Questions on Algebra: Real numbers, Irrational numbers, etc answered by real tutors!

You can put this solution on YOUR website!
-10 + 15
its like you have a debt of $10 and you paid them $15 dollars....Guess how much you get back...
-10 + 15 = 5
so if you paid them $15 dollars for a $10 debt, you get $5 back as change.

You can put this solution on YOUR website!
There are simple rules for adding integers.

- If the signs are the same add them and carry the sign.
- If the signs are different subtract the smaller number from the larger, then carry the sign of the larger.

-10 + +15. The signs are different:
15-10 = 5
Carry the sign of the larger (+15), which makes it +5.

If you need help understanding math so you can solve these problems yourself, then one on one online tutoring is the answer ($30/hr). If you need faster solutions with guaranteed detailed answers, then go with personal problem solving ($3.50-$5.50 per problem). Contact me at fcabanski@hotmail.com

You can put this solution on YOUR website!
Suppose we use two three-digit numbers.

To get 5 as a units digit, we need either 4+1, 3+2. Since 9+6 = 5 and 8+7 = 5 (mod 10) we cannot use 8 and 9 for the units digit (since we would need a 6 or 7).

Therefore we have either {4,1} or {3,2} as the units digits. Note that the tens digits have to be 8 and 9 since putting them in the hundreds place would create numbers too large. For the hundreds digits, use the set that wasn't used for the units digits (e.g. if 4,1 are units digits, use 3,2). Due to carrying, the hundreds digit will always be 6.

This now becomes a combinatorics problem where we assign digits to each number. We can evaluate the number of ways using combinatorics, but we have to account for overcounting and commutativity (e.g. 281+394 = 394+281), so I'll just list them out:

183 + 492
182 + 493
193 + 482
192 + 483
281 + 394
284 + 391
291 + 384
294 + 381
This leaves 8 ways.

Now, suppose we use a three-digit number, a two-digit number, and a one-digit number. This is obviously impossible, since the largest value we can obtain is 498 + 32 + 1 < 675. Additionally, no other combination of digits (e.g. four-digit plus two-digit) can work, so we have 8 ways.

You can put this solution on YOUR website!
the product of two consecutive odd numbers is 399. what are these numbers?
-----------
If you factor 399, you find it has a factor of 19.
399 = 19*21
--------------
If you do it the "hard way"
x*(x+2) = 399

Now you have to factor 399 anyway.
--> 19 & 21
---------------
Another way:
is almost 20, the middle of the 2 numbers.
--> 19 & 21

You can put this solution on YOUR website!
5/9 is real and it's rational, so it's NOT irrational.

You can put this solution on YOUR website!
How do I change 33 1/3% to a fraction?
---------
33 1/3 = 100/3%
-----
(100/3)/100 = 1/3

You can put this solution on YOUR website!


In a word, no. Draw yourself a number line. One number is greater than the other if and only if the greater number is to the right of the other number on the number line. All negative numbers are to the left of zero. All positive numbers are to the right of zero. In order for a negative number to be greater than a positive number, the negative number would have to be somewhere on the right hand side of zero, which is to say that it wouldn't be negative.

John

My calculator said it, I believe it, that settles it

You can put this solution on YOUR website!
-0.002 = -2/1000 = -1/500, which makes it a rational number. So it is NOT irrational.


It's also NOT an integer since it has a decimal part (that is nonzero). In other words, it is NOT a whole number (since it's NOT an integer).

You can put this solution on YOUR website!
What is the difference between rational, irrational, etc.?
Rational and irrational are the exact opposite of each other. A rational number is one that can be wrote as a fraction. Irrational numbers cannot be written as fractions.

You can put this solution on YOUR website!
How long will my shadow be if im 4 feet 7 inches. For four hours- nine, ten,twelve, and eleven in the morning
------------
It will vary with the latitude and the date.

You can put this solution on YOUR website!
2-(x-7)
(distribute the negative first)
2(-x+7)
(now, distribute the 2)
-2x+14

You can put this solution on YOUR website!

FACTORING BY GROUPING
--> -->
The real solution is the solution to -->
The imaginary solutions are the solutions to
--> and

You can put this solution on YOUR website!
the distance between ;
J(-9,5) and K(-4,-2)
-----------------
d = sqrt[(5--2)^2 + (5--4)^2]
---
d = sqrt[49 +81]
----
d = sqrt[130]
====================
Cheers,
Stan H.
======================

You can put this solution on YOUR website!
Use the distance formula


d = sqrt((x2-x1)^2+(y2-y1)^2)


Remember that the two generic points are (x1, y1) and (x2, y2)
So (x1, y1) = (-3, -4), which means x1=-3 and y1=-4
and (x2, y2) = (-1, -2), which means x2=-1 and y2=-2

So in short, x1=-3, y1=-4, x2=-1, and y2=-2.

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


d = sqrt((x2-x1)^2+(y2-y1)^2)


d = sqrt((-1-(-3))^2+(-2-(-4))^2)


d = sqrt((-1+3)^2+(-2+4)^2)


d = sqrt((2)^2+(2)^2)


d = sqrt(4+4)


d = sqrt(8)


d = 2*sqrt(2)


d = 2.8284271247462



So exact distance between the two points is approximately 2.8 units.

You can put this solution on YOUR website!
-3/1 is rational (since it's a fraction of two integers) and it's an integer (since -3/1 = -3)

You can put this solution on YOUR website!

There is no common difference, because that is not an arithmetic sequence.
It's also not a geometric sequence, because there is no common ratio.

However the nth term has this formula:

an = -21n²+55n-38.5 

And the sequence taken to a few more terms is:

-4.5,-12.5,-62.5, -154.5, -288.5, -464.5, ...


Edwin

You can put this solution on YOUR website!
sqrt(48) is both a real number and an irrational number (since you cannot represent it as a fraction of integers).

You can put this solution on YOUR website!


If the primes are closed under subtraction, then the result of any prime subtracted from any prime will have a prime result. Is 7 minus 3 a prime number?

John

My calculator said it, I believe it, that settles it

You can put this solution on YOUR website!
1/2 + (2/3 divided by 3/4) - (4/5 times 5/6)
= 1/2 + (2/3 * 4/3) - (4/5 times 5/6) Invert the divisor and multiply
= 1/2 + 8/9 - 20/30
= 1/2 + 8/9 - 2/3
Find a common denominator. 54 works
= 27/54 + 48/54 - 36/54
= 39/54
= 13/18

You can put this solution on YOUR website!
Real numbers are all the numbers that we use for real measurements. (That's not an official definition, but may help you understand what "real number" means).
Real numbers include all integers, like, 2, 0, and -12.
Real numbers include all RATIOnal numbers that can be expressed as RATIOs of two integers, like 3/4, -5/7, 2, 0, and -12. (Some of those rational numbers are integers; the others are what you used to call fractions).
Real numbers also include numbers that are not rational, but are real anyway, like , and . We know is real because it's the length of the circumference of a circle with a diameter measuring . We know is real because it's the length of the diagonal of a square with sides measuring 1. We cannot express or as fractions (rational numbers), or a decimal number that end or repeat, like =0.28, or =0.0833333.... . The best we can do with irrational numbers is write approximations like 3.14, or 3.142, or 3.1416, or 3.14159 for , but there is no rhyme or reason to what the next digit will be.
The number -12 is definitely real. Sometimes that's been the temperature outside; it was really cold. It is also a rational number, and it is also an integer. It is not an irrational number.