All Answers 355864 Answers

(x+1)/(x-2)≥(x+3)/(x-4)

Move the right to the left:

(x + 1) / (x - 2) - (x + 3) / (x - 4) >= 0

Find the LCD:

(x + 1)(x - 4) / (x - 2)(x - 4) - (x + 3)(x - 2) / (x - 4)(x - 2) >= 0

Combine the two fractions:

(x + 1)(x - 4) - (x + 3)(x - 2) / (x - 4)(x - 2) >= 0

Multiply both sides by (x - 4)(x - 2):

(x + 1)(x - 4) - (x + 3)(x - 2) >= 0

Expand:

x^2 - 3x - 4 - (x^2 + x - 6) >= 0

Distribute negative:

x^2 - 3x - 4 - x^2 - x + 6 >= 0

Combine like terms:

-4x + 2 >= 0

Subtract 2:

- 4x >= -2

Divide - 4:

x <= 1/2

:)
 

Thanks ilorty,

It took a little while for me to get my head around what you have done.

It is an impressively simple answer.     

Please put only one question per post.

a)  I would prove this using induction.     I will outline the method here.

Step 1:

Show true for n=0

Step 2:

Assume true for n=k where k is some integer.

then prove that it will be true for n=k+1   (I've done this myself so I know it works)

Step 3

Assume true for n=k

Prove it is true for n=k-1

Step 4.  (Summary)

Since it is true for n=0 it must be true for n=1, n=2 .......etc

also, since it is true for n=0 it must be true for n=-1, n=-2 ..... etc

Therefore it must be true for all integer values of n.

Now try filling in the blanks.

Believe it or not initial guest answerer, this is Ginger's way of saying that she likes you.

OR at least that she does not dislike you yet.     LOL

Here is an answer that you can learn from.

The probability that 1 person has it is     1/3000

The prob that a person does not have it is  2999/3000

If there are 6 people in a room the prob that no one has it is    (2999/3000)^6

so

the prob that at least 1 of the 6 people has it is     1-  (2999/3000)^6   which is approx    0.002

Which inequality is represented by the graph?

Hello Guest!

\(y\le \frac{5}{3}x-3\)

is the applicable functional equation.

  !

How much 45% disinfectant solution must be mixed with a 30% disinfectant solution to produce 20 gal of 39% solution?

Hello Guest!

\(\color{blue}x\cdot 45\%+(20-x)\cdot 30\%=20\cdot 39\%\\ x\cdot 45\%+20\cdot 30\%-x\cdot 30\%=20\cdot 39\%\)

\(45x+600-30x=780\\ 15x=180\)

\(x=12\)

12 gal 45% disinfectant solution must be mixed with 8 gal 30% disinfectant solution to produce 20 gal of 39% solution.

  !

In square ABCD, point P is in the square, such that triangle CDP is equilateral.  What is angle CPB?

angle CPB = 75º  

Find the equation of the line T=through (-3,-5), perpendicular to -2x - 5y = -19

Hello Guest!

\(y_A=3.8-0.4x\)

\(y_B=m(x-x_1)+y_1\)

\(m=-(\frac{1}{-0.4})=2.5\\ x_1=-3\\ y_1=-5\)

\(y_B=2.5(x+3)-5\\ y_B=2.5x+7.5-5\)

\(y_B=2.5x+2.5\)

  !

∠A = 60º

∠B = 65º

∠C = 55º

∠D = 75º

You can use modular arithmetic.

Did you come here to criticize me, or to help the student who asked a question? 

If it was the former, thanks for the input.  If it was the latter, nice try but no cigar. 

If I wanted to help the student, I would have (also) posted a solution.  I chose not to because this question is presented (seemingly) by an indifferent, uninterested student. There are dozens of questions on this forum that use the Binomial CDF for a solution. This question is very basic: it’s a homework question assigned by a teacher. It is reasonable to assume the student attended a lecture and lesson prior to its assignment. So the student should be familiar with the term Binomial CDF and its application for this question –at least enough to research and learn the rote mechanics to present a solution.   

You could research this, and present a solution to the student.  I doubt the student will return to his question, but you will learn something and then can tutor next student who presents a similar quest. …And you can keep the cigar as a tip. 

From this, it should be clear that I posted to criticize you. However you should note the criticism is in a constructive form, without the aggressive, ass-ripping commentary peppered with vulgarities usually reserved for the forum’s BB class (Blarney Bag, Bullshit Bug, Bubble Bain).

These BBs are the poster children old farts representing the indefatigable dumbshits united in errant math, and the personifications of stubborn, relentless, intractable bullshitters of mathematical lore. They are pseudo intellectuals who are all titled with a multiplicity of advanced dimwit degrees in arrogant stupidity. This forum does not lack for these professors of misinformation, who teach their absurdities with authority, irritation, and brain-dead dumbness.  ... One reason for this excess is this forum allows for anonymous posting. Anonymous posting is one of several common denominators for all of the “BBs”.  

You are anonymous and you are a (near) retirement-age male with an interest in mathematics, but with limited skills. I’m not yet sure to which category you belong. …Time will tell..., but I don’t believe you will become another BB. At least I hope not; we already have more than our fair share. 

--. .-

AOPS...! 

who is the owner??? 

1. Find out what 223*634 is. (area of the piece of sheet metal in square feet)

2. Multiply the product by 144 (aka 12^2 since 1 square foot=144 square inches, and 1 foot is 12 inches)

3. YOU GET THE ANSWER!!! 

Ohhhh I see this makes so much sense! Thank you so much!!!

This is not my explanation btw... credits to the owner.

"Since current is directly proportional to voltage, multiplying the voltage by a factor of 6 (going from 50V to 300V) will also multiply the current by a factor of 6. Since current is inversely proportional to resistance and resistance is directly proportional to length, halving the wire will halve the resistance and thus double the current. Therefore the new current will be 6*2=12 times the original current or 12*200=2400 milliamps." 

Excuse me guest, don't just give out wrong answers without any real work shown; it's not helping anyone learn. 

For anyone who can't seem to see the LaTeX, here is the picture:

(I plugged it into a latex site and screenshoted it)

But I'm not just here to give you a picture of something you probably already know. 

\(6x^3y^4+24x^6y^2-36x^3y^3\)

Hint:

What is the greatest number that goes into 6,24 and 36?

You can also factor out x^3,  that is the biggest one for x

And what is the biggest factor of y that you can factor out?

Now, what is the answer?

S = Speed in still air.
D = Distance between the 2 towns.

6.4S = 2D,   
3.2S + 3.4667*(S - 50)=2D, solve for D, S

D =~ 2,080 miles - the distance between the 2 towns.
S =~ 650 mph - plane's speed in still air.

We need to simplify 3y= 12x-6 until the y is isolated. Thus, we divide by 3:

3y= 12x-6

y = 4x - 2

Therefore, the answer is F

We can graph both lines just to make sure:

And....it looks like they are the same!

:)

EDIT: Sorry for the large pictures  I adjusted the resolution but it did not come out correct...

I have not heard these terms used although most of the time I am sure they are self-explanatory.

I'm not sure about the first one, is it infinite or is it a jump?  Looks like both .....

the others I would check using desmos.

I have said this to you before.  Don't you know what I mean?

I'll do 3 just to show you.