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Happy Birthday Hectictar But post it like off-topic

So we take this first (x-1)/3<5/7 and after this 5/7<(x+4)/5

(x-1)/3 < 5/7                                                5/7<(x+4)/5

7(x-1) < 3(5)                                                5(5) < 7(x+4)

7x - 7 < 15                                                  25 < 7x + 28

7x < 22                                                       -3 < 7x

x<22/7                                                        -3/7 < x 

or x< 3.1...                                                 or x > -0.4...

We find  -0.4 < χ < 3.1 

so the answer : integer values ​​satisfy is 0,1,2,3

Hope this helps!

That cannot be right!! How about 10, 11, 12 O'clock.......etc.!!!!

In the 12 hours of AM, it will show for 1 full hour between 1 AM and 2 AM. So, that is: 1 in 12 hours.

In the 12 hours of  PM, it will show for 1 full hour between 1 PM and 2 PM. So, that is: 1 in 12 hours.

So: 1 + 1 =2 hours in 12 + 12 = 24 hours. Or 2 / 24 = 1 / 12, or 1 in 12 hours, not 1/2 as you have it written.

Note: I'm only counting the HOURS HAND!. The MINUTE HAND will show 16 ones EVERY HOUR!.

Rom: I think you skipped one:
Listfor(n, 5, 20, (72 % n)) = 6 x 12,  8 x 9,  9 x 8,  12 x 6,  18 x 4 

When z³=a there are 3 possible values for z not 1 (unless a=0)

But he got the same answer as you... and only 3 users answered this question...

Suppose z  is a complex number such that \(z^3 = 100+75i\) . Find |z|

\(|z^3| = \sqrt{100^2+75^2}\\ |z^3| = \sqrt{100^2+75^2}\\ |z^3| = 125\\ z^3=125[\frac{100+75i}{125}]\\ z^3=125[\ 0.8+0.5i]\\ \)

Let

\(z=re^{i\theta}\\ z^3=r^3e^{3i\theta}\\ z^3=r^3(cos(3\theta) +isin(3\theta))\\ \)
\(r^3(cos(3\theta) +isin(3\theta))=125[\  0.8+0.6i]\\ r^3=125\\ r=5\\ cos(3\theta)=0.8\\ sin(3\theta)=0.6\\ 3\theta \approx 0.6435\\ \theta \approx 0.2145\;radians\\ \)

anyway, I digress,

\(|z|=5\)

(x^2 + 3x - 4) + (2x^3 - 2x + 5)   = ???

If A and B are positive prime numbers that add up to 100. Then what is the smallest possible value of |A-B|.

\(i=\sqrt{-1}\)

\(z = 5 e^{i \theta} \\ z^3 = 5^3 e^{i3\theta} \\ |z^3| = 5^3 = 125\)

\(72 = 2^3 3^2 \\ \text{This gets us, given the constraints on row length,}\\ 6\times 12,~8\times 9,~9\times 8,~12\times 6\\ \text{so 4 different row lengths}\)

\(\text{The odd numbers will be relatively prime to }2^{100} \\ \text{so }\phi(2^{100}) = \dfrac 1 2 2^{100} = 2^{99}\)

-1/2 + (3/4 * 4/9)  Here we need to start by finding the common denominator for 3/4 and 4/9.

For this problem, you can just multiply the numerators: (3*4)=12 

And the denominators: (4*9)=36

So we get the fraction 12/36.

To simplify this equation we will reduce the fraction by dividing by 4. We then get 3/9

Now we have -1/2 + 3/9

To get a common denominator we will cross multiply:

-1*9= -9

2*3=6

2*9 and 9*2 = 18 and 18 so we get:

-9/18+6/18

Now we can add the numerators and the denominator remains the same and we get the answer: -3/18

Hope this helps!

'i' is not a variable, it is a constant.

OK let's get started!

36x - 8y²    Where 3= x and y= -6.

36x- 8y² = 36·3 - 8·(-6)² 
= 108 - 8·36 } Here you multiply 8*36 before you subtract according to PEMDAS. 

= 108 - 288

= -180
 

Hope this clears things up! Don't hesitate to ask more questions here on the forum!

thx so much

First thing you do is input 3 into x(if 3 is x the question doesnt make sense) and -6 into y 

 36x - 8y^2

36(3)-8(-6)^2

108-8(36)

108-288

the answer would then = -108 

210/2 = 105 if the home team won by 20 points then 105+10=115 and 105-10=95. Therefore the home team scored 115 points.

This may not be correct but if there is 5 letters(abcde) then there is with each letter a possibilty of 5 different sets with a cobination of 3 letters. for example aaa,aab,aac,aad,aae,the switch the last letter to the middle for each letter aba,aca,ada,aea, etc. this leads to there being 5 for each letter using only a and since there is 5 letters you multily 5 by 5 for the different sets then by another 5 or 5^3. so 125 if u still need the answer. 

36x- 8y² = 36·3 - 8·(-6)² 
= 108 - 8·36 
= -180 

How did you work it out though 

Do you take 108 - 8 x 36 ? sorry I'm just trying to figure out how you get the answer so i can understand it better