All Answers 356005 Answers

Look at line   20

$67,400 is between $56800  and $114,649.99....so the tax  is :

.25 (67400) - 6380   =   $10470 ⇒  "A"

Allie has   5 (5 + 3)   = 5 * 8  = 40  items

So...in 4 baskets, Alex must have  40/4  = 10  items

So....she must have 2 toys in each basket

Hi MobiusLoops,

I do not believe you are using the word correctly.

This is an Integer or integer value question.  

Integrals are completely different.  They are a part of calculus and nothing to do with integer values.

I understand the confusion, Integral is an normal English word and  integral and integer would have the same origin in speech.  But in maths the two meanings are very different.

The GCD(54, 12) = 6 The largest size tank that Clara can use.

12/6 =2 full tanks from the first well

54/6 =9 full tanks from the second well.

a(n) =( 2^(-2 n) (2 n - 1))

Let n = 100

∑[( 2^(-2 n) (2 n - 1)), n, 1, 100]  = 5/9

What is the definition of  "the maximum bad debt payment" and also "being in credit overload" in your textbook?

I think it would help a lot if you posted a diagram or a picture of your problem, especially if there is one in your textbook or assignment. If there isn't one, I recommend that you make an effort in drawing one to the best of your understanding and ability. It will also make it a lot easier for other people to see your problem in black and white, and they would be much more likely to attempt to solve it.

Why did you re-post your question with "heureka's" solution appended to it? Is it because you don't understand his solution? Or, is the solution very different from your teacher's way of solving it? Or, is it very different from the solution taught in your textbook?

He is the expert in understanding and solving these "Mod" equations. His solutions of these mod equations is the "formal way" of solving them. If you don't understand the formal solution, then you should consult with your teacher and see what he/she has to say. Maybe they know of a simpler method of solving them, such as "trial and error method", or some other such methods.

You may go online to sites such as this one and see the various methods and theorems used in solving such congruences: 

   https://www.cs.cmu.edu/~adamchik/21-127/lectures/congruences_print.pdf        

Good luck to you.                                                                       

300,000 inches

6 = 35/x  - 49/x^2       mutliply through by x^2

6x^2 = 35x   - 49      rearrange as

6x^2 - 35x  + 49   =  0        factor as

(3x - 7) (2x - 7)   = 0

Set both factors  = 0   and solve for x and we get that    x  = 7/3   or x  = 7/2

where is x in the equation?

Rate * Time  = Distance

Since the distances are equal, we have that

x^2 * 3  = (16 - 4x) * 4

3x^2 = 64  - 16x      rearrange as

3x^2  + 16x   - 64   = 0    factor

(3x - 8) (x + 8)   = 0

Set both factors  = 0   and solve for x  and we have

x  = 8/3    or  x  = -8

Since x > 0, then   x  = 8/3  is correct

Thanks, Rom....tricky....to say the least.....!!!

No prob, ML....!!!

Thanks.

We have 5 locations and we wish to visit 3 of them in any order....so   5C3   = 10 ways

Here's the solution.

First, rearrange the terms:-4p+2p+(-2)+3

Then, add like terms:-2p+1

And that's how you solve it.

Do you want us to simplify?

Thanks for the insight. I'm pretty new to integrals.

Here's an alternative approach:

.

Here is another method:  

Let the numbers be x and y    

\( (x-y)^2=x^2-2xy+y^2\\ \text{But we are told that } x-y=9 \text{ and that } x^2+y^2=153\\ so\\ (9)^2=153-2xy\\ 81-153=-2xy\\ -72=-2xy\\ xy=36\)

So the product of the 2 numbers is 36.

Yes you are right guest, I screwed up.

Thanks Heureka :)

\(7-7(2+3x)\\ =7 +\;\; -7(2+3x)\\ =7 +\;\; -7*2\;\;+\;\;-7*3x\\ =7 +\;\;\; -14\;\;\;\;\;+\;\;-21x\\ =7 \;\; -\;\;\; 14\;\;\;\;\;-\;\;\;\;21x\\ =\quad -7\;\;\;\;\;\qquad -\;\;\;\;21x\\~\\ =-7-21x\)

If this is base 2 then it is equivalent to:  2 + 1 + 1/2 + 1/4 + 1/8 + ... = 4

If it is base 10 then it is equivalent to:  10/9 + 1/9 + 1/90 + 1/900 + ... = 100/81

.