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Tutors Answer Your Questions about real-numbers (FREE)
Question 241319: what makes a number to be called irration?
Answer by Theo(675)   (Show Source):
You can put this solution on YOUR website!if c is a number and you can't find two integers, a and b, such that a/b or b/a equals c, then c is irrational.
irrational means it is not rational.
rational means it can be expressed as a ratio of two integers.
irrational means it can't.
Question 241267: when I worked on to problems using the elimination method I came up with 0=0 in both equations. Is this a solution or non solution or infinite solution
Answer by rapaljer(3622)  (Show Source):
You can put this solution on YOUR website!When you get 0=0, this means that the statement is ALWAYS TRUE, so the lines are actually the SAME LINE. There are infinitely many solutions.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
Question 240882: what are the properties of real numbers
Answer by solver91311(5072)  (Show Source):
Question 240889: prime factorization???
Answer by stanbon(26291) (Show Source):
You can put this solution on YOUR website!prime factorization???
============
Every integer can be expressed as a product of prime numbers.
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Cheers,
Stan H.
Question 239507: how would you begin to solve this problem 1+i over 1+2i + 1-i over 1-2i
Answer by Alan3354(6092)  (Show Source):
You can put this solution on YOUR website!how would you begin to solve this problem 1+i over 1+2i + 1-i over 1-2i
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Get a common DEN, as with any fraction problem.
CD = (1+2i)*(1-2i) = 5
= 
= 
= 6/3
= 2
Question 240280: the simplest form of ratio for 49:35
Answer by Alan3354(6092) (Show Source):
Question 239795: 1.integer
_______=undefined
0
2.what kind of integer is ZERO?
Answer by College Student(210)  (Show Source):
You can put this solution on YOUR website!1. Any integer (positive, neutral, or negative) divided by zero is undefined.
2. Zero is a neutral integer... it is neither positive nor negative.
Question 239796: 1.integer
_______=undefined
0
Answer by vleith(1977) (Show Source):
Question 239571: What is a rational number?
Answer by College Student(210) (Show Source):
Question 238854: If Jessica only spent 20% instead of the 25% allotment for food in May of 2001, how much did she save?
Answer by checkley77(7072) (Show Source):
Question 238843: Find the distance between the given numbers.
(a) 7/15 and -1/24
Answer by rfer(2688) (Show Source):
Question 238539: How do you simplify 2{[4(a-4)+18]-[3(3a-2)+5]}
Answer by user_dude2008(716) (Show Source):
You can put this solution on YOUR website!2{[4(a-4)+18]-[3(3a-2)+5]}
2{4a-16+18-[9a-6+5]}
2{4a-16+18-9a+6-5}
8a-32+36-18a+12-10
-10a+6
Answer: 2{[4(a-4)+18]-[3(3a-2)+5]} = -10a+6
Question 238188: Knowing that √2 is an irrational number, argue that √2/2 is also an irrational number.
Please help. Even just some ideas would be great. Thank you!
Found 2 solutions by Theo, College Student:
Answer by Theo(675) (Show Source):
You can put this solution on YOUR website!assume that sqrt(2) / 2 is a rational number.
then you can set y = sqrt(2)/2 then this means that y is a rational number.
if you multiply both sides of this equation by 2, then you would get 2 * y = sqrt(2).
2 * y would still be a rational number because a rational number times a rational number is a rational number, but sqrt(2) would not because that's how we started.
the equation would be false negating the claim that sqrt(2) / 2 is a rational number.
how do we know that multiplying a rational number by 2 yield a rational number.
first of all 2 is a rational number because it is an integer and any integer can be represented by that number divided by 1 which is a rational number.
take the number y = 1/2
this is clearly a rational number because it's a division of two integers.
now multiply both sides of this equation by 2.
you get 2y = 1 which is also clearly a rational number because an integer is a rational number.
bottom line is the assumption that sqrt(2)/2 is a rational number is a false assumption proven by multiplying both sides of that equation by 2 yielding a false equation.
Answer by College Student(210) (Show Source):
You can put this solution on YOUR website!An Irrational Number is a number that cannot be written as a simple fraction - the decimal goes on forever without repeating. So, since  is an irrational number, dividing its result in half  is also irrational.
Question 238194: Write each of the following square roots in the form a√b, where a and b are integers and b has the least value possible. For example, √180=6√5.
1. √360
2. √40
3. √240
Please, please help! Thank you.
Answer by solver91311(5072) (Show Source):
You can put this solution on YOUR website!
The process needed is to complete the prime factorization of the radicand.
360, even so divisible by 2
180, even so divisible by 2
90, even so divisible by 2
45, not even, but digits sum to 9 which is divisible by 3, so is divisible by 3
15, digits sum to 6, so divisible by 3
5, prime.
Prime factors are 2, 2, 2, 3, 3, 5. Take out one pair of 2s and one pair of 3s leaving a 2 and a 5. 2 times 3 is 6 and 2 times 5 is 10 so:
John
Question 236989: What is a decimal between 1/4 and 1/3?
Answer by thrasherlax74(11) (Show Source):
Question 235842: what is the real number between sqaure root of 50 and square root of 55?
Answer by josmiceli(3012) (Show Source):
You can put this solution on YOUR website!
These numbers are rounded off, but they
continue adding digits forever, so they
are not real numbers.
Any number between them that has a final
digit is a real number, like
 ,
 ,
 etc. etc.
Question 235390: trains a and b are traveling in the same direction on parallel tracks. train a is traveling at 80 miles per hour and train b is traveling at 100 miles per hour. train a passes a station at 3:10 pm. If train B passes the same station at 3:22 pm at what time will train b catch up to a.
Answer by Alan3354(6092) (Show Source):
You can put this solution on YOUR website!trains a and b are traveling in the same direction on parallel tracks. train a is traveling at 80 miles per hour and train b is traveling at 100 miles per hour. train a passes a station at 3:10 pm. If train B passes the same station at 3:22 pm at what time will train b catch up to a.
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In the 12 mins from 310 to 322, train a goes 16 miles (80 * 1/5 hour)
Train B gains on train A at 20 mph (100 - 80)
16/20 = 4/5 hours = 48 minutes
322 + 48 = 4:10 PM
Question 235162: Can you simplify this problem?
Found 3 solutions by mando271, stanbon, Alan3354:
Answer by mando271(42) (Show Source):
Answer by stanbon(26291) (Show Source):
Answer by Alan3354(6092) (Show Source):
Question 235115: I understand that the irrationals are not closed under addition, mult, div, subtr, etc. However,
Is it possible to construct a line segment on a cartesian coordinate system such that all points on the line have irrational values for the y coordinate when x is rational (i'm using the relationship y = mx + b)? It's okay if there are restrictions, like, the segment length must be transcendental or something.
I'm looking for non-zero-length line-segments that avoid all points with rational coordinate pairs.
I also don't expect this to be true for ALL line segments with, say, irrational coordinates for the endpoints. I'm just interested in constructing a line segment of non-zero length that has only irrational values for y when x is rational. If x is irrational i won't care about y - as long as x and y are never rational together.
I don't know how constraints are explored in mathematics, nor how one looks for solutions to a problem like this, nor how one goes about testing for the existence of such a construction, let alone constructing one. if this problem is in a well-known class of problems i can research that myself if somebody can help me identify the class.
Answer by jim_thompson5910(13794) (Show Source):
You can put this solution on YOUR website!If 'x' is rational, then we can say that  where 'p' and 'q' are integers or whole numbers. This is simply the definition of rational numbers. Note: 
If we multiply 'x' by 'm', then we get  which is still rational since 'mp' is an integer (integer multiplication is closed) and 'q' is an integer.
If we then add on 'b', we get  . Because  is an integer (using the reasoning above) and  is an integer (same reasoning),  is an integer since integer addition is closed. Since and  are integers,  is rational.
This means that if 'x' is rational, then  is rational. So it is never possible to find an irrational 'y' value given a rational 'x' value.
I'm not sure what you're asking about in terms of the restrictions, but you'll still find that plugging in rational x values will get you rational y values.
Question 235111: A real number between 5/9 and 6/9?
Answer by solver91311(5072) (Show Source):
Question 234802: 6x-(4-3x)
Answer by checkley77(7072) (Show Source):
Question 234588: Whatwould order would these numbers be from least to greatest 2.3, .23, 23??
Answer by nyc_function(260)  (Show Source):
Question 234234: Can you show me how to slove these problems?:
Answer by solver91311(5072) (Show Source):
Question 233680: one base of a trapezoid is three less than twice the length of the other base. The altitude of the trapezoid is 14 inches. if the area of the trapezoid is 63 square inches, find the length of each base
Answer by mestrydilip(9) (Show Source):
You can put this solution on YOUR website!Length of one base = x
Lenght of other base = 2x - 3
Altitude = 14
Area = 1/2 (sum of the bases) X Altitude
63 = 1/2 ( x + 2x - 3) X 14
63 = 1/2 (3x - 3) X 14
63 = 7 (3x - 3)
9 = 3x - 3
12 = 3x
x = 4
other base = 2x - 3 = 2(4)-3 = 8 - 3 = 5
Question 233644: A rectangle's width is 1 meter more than half of its length. Find the dimensions if the perimeter measures 53 meters.
Answer by stanbon(26291) (Show Source):
You can put this solution on YOUR website!A rectangle's width is 1 meter more than half of its length. Find the dimensions if the perimeter measures 53 meters.
-------------
Let length = L
The width = (1/2)L+1
------------------------------
Perimeter = 2(W + L)
53 = 2((1/2L+1 + L)
53 = 2((3/2)L + 1)
52 = 3L + 2
3L = 51
L = 17 meters (length)
W = (1/2)L + 1 = 8.5+1 = 9.5 meters (width)
=============================================
Cheers,
Stan H.
Question 233353: how can you tell when an equation has a solution of all real numbers?
Answer by solver91311(5072) (Show Source):
You can put this solution on YOUR website!
Not sure what you are talking about. Do you mean a system of linear equations that is consistent and dependent? Or are you talking about a polynomial equation and asking if you can tell if all of the roots are real numbers? Or are you talking about an identity where any real number will satisfy the equation?
John
Question 233271: i want to know how youh turn decimals into percents | or the other way around.. or turn fractions into percents/ decimals ?
Answer by rfer(2688) (Show Source):
You can put this solution on YOUR website!1/4=.25=25%
1/2=.5=50%
2/5=.40=40%
Divide a fraction, the bottom into the top to get a decimal.
Move the decimal two places to the right to change a decimal into %
With a % move the decimail two places to the left for a decimal.
decimal to a fraction if two place put the number over 100.
.40=40/100=reduce 4/10=2/5
.5=5/10=1/2
Question 233277: Mark every set that 1/2 is a member of.
Whole Numbers
Integers
Rational Numbers
Real Numbers
Answer by stanbon(26291) (Show Source):
You can put this solution on YOUR website! Mark every set that 1/2 is a member of.
Whole Numbers---no
Integers--------no
Rational Numbers--yes
Real Numbers------yes
=======================
Cheers,
Stan H.
Question 229094: Which of the following is equal to 5.93 x 10^-2
why the quiz i took says the right anwer is 0.0593 instead of 593.00 or just 593? why are the 0 in the left side? :S
Answer by Alan3354(6092) (Show Source):
You can put this solution on YOUR website!Which of the following is equal to 5.93 x 10^-2
why the quiz i took says the right anwer is 0.0593 instead of 593.00 or just 593? why are the 0 in the left side? :S
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10^-2 = 1/10^2 = 1/100 = 0.01 (different ways of writing it)
5.93 x 0.01 = 0.0593
Question 232292: find the LCM of 8,12,and72
Answer by stanbon(26291) (Show Source):
You can put this solution on YOUR website!find the LCM of 8,12,and72
---
8 = 2^3
12 = 2^2*3
72 = 2^3*3^2
------------------
The lcm must have each of the prime factors at their highest power:
lcm = 2^3*3^2 = 72
--------------------
Cheers,
Stan H.
Question 232144: -(a+2b)+4(a+2b)-2(a+2b)
Answer by rfer(2688) (Show Source):
Question 231490: How many different 5-card poker hands would contain only cards of a single suit?
I know there are 52 cards in a deck and there are 4 different suits with 13 cards in each suit. From here, I am lost.
Answer by Alan3354(6092) (Show Source):
You can put this solution on YOUR website!How many different 5-card poker hands would contain only cards of a single suit?
I know there are 52 cards in a deck and there are 4 different suits with 13 cards in each suit. From here, I am lost.
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It's 5 cards out of 13.
The 1st is 1 of 13, then 1 of 12, etc = 13*12*11*10*9
= 154,440
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But, since 2, 3, 4, 5, 6 is the same as 6,5,4,3,2 it's necessary to divide by 5*4*3*2*1 = 120
--> 154440/120 = 1287 possibilities.
-----------------
To be more formal, it's
13!/(5!*(13-5)!)
! is factorial. 5! = 5*4*3*2*1, etc.
Question 230304: I am supposed to show that the number is rational by writing it as a quotient of two integers. I am not show how to do that in the number 0.3 Thanks! 0.3
Answer by user_dude2008(716) (Show Source):
Question 229888: # 679
#308
#214
Thank you
Answer by Alan3354(6092) (Show Source):
Question 229306: when is the answer all real numbers?
Answer by solver91311(5072) (Show Source):
Question 227884: (18)^56 * (18)^-14=
Answer by rfer(2688) (Show Source):
Question 226481: the sum of two consecutive intergers is 59. find the values of the two intergers
Answer by user_dude2008(716) (Show Source):
Question 226011: What is x in 17=2(3x+1)-x?
Answer by edjones(3298)  (Show Source):
Question 226000: For three consecutive odd integers, the sum of the least and greatest is 146. What is the sum of all three integers?
Found 2 solutions by josmiceli, drj:
Answer by josmiceli(3012) (Show Source):
Answer by drj(1380)  (Show Source):
Question 225018: find the product of -3(-5)(-4X), justify the steps
Answer by rfer(2688) (Show Source):
Question 223632: If a clock strikes every hour the same amount of times as that hour, how many strikes in 24hours.
Answer by RAY100(1637) (Show Source):
You can put this solution on YOUR website!This is basically an arithmetic series 1,2,3,,,24
.
form is a(n) = a(1) +(n-1)d,,,,,where d is difference btwn terms, and n = 3 terms
.
a(24) = 1+(24-1)1 = 24
.
The sum of an arithmetic series is,,S= n{ a(1) +a(n)} /2
.
S= 24(1+24)/2 = 300
.
.
check,,,use calc to manually add series,,,300,,,,ok
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