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Question 751315: What two numbers add to be -16 but when multiplied equal 192?
Answer by stanbon(57361)

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What two numbers add to be -16 but when multiplied equal 192?
----
Equations:
x + y = -16
xy = 192
--------------
Rearrange:
x = -16-y
----
(-16-y)y = 192
-16y - y^2 = 192
y^2 + 16y + 192 = 0
-----
No Real Number solution.
Please check your posting for accuracy.
Cheers,
Stan H.

Question 750523: 2√3+6√3-4√3
Answer by stanbon(57361)

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2√3+6√3-4√3
------
= (2+6-4)sqrt(3)
------
= 4sqrt(3)
=============
Cheers,
Stan H.

Question 750394: if the sum of two consecutive integers is -15< what is the value of the larger integer?
Answer by tommyt3rd(601)

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(n)+(n+1)=-15

2n+1=-15
2n=-16
n=-8
but -7 is greater (larger)

:)

Question 750392: can a negative number be considered a real number ?
Answer by tommyt3rd(601)

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Yes - any number that can be graphed on the number line is a real number :)

Question 750353: divided by
Answer by JoeTaxpayer(135)

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When multiplying two numbers whose base is the same, we just add the exponents.
X%5EA%2AX%5EB=X%5E%28A%2BB%29

So,

And similarly, dividing is to subtract the exponent.
So x%5E5%2Fx%5E4=x

Over time, this will become intuitive, and you'll know the answer is X just by glancing at the problem. Of course, you may need to show steps to keep a teacher happy, but in longer problems, likely, not.

Question 750283: using -1 as a factor, what is x^2 + 2x + 1/-1 - x in simplified form?
Answer by josgarithmetic(1530)

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What you mean is this: %28x%5E2+%2B+2x+%2B+1%29%2F%28-1+-+x%29

in simplified form.

Factor.
%28x%2B1%29%28x%2B1%29%2F%28%28-1%29%281%2Bx%29%29

%28x%2B1%29%28x%2B1%29%2F%28%28-1%29%28x%2B1%29%29

cross%28%28x%2B1%29%29%28x%2B1%29%2F%28%28-1%29cross%28%28x%2B1%29%29%29

which only slightly unfinished.

Question 698304: What is the real number solution for x^4-16=0?
Answer by tommyt3rd(601)

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x=2 or x=-2

Question 730526: if
"find the value of a^+b^=5ab"
Answer by tommyt3rd(601)

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what is the value of b?

Question 732990: The highest temperature ever recorded in a desert was 105 degrees F. the coldest temperature recorded in a deert was 5 degrees Fahrenheit below zero. State which real numbers correstpind on the situation.
The real number that corresponds to the highest temp. in a desert is ?
The real number that corresponds to the coldest temp. in a desert is ?
Answer by tommyt3rd(601)

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a) 105
b)-5

Question 749636: how many real number solutions? 4x^2+8x-4=0
Answer by tommyt3rd(601)

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two:
sqrt%28+8%5E2-4%2A4%2A%28-4%29+%29=8sqrt%282%29

so there are 2 irrational solutions

:)

Question 702939: write each rational number as a ratio in the form a/b 1) -3 ??
Answer by tommyt3rd(601)

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-3=-3%2F1

Question 747469: For any positive integer 'n' prove that 'n3-n' is divisible by 6.

Answer by tommyt3rd(601)

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not true:
n=1
n^3-n=0
Maybe you mean if n is 2 or greater?
%0D%0A%0D%0An%5E3-n=%28n%29%28n%5E2-1%29=%28n-1%29%28n%29%28n%2B1%29%0D%0A

%0D%0A%0D%0An%5E3-n=%28n%29%28n%5E2-1%29=%28n-1%29%28n%29%28n%2B1%29%0D%0A

now for

this product will include 3 consecutive numbers and that means at least one of them will be even and exactly one will be a multiple of 3. Therefore each will be a multiple of 6.

:)

Question 708644: what is the smallest set of real numbers which 12 belongs to
Answer by tommyt3rd(601)

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{12}

Question 708371: (7*5)+[5/(4/4)]
Answer by tommyt3rd(601)

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(7*5)+[5/(4/4)]=35+5=40

Question 713755: 7+3(9-4)2 / 5 +
Answer by tommyt3rd(601)

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please repost the question seems to be incomplete :)

Question 749614: Divide (-1)^9
Answer by Alan3354(30993)

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Divide (-1)^9
divide what?

Question 749598: Find two expression for the number with negative signs in different places. -5/6. - 8/7. 19/-3
Answer by stanbon(57361)

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Find two expression for the number with negative signs in different places.
-5/6 = -(5/6)
---------------------
- 8/7 = (-8/7)
---------------------
19/-3 = -19/3
===================
Cheers,
Stan H.
===================

Question 748340: Solve the equation, if possible. Write irrational numbers in simplest radical form. Describe the strategy you used to get your solution and tell why you chose that strategy.
x^2-6x+1=0
Answer by stanbon(57361)

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Solve the equation, if possible. Write irrational numbers in simplest radical form. Describe the strategy you used to get your solution and tell why you chose that strategy.
x^2-6x+1=0
----
x = [6 +- sqrt(36-4*1*1)]/2
----
x = [6 +- sqrt(32)]/2
---
x = {6 +- 4sqrt(2)]/2
---
x = [3 +- 2sqrt(2)]
========================
Cheers,
Stan H.
=======================

Question 747631: -5/8+(-1/6)
Found 2 solutions by Alan3354, obulee:
Answer by Alan3354(30993)   (Show Source):
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-5/8+(-1/6)
= -(5/8) - (1/6)
= -30/48 - 8/48
= -38/48
= -19/24

Answer by obulee(5)   (Show Source):
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note dat
+ - = -
-5/8 - 1/6
find the lcm of 8 and 6
- 30-8/48
-22/48
-11/24

Question 747381: what is the discriminant of x^2 + 15x - 1 = 0

Answer by Alan3354(30993)   (Show Source):
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what is the discriminant of x^2 + 15x - 1 = 0
-----------

Question 747101: what is the number of real solutions in -x^2+9x+7=0
Answer by tommyt3rd(601)   (Show Source):
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We can use the discriminant to determine the number and type of solutions:

since the discriminant is real and not 0 we know that there are 2 real solutions

:)

Question 738228: Show that there are infinitely many positive primes.
Answer by tommyt3rd(601)   (Show Source):
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Suppose that there are only n-prime numbers and denote the product of all of the primes as A. Next let B be the product of all of the primes plus 1. Now 1 is not a prime number by definition so for any particular prime p>1. By the fundamental theorem of algebra, our p had to be a divisor of A as well as a divisor of B. Furthermore it also must divide their difference, B-A - which is 1. Since the difference is 1, p must be a divisor of 1 and this is impossible.
Our contradiction tells us that our first statement must be false. There are infinitely many primes.

Question 725020: The number 18 can be written as the sum of 9 consecutive integers.What's the product of these integers?
Answer by tommyt3rd(601)   (Show Source):
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which when solved leads to x=-2
so our product is

Question 741951: - 144/4 to which set does the number belong
Answer by tommyt3rd(601)   (Show Source):
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this number is a fraction so it belongs to the rational numbers - this also means it belongs to the sets of numbers for which the rational numbers are a subset

Question 745363: square root 9u-13=square root7u-8
Answer by nyke@rediffmail.com(5)   (Show Source):
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you mean

squaring both sides
=> 9u-13 = 7u-8
=> 9u - 7u = -8 + 13
=> 2u = 5
=> u = 5/2
=> u = 2.5

Question 744576: Find the remainder when is divided by 2013 .

Answer by lynnlo(4164)   (Show Source):
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Question 744288: Twenty times the square of a non-zero number is equal to 20 time the number. What is the number?
Answer by josgarithmetic(1530)   (Show Source):
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n is some nonzero number.

is exactly what you wrote in words. n=1.

Question 743587: 4(x-5)+2=x+3
Answer by jim_thompson5910(28595)   (Show Source):
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Start with the given equation.

Distribute.

Combine like terms on the left side.

Add to both sides.

Subtract from both sides.

Combine like terms on the left side.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

----------------------------------------------------------------------

Answer:

So the solution is

Question 740828: I am trying to indicate what kind of number -144/4 is.
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(57361)   (Show Source):
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I am trying to indicate what kind of number -144/4 is.
----
It's Rational.
----
= -38
-----
It is an Integer
====================
Cheers,
Stan H.
====================

Answer by solver91311(16897)   (Show Source):
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Hint: is the ratio of two integers. What kind of numbers has the word ratio as part of the name?

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 739933: Is 2-square root 5 rational or irrational number?
Answer by KMST(1868)   (Show Source):
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is irrational because is irrational.
You know that the result from adding, or subtracting, or multiplying rational numbers is always rational.
If is rational, must be rational.
If was rational,
would be rational,
but it is not.

NOTE:
Watch out for trick questions.
Sometimes rational numbers are written in an unusual way to make them look irrational, just to trick you.
is a rational number, even when it is written as
Similarly, is rational, and so is

Question 740089: is -144/4 a real number? I know it can reduce to -36, so that is what is confusing me...
Answer by MathLover1(6634)   (Show Source):
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Real Numbers include:
Whole Numbers (like 1,2,3,4, etc)
Rational Numbers (like 3/4, 0.125, 0.333..., 1.1, etc )
Irrational Numbers (like ,sqrt(3), etc )
Real Numbers can also be positive, negative or zero.
so, your answer is: is a real number

Question 739950: INSERT TWO RATIONAL NUMBERS BETWEEN 2 AND 3
Answer by KMST(1868)   (Show Source):
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There is an infinite number of choices. Just pick a denominator (or 2), make up fractions that are less than 1, and add those fractions to 2.
For example,
and are between and

and would work too
and so would and ,
or any combination.
There are many fractions of that we can add to 2 and still end up with less than 3.

If asked for 5 rational numbers between 2 and 3, you could use
, , , , and

Question 739947: insert a rational number between 2 and 3
Answer by KMST(1868)   (Show Source):
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One of the infinity of choices is:

Question 738382: X^2-25x=0
Answer by checkley79(3050)   (Show Source):
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X^2-25x=0
(X+5)(X-5)=0
X+5=0
X=-5 ANS.
X-5=0
X=5 ANS.

Question 738376: 10c^2 + 25c – 6c – 15 factor by grouping
Answer by jim_thompson5910(28595)   (Show Source):
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Start with the given expression

Group the terms in two pairs

Factor out the GCF out of the first group. Factor out the GCF out of the second group

Since we have the common term , we can combine like terms

So factors to

In other words,

Question 738342: (x-2)(x+2)/3x-6 simplify
Answer by jim_thompson5910(28595)   (Show Source):
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Final Answer:

Question 738243: what is the fraction of 16.62?
Answer by ankor@dixie-net.com(15656)   (Show Source):
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what is the fraction of 16.62?
just like you say it: 16 and
Both numerator and denominator are even, reduce by dividing both by 2
16
31 is prime so you're done

Question 738231: If a & b are two odd prime numbers, show that a^2-b^2 is composite.
Answer by MathLover1(6634)   (Show Source):
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Assume p > q. Since p, q are both odd, p - q ≥ 2. Also, q ≥ 3, p ≥ 5.
Since p² - q² = (p + q) (p - q) where p + q, where p + q > p ≥ 5, and p - q ≥ 2, p² - q² is composite.

Question 737749: Evaluate ((100001^2)-(99999^2))/100000.
Answer by MathLover1(6634)   (Show Source):
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Question 736715: Solve:
If (-6/n) is not a rational number, what MUST the value of n be?

Answer by stanbon(57361)   (Show Source):
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Solve:
If (-6/n) is not a rational number, what MUST the value of n be?
------
n must be an irrational number.
============
Cheers,
Stan H.

Question 734572: Solve for x
2x-1/7=3(1-2x)/2
I got the answer x=23/46
is this right? can you show me your working for this so i can compare it to mine?
Answer by MathLover1(6634)   (Show Source):
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.....cross multiply

.....so, your answer is correct!!!!!

Question 733816: X2+5x-2
Answer by jim_thompson5910(28595)   (Show Source):
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What do you want to do here? Graph it? If so, then the graph is below

Question 731893: Perform the indicated operation (2x^3+x^2-x+1) / (2x+3) (use long division)
Answer by lynnlo(4164)   (Show Source):
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x^2-x+1-2/2x+3