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Recent problems solved by 'gsmani_iyer'
gsmani_iyer answered: 180 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209, >>Nexttest/644808: 4x^2-10x-14=0
1 solutions
Answer 405291 by gsmani_iyer(180)   on 2012-09-03 12:25:27 (Show Source):
You can put this solution on YOUR website! 
= 
= 
= 
So, either of the factors is equal to zero. Because anything multiplied by '0' is 0.
If (x+1)=0, then x = -1.
If (4x-14)=0, then 4x = 14. So x = 
So x = {-1, 3.5} Answer.
I think you have understood. For doubts, feel free to contact me at gsmani9@yahoo.com.
All the best.
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Geometry_Word_Problems/644826: a rectangular room has a floor area of 32 square meters.how many tiles,each measuring 50 cm x 50 cm, are needed to cover the entire floor
1 solutions
Answer 405271 by gsmani_iyer(180) on 2012-09-03 09:42:21 (Show Source):
You can put this solution on YOUR website! 1 meter = 100 Cms.
1 Sq.meter = 100 X 100 = 10000 Sq.Cms.
32 Sq.meters = 320000 Sq.Cms.
Area of 1 tile = 50 x 50 = 2500 Sq.Cms.
To cover the entire floor = 
So, to cover the entire floor, one needs 800 tiles.
First convert the area of the floor into centimeters as the tiles are in the measure of centimeters. Then find the area of a tile. Now both are in centimeters. You can easily find out the no. of tiles by dividing the area of the floor by area of the tile. There you get the answer. I hope you understood. In case of doubts, feel free to contact me Y!messenger: gsmani9.
All the best.
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test/548420: 4x+3y=9
2x-y=7
Y=2x-7
4x+3+2x-7)=9
Solve each system by substitution
1 solutions
Answer 356988 by gsmani_iyer(180) on 2011-12-17 12:23:37 (Show Source):
You can put this solution on YOUR website!
From the equation (2), y=2x-7; Replacing the value of this y in Eqn.(1), we get
By simplifying (3), 4x+6x-21 = 9
= 10x = 21+9
= 10x = 30
x = 3; (Dividing both the sides by 10)
Replacing the value of x by 3 in eqn.1, we get
4*3+3y = 9
12-9 = -3y
y = 
So x=3; y=(-1) Answer.
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Pythagorean-theorem/523349: Jenn and Aaron are adding an extra room to their house. The blueprints indicate the room should be a rectangle with dimensions 9 feet by 12 feet. If they construct the rectangular room correctly, how long should each diagonal be?
1 solutions
Answer 347309 by gsmani_iyer(180) on 2011-10-30 14:35:33 (Show Source):
You can put this solution on YOUR website!
The diagonal should be 15 feet.
The diagonal is not given. So the given data, 9 feet and 12 feet must be the two sides of a right angled triangle. As per Pythagorean theorem,
Hypotenuse(diagonal) = 
= 
= So diagonal which is the hypotenuse = 15 feet.
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Money_Word_Problems/523363: Carlos bought a computer game for 20% off its original price. He paid a total of $30.24, including 8% tax on the purchase. What was the original price of the game?
---Please help. I am so confused! How do you solve this problem?
1 solutions
Answer 347304 by gsmani_iyer(180) on 2011-10-30 14:01:09 (Show Source):
You can put this solution on YOUR website!
Let the purchase price = 100
Tax @ 8% += 8
Total purchase price: 108
If 108% = $ 30.24
then 100% = 
So the purchase price = $28 (discounted price);
Let the original price = 100
Discount @ 20% (-) 20
So discounted price = 80
If 80% = $28
So the original price: 
So the original price = $35 Answer. I hope you have understand this. All the best.
gsm/-
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Quadratic_Equations/523334: I have an equation: 4x^2 - 24x + 27 = 0
The first part of the question requires me to complete the square so I get:
4*(x-3)^2 - 9 = 0
Using this, how can I solve x, WITHOUT using a calculator?
1 solutions
Answer 347303 by gsmani_iyer(180) on 2011-10-30 13:30:56 (Show Source):
You can put this solution on YOUR website!  This is to be factorized first.
= 
=  . So either of the factors is equal to 0. Because 0 multiplied by any number is equal to 0.
= If  , then 2x = 3; x = 3/2 = 1.5
= If  , then 2x = 9; x = 9/2 = 4.5
x = {1.5, 4.5} Answer.
I hope you understood this. All the best.
gsm/-
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Problems-with-consecutive-odd-even-integers/507901: find the set of three consecutive even integers whose sum is 93
1 solutions
Answer 340797 by gsmani_iyer(180) on 2011-10-02 13:45:40 (Show Source):
You can put this solution on YOUR website!
Sum of even integers can never be an odd integer irrespective of no. of integers.
I hope it is three consecutive odd integers. They are 29, 31, 33. i.e.
A = {29, 31, 33}. I have not explained how I got these. Because you check up with your question. If it is odd integers, contact me gsmani9@yahoo.com.
All the best.
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Angles/471065: the sum of the measures of an obtuse and an acute angle is 160. the sum of the complement of the acute angle and one-half the supplement of the obtuse angle is 75. find the measures of the two angles.
1 solutions
Answer 323136 by gsmani_iyer(180) on 2011-07-17 07:51:15 (Show Source):
You can put this solution on YOUR website! Let the obtuse angle be = x
Let the acute angle be = y
x + y = 160 ....... ........ (1)
 ......... ........Multiplying both the sides by 2, we get:
 ........ ........ (2)
From Eqn.(2) - (1) we get,
Applying y's value in Eqn.(1), we get
x + 50 = 160; So, x = 160 - 50 = 110.
So, the measure of obtuse angle = 110 ;
and the measure of acute angle = 50. Answer.
I hope you have understood the above solution. All the best.
gsm
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Trigonometry-basics/318408:
1 solutions
Answer 227931 by gsmani_iyer(180) on 2010-06-29 00:50:22 (Show Source):
You can put this solution on YOUR website!
Identity used in solving the problem: 1-(cos^2x)=(sin^2x)
sinx/(1+cosx)+ sinx/(1-cosx) = 2 cosec x. By taking out lcm of the denominators,
sinx(1-cosx) + sinx(1+cosx)/(1 - cos^2x)
= (sinx - sinx*cosx + sinx + sinx*cosx)/sin^2 x
= 2sinx / sin^2x i.e 2*(sinx)/(sin^2x) after cancelling,
= 2*1/sinx = 2 cosec x Answer.
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Circles/318452: A circle has a radius of 8 inches. Find the area of a sector of the circle if the sector has an arc that measures 45°.
1 solutions
Answer 227922 by gsmani_iyer(180) on 2010-06-28 23:31:44 (Show Source):
You can put this solution on YOUR website!The formula for area of the sector: 
Here in your problem, theta = 45, r = 8.
Area of the sector: 
=  = 3.14 x 8 = 25.12 Sq.inches.
Area of the sector:  Sq.inches. ANSWER
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Rectangles/299263: the area of a rectangular garden is 42 square meters. the width is 5 meters longer than one-third of the length. find the length and the width of the garden
1 solutions
Answer 215097 by gsmani_iyer(180) on 2010-05-02 09:53:11 (Show Source):
You can put this solution on YOUR website!
Let the length of the rectangle = x
So, the breadth of the rectangle = (x/3)+5
Area = length * breadth.=> 42 Sq.mtr.
= x * [(x/3) + 5] = 42 Sq.mtrs.
= x^2/3 + 5x = 42 Sq.mtrs.
= x^2/3 + 5x - 42 = 0 ......... ( 1 ). Now Eqn.1 * 3, we get
= x^2 + 15x - 126 = 0 ......... ( 2 )
= (x + 21)(x - 6) = 0 So either (x+21) or (x-6) = 0
If x+21 = 0, then x=-21 whereas the length cannot be negative. So,
x = 6. [(x/3)+5] = 7.
Length of the rectangle = 6 mtrs.; breadth = 7 mtr.;
I hope this is clear to you. All the best. Feel free to contact me if you have doubts in maths.
gsm
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Rectangles/292878: The area of a rectangle is 4 times the area of a square. The length of the rectangle is 90 centimeters and the breadth of the rectangle is two-third of the side of the square. What is the side of the square?
(1) 10 cms (2) 20 cms (3) 9 cms (4) Cannot be determined (5) None of these.
1 solutions
Answer 211501 by gsmani_iyer(180) on 2010-04-16 12:28:02 (Show Source):
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Length-and-distance/291184: How far would I have traveled if I drove for 3 hours and 45 minutes at 80 mph?
1 solutions
Answer 210620 by gsmani_iyer(180) on 2010-04-12 14:20:07 (Show Source):
You can put this solution on YOUR website! Speed = 80 mph (miles per hour)
Time =  hours. (3 hours 45 mins)
Distance = ???? (Here use this formula)
Distance = Speed x Time
= 80 x
= 80 x 
=  x 
= 20 x 15 = 300 miles.
I think you have understood this. God bless you.
gsm
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Angles/291168: The angle is 64° - find the complement and the supplement
1 solutions
Answer 210619 by gsmani_iyer(180) on 2010-04-12 14:05:18 (Show Source):
You can put this solution on YOUR website!
The angle = 64 degrees.
complement angle = 90-64 = 26 degrees. So 26 and 64 degrees are complement to each other. If an angle is subtracted from 90 degrees, then it is complementary angle.
Supplementary angle = 180 - 64 = 116 degrees. So 116 and 64 degrees are supplementary angles to each other. In other words, if an angle is subtracted from 180 degrees, then the difference is known as supplementary angle.
I hope this is clear to you. All the best.
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Systems-of-equations/290780: A garden supply store sells two types of lawn mowers. Total sales of mowers for the year were $8379.70. The total number of mowers sold was 30. The small mower costs $249.99. The large mower costs $329.99. Find the number sold of each type of mower.
1 solutions
Answer 210409 by gsmani_iyer(180) on 2010-04-11 13:43:01 (Show Source):
You can put this solution on YOUR website!
The total No. of mowers = 30
Let the No. of small mowers be = x; So,
the No. of large mowers = (30-x)
Sale of small mowers = ($249.99)(x) and the
Sale of large mowers = $329.99(30-x)
= $9899.70 - 329.99x
Total sale = $249.99x + $9899.70 - 329.99x = $8379.70
= -80x + $9899.70 = $8379.70. (By transposing,
$9899.70 - $8379.70 = 80x
= $1520.00 = 80x. Therefore,
= x = $1520/80 = 19 small mowers.
So the large mowers (30 - x) = 30 -19 =11 large mowers.
Small mowers = 19; Large mowers = 11. Answer.
I think you have understood this. If not, feel free to contact me anytime for any doubts in maths online.
God Bless you.
gsm
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Polynomials-and-rational-expressions/290730: if x^2 + y^2 =36 and (x+y)^2 =64 what is the value of xy
1 solutions
Answer 210402 by gsmani_iyer(180) on 2010-04-11 13:11:06 (Show Source):
You can put this solution on YOUR website! Remember an identity  .. With this identity, we can solve the problem.
=  or  . whereas  ok?
But  ; in the above identity, we dont have the value of 2xy.
So,  which is = 28. Therefore, 2xy = 28.
So, xy = 28/2 = 14. Answer. Therefore the value of xy = 14. I hope this is clear to you. Best of luck. Feel free to contact me anytime online on any doubts in mathematics.
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Numbers_Word_Problems/290744: please help me solve:(-8x7 + 5x9 - 1 + 3x8) - (7 + 7x8 + 7x9 + 2x7)
1 solutions
Answer 210391 by gsmani_iyer(180) on 2010-04-11 12:41:32 (Show Source):
You can put this solution on YOUR website!
(-8x7 + 5x9 - 1 + 3x8) - (7 + 7x8 + 7x9 + 2x7)
=  ..Let us now remove the curved brackets. Keep one thing in your mind : if negative sign is found immediately before the bracket, then change all the signs inside the bracket. In the second bracket, we find -ve sign before the bracket starts. so we will change all the signs inside the bracket.
=  Now arrange the terms degree-wise and simplify.
= 
=  Answer.
I hope this is clear to you. Feel free to contact me anytime for any doubts in maths. I am available atleast 18 hours online.
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Square-cubic-other-roots/91072: Can you show the steps to simplify this square root fraction problem? Thank you!
Square root of 162x^6 over 64x^2
square root 162x^6
___________________
square root 64x^2
1 solutions
Answer 66097 by gsmani_iyer(180) on 2007-08-01 12:12:20 (Show Source):
You can put this solution on YOUR website!
 =  =  =  =  =  =  =  Answer.
I have explained step by step how to solve such problems and I hope you have understood too. All the best.
gsm
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Polynomials-and-rational-expressions/90969: Perform operation and simplify. I need to know how to set this equation up and solve it.
x^2-6x+8/x^2-17x+70 . x^2-15x+56/x^2-15x+44
1 solutions
Answer 66096 by gsmani_iyer(180) on 2007-08-01 10:36:43 (Show Source):
You can put this solution on YOUR website!Hello,
First of all, factorise the expressions wherever possible and then start simplifying by cancelling/factoring. Now coming to the problem, you can factorise all the expressions (numerators & denominators). I think you know how to factorise.
 *  =  *  =  *  =  Answer.
I think this is clear to you now. If not, feel free to contact me anytime. All the best.
gsm
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Reduction-of-unit-multipliers/83598: A rectanular plot has been fenced with 500ft of wire. find the length and width of th plot if the length is 4 more than twice the width. Be sure to show both length and width along with units in your answer
1 solutions
Answer 60108 by gsmani_iyer(180) on 2007-05-28 11:17:15 (Show Source):
You can put this solution on YOUR website!
When the rectangular plot has been fenced all the sides, the length of the fence is the perimeter of the rectangle. Here,
Let the width = x
So the length = 2x + 4 (as per the condition in the problem)
Perimeter 2L + 2B = 2(l+b)
 = 500 Ft.
 Dividing both the sides by 2, we get,
 = 
So x =  = 82Ft.
2x+4 =  = 164+4 = 168 Ft.
Width = 82 Ft.
Length = 168 Ft. Answer.
I guess you understood this.
gsm/-
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real-numbers/83594: This is a rational expression, the answer should be in the form of a rational expression.
Simplify:
(x^2-13x+42)/ (x^2-36)
1 solutions
Answer 60106 by gsmani_iyer(180) on 2007-05-28 10:53:47 (Show Source):
You can put this solution on YOUR website!
 . Here you have to factorise both the denominator and the numerator. By doing so, you get
 =  =  Answer.
Is this clear to you now? Pls let me know.
gsm
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Polynomials-and-rational-expressions/83571: This question is from textbook Algebra 1
Write the indicated equation for each geometric solid.
1.)The surface area of a cube with an edge of x centimetres long.
I got the answer s=24x
2.)The volume of a cylinder with an height of 5 metres and a radius of x metres.
I got the answer V=≈x^2*5 ≈ is pie (3.14).
1 solutions
Answer 60103 by gsmani_iyer(180) on 2007-05-28 10:32:25 (Show Source):
You can put this solution on YOUR website!
Surface area of a cube = 
Here 'a' represents the length of the edge of the cube.
Applying the same formula above, we get
the answer =  cms.
Explanation: A cube has got 6 sides and its sides are equal/congruent.
So the area of one side =  cms.
So 6 * = cms.
I hope this is clear to you.
Coming to the second problem,
Volume of a right cylinder = 
Again applying the above formula and the given data, we get
Volume =  cu.mtrs. Answer.
i.e.  . Here the value of pi has been taken as '3.14'
I hope this too is clear to you.
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Evaluation_Word_Problems/68195: Ricardo is 4 years less than twice as old as his sister. The sum of their ages is 20. How old is Ricardo?
1 solutions
Answer 48515 by gsmani_iyer(180) on 2007-01-27 13:33:11 (Show Source):
You can put this solution on YOUR website!
Let sister's age = x
So, Ricardo's age = 2x-4 (Given)
The sum of the ages = x + 2x - 4 = 20 (Given)
= 3x - 4 = 20
= 3x = 20 + 4 = 24
= x = 24/3 = 8.
So the sister's age = 8 yrs.
and Ricardo's age = (2*8)-4 = 16-4 = 12 yrs. Answer.
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Numeric_Fractions/62532: 6x+12/3x-9 * x2(sq)-5x+6/x2(sq)-4
1 solutions
Answer 43371 by gsmani_iyer(180) on 2006-11-23 04:54:21 (Show Source):
You can put this solution on YOUR website!
 Answer.
Here also first of all factorise all the expressions in the numerators and the denominators and then you can easily cancel the common factors to get the correct answer. Isn't it easy? Try some for yourself and see how easy this algebra is. All the best.
gsm
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Exponents/62272: Perform the operations and simplify. 2/(x^2 - 4x +3) + 3/(x^2 - 8x + 15) - 6/(x^2 - 6x + 5)
1 solutions
Answer 43180 by gsmani_iyer(180) on 2006-11-21 13:18:53 (Show Source):
You can put this solution on YOUR website!
 Now let's factorise the denominators as under:
= 
Now, let's take the LCM of the denominators which comes to  and simplify the above expression as under:
=  . By expanding the numerator, we get
=  = 
=  = 
=  . Answer. That's all. I hope this is clear to you. In case of any doubt, feel free to contact me. All the best.
gsm
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