) on 2010-11-07 23:04:01 (Show Source):
You can put this solution on YOUR website!sqrt(x+3)+1=sqrt(3x-2) Solve for x
...
square both sides
..
(sqrt(x+3)+1)^2=(sqrt(3x-2))^2
(x+3)+2sqrt(x+3)+1 = 3x-2
x+3 -3x+2+1= -2sqrt(x+3)
-2x+6=-2sqrt(x+3)
-2(x-3)=-2(sqrt(x+3)
divide by -2
(x-3)^2= sqrt(x+3)
square
x^2-6x+9 = x+3
x^2-6x-x+9-3=0
x^2-7x+6=0
x^2-6x-x+6=0
x(x-6)-1(x-6)=0
(x-6)(x-1)=0
x 6 Or 1
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m.ananth@hotmail.ca
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Miscellaneous_Word_Problems/367438: A 200-ft diagonal brace on a bridge connects a support of the center of the bridge to a side support on the bridge. The horizontal distance that it spans is 40 ft longer that the height that it reaches on the side of the bridge. Find the horizontal and vertical distances spanned by this brace.
1 solutions
Answer 261919 by mananth(12270) on 2010-11-07 20:13:59 (Show Source):
You can put this solution on YOUR website!A 200-ft diagonal brace on a bridge connects a support of the center of the bridge to a side support on the bridge. The horizontal distance that it spans is 40 ft longer that the height that it reaches on the side of the bridge. Find the horizontal and vertical distan
..
diagonal = 200 ft.
let the vertical height at which it is fitted be x
the horizontal distance = x+40
..
they form a right triangle
...
x^2+(x+40)^2=200^2
x^2 + x^2 +80x+1600=40000
2x^2+80x-38400=0
/2
x^2+40x -19700=0
discriminant = 80,400
x1= (-40+sqrt*80400))/2
x1= 121.77
vertical distance = 121
horizontal distnace = 161
x2 will be negative so ignore
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m.ananth@hotmail.ca
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Numbers_Word_Problems/367439: Find the number that is 7/12 less than its reciprocal
1 solutions
Answer 261916 by mananth(12270) on 2010-11-07 20:01:46 (Show Source):
You can put this solution on YOUR website!let the number be x
its reciprocal = 1/x
x= 1/x -7/12
x-1/x = -7/12
x^2- 1 /x = -7/12
12(x^2-1)= -7x
12x^2-12 = 7x
12x^2+7x-12 =0
use quadratic equation to find the roots
x1=(-7+sqrt(625))/24
x1= 0.75
x2=(-7-sqrt(625))/24
x2= -1.333
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m.ananth@hotmail.ca
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test/367432: If the y intercept of the graph 3x-ky=14 is -8 what Is the value of k
1 solutions
Answer 261914 by mananth(12270) on 2010-11-07 19:53:28 (Show Source):
You can put this solution on YOUR website!If the y intercept of the graph 3x-ky=14 is -8 what Is the value of k
3x-ky=14
..
ky = 3x-14
plug x=0
ky =-14
-14/k = y
-14/k = -8
k= -14/-8
k=7/4
..
m.ananth@hotmail.ca
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Word_Problems_With_Coins/367434: Mia spent one third of her money on lunch. At lunch, her friend gave her $2.50 to repay a loan. Then Mia spent $3.25 for a movie ticket and $.75 for a snack. She had $4.90 left. How much did Mia have before lunch?
1 solutions
Answer 261911 by mananth(12270) on 2010-11-07 19:46:22 (Show Source):
You can put this solution on YOUR website!Mia spent one third of her money on lunch. At lunch, her friend gave her $2.50 to repay a loan. Then Mia spent $3.25 for a movie ticket and $.75 for a snack. She had $4.90 left. How much did Mia have before lunch?
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let Mia have $x
she spent x/3 on lunch
so she has 2x/ 3 balance
..
friend gace 2.5 = 2 1/2 = 5/2
..
she now had 2x/3 + 5/2
she spent 3.25 = 3 1/4 = 13/4 for amovie ticket & 3/4 for a snack
2x/3 +5/2 - 13/4 -3/4
LCD = 12
(8x+30-39-9)/12 = 4.90
(8x-18)/12 =4.90
8x-18= 58.80
8x = 58.80+18
8x= 76.80
/8
x= 76.80/8
x= $9.60 amount she had
.
m.ananth@hotmail.ca
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Graphs/367061: many elevators have a capacity of 1000 kg.suppose that children(each weighing 35 kg)and adults(each weighing 80 kg) are on elevator.graph a system of linear inequalities that indicates when the elevator is overloaded
1 solutions
Answer 261725 by mananth(12270) on 2010-11-07 08:41:44 (Show Source):
You can put this solution on YOUR website!many elevators have a capacity of 1000 kg.suppose that children(each weighing 35 kg)and adults(each weighing 80 kg) are on elevator.graph a system of linear inequalities that indicates when the elevator is overloaded
..
let number of children be x
let adults be y
35x+80y>1000
/5
7x+20y>200
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m.ananth@hotmail.ca
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Exponential-and-logarithmic-functions/367074: My daughter is having trouble with real exponents and exponential functions in Algebra 2 could you please show me how to work this problem out. There are not enough textbooks in her class for each student to have one to bring home so therefore I have nothing to go by. Thanks.
The problem is: {(n sqrt(6) + w sqrt (3) )}x{(n sqrt (6) - w sqrt (3) )}
1 solutions
Answer 261723 by mananth(12270) on 2010-11-07 08:29:48 (Show Source):
You can put this solution on YOUR website!{(n sqrt(6) + w sqrt (3) )}x{(n sqrt (6) - w sqrt (3) )}
There is a formula for difference of squares
which is (a+b)(a-b ) = a^2-b^2
..
in this problem
a= nsqrt6
b= wsqrt3
a^2-b^2
= (n sqrt(6))^2-(wsqrt(3)^2)
= n^2*6-w^2*3
=6n^2-3w^2
=3(2n^2-w^2)
OR
...
(n sqrt(6){(n sqrt (6) - w sqrt (3)+( w sqrt (3) )}{(n sqrt (6) - w sqrt (3)
(nsqrt(6)^2-nsqrt(6)*wsqrt(3)+nsqrt(6)*wsqrt(3)-(wsqrt(3))^2
(nsqrt(6)^2-(wsqrt(3))^2
which is same as above when simplified
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m.ananth@hotmail.ca
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...
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Quadratic_Equations/367066: The wages of 8 men & 6 boys amount to Rs 33. If 4 men earn Rs 4.50 more than 5 boys determine the wages of each man & boy.
1 solutions
Answer 261719 by mananth(12270) on 2010-11-07 08:17:36 (Show Source):
You can put this solution on YOUR website!let 5 boys earn Rs x
each boy earns x/5
.....
4 men earm x+4.50
each man earns (x+4.50)/4
..
8 men and 6 boys earn Rs. 33
8/4 * (x+4.50) + 6x/5 = 33
2(x+4.50)+6x/5 =33
2x+9+6x/5=33
2x+6x/5=33-9
(10x+6x)/5 = 24
16x= 5*24
x= 5*24/16
5 boys earn 7.50
1 boy earns 7.50/5
=1.50
Man earns (7.50+4.50)/4
12/4
=3
CHECK
8*3+6*1.5=33
..
m.ananth@hotmail.ca
Man earns Rs3 & boy earns Rs.1.50
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Quadratic_Equations/367055: If a car is travelling at a constant rate of 45 miles per hour, how many miles does it travel from 10.40a.m. to 1.00p.m of the same day?
1 solutions
Answer 261705 by mananth(12270) on 2010-11-07 05:37:44 (Show Source):
You can put this solution on YOUR website!If a car is travelling at a constant rate of 45 miles per hour, how many miles does it travel from 10.40a.m. to 1.00p.m of the same day?
..
10.40 am to 1.00 pm
= 2 hours 20 minutes
= 2 20/60
=2 1/3
=7/3 hours
...
speed = 45 mph
..
d = rt
d= 7/3 * 45
d=105 miles
...
m.ananth@hotmail.ca
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Quadratic_Equations/367054: The diagonal of a rectangle is 5cm & one of its side is 4 cm. Its area is?
1 solutions
Answer 261704 by mananth(12270) on 2010-11-07 05:35:28 (Show Source):
You can put this solution on YOUR website!diagonal = 5
one side = 4
let other side be x
..
they form a right triangle.
so use pythagoras theorem
diagonal is hypotenuse
..
x^2+4^2= 5^2
x^2+16=25
x^2= 25-16
x^2= 9
x= 3 the other sides
...
m.ananth@hotmail.ca
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Equations/367052: I really appreciate the help and have attempted to solve the problem below.
Did I do this correctly?
Please help...
-2(4x+1)=24
my answrer: -13/16
Any Suggestions?
1 solutions
Answer 261697 by mananth(12270) on 2010-11-07 05:16:54 (Show Source):
You can put this solution on YOUR website!-2(4x+1)=24
..
-8x-2 = 24
add +2
-8x-2+2 = 24+2
-8x = 26
divide by -8
x= 26/-8
x= -13/4
...
Plug value in the equation to check
-2(4*(-13/4)+1)
-2(-12)
=24
...
m.ananth@hotmail.ca
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Rate-of-work-word-problems/367053: a can finish a job in 3 hour and b can finish the same ob in 6 hours. how long will it take both of them working together to finish the job?
1 solutions
Answer 261696 by mananth(12270) on 2010-11-07 05:12:01 (Show Source):
You can put this solution on YOUR website!A does in 3 hours
so A does 1/3 of the job in 1 hour
..
B does in 6 hours
B can do 1/6 of the job in 1 hour.
..
together they can dp 1/3 + 1/6 of the job in 1 hour
= 3/6
= 1/2 job in 1 hour
..
they will do the job in 2 hours
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m.ananth@hotmail.ca
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