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[[999 x 1000] / 2]  -  [[99 x 100] / 2] ==494,550

\(\dfrac{(8x^3 + 36x^2 + 54x + 27){(x-1)}^2}{(x^3 + 6x^2 + 12x + 8){(x+1)}^2} < 0\)

The first thing I notice is the 1st and last term on the bottom are cubic.

so I check but the long bracket simplifies to (x+2)^3.

The top also looks promising ... (2x+3)^3

so we have:

\(\dfrac{(2x+3)^3{(x-1)}^2}{(x+2)^3{(x+1)}^2} < 0\)

x cannot be -2 or -1 because I can't divide by 0

x is not going to be -1.5  or 1 either since 0 is not less than 0

if x is not 1 or -1 then both (x-1)^2  and  (x+1)^2 will be positive

cubics have the same sign as the term that is being cubed so I only need to think about 

2x+3      and      x+2      

If they have the same sign, both pos or both neg then the outcome will be positive

If they have different signs the outcome will be negative.

So we want

2x+3<0        and   x+2>0                    OR           2x+3>0    and   x+2<0

x  <  -1.5      and   x > -2                    OR             x > -1.5    and   x <-2

-2 < x < -1.5                                       OR                 no solution

so

-2  < x < -1.5

Here is the graph

There are 120 girls and 57 boys in a school. If 5% of the girls leave the school and no new candidates take up admission, what will be the total percentage of boys in the school?

Hello Guest!

\(120\times 5\%=\color{blue}6\)

5% of the students are 6 girls.

\(120+57-6=\color{blue}171\)   \(⇒ 100\%\)

\(171:100\%=57:x\\ 171x=57\cdot 100\%\\ x=\frac{57\cdot 100\%}{171}\)

\(x=33\frac{1}{3}\%\)

The percentage of boys in the school is \(33\frac{1}{3}\%\).

  !

All the info you need is contained in these 2 diagrams. 

Incorrect graph has been deleted :  sorry about that.

Two sides of a parallelogram are 30 and 20.  One diagonal has a length of 40. What is the length of the other diagonal?

The length of a diagonal is 10√10

Let the numbers be a, b, c, and d.  Then from the given information,

a/(a + b) = 0.6

b/(a + b) = 0.25

c/(c + d) = 0.3333 = 1/3

d/(a + d) = 0.5

Solving this system gives us

\(\begin{matrix} 2 & 5 \\ 3 & 5 \end{matrix}\)

Someone please answer

It's wrong

The answer is

2 5

4 5

Can someone that is a mod or admin help me with this?

Theres no question. It just explains what a peachy number is.

Ginger ale your father seems abusive for yelling at a six-year old for discovering that Santa Clause isn’t real. Most fathers would be proud when their children discover and learn things. Was your father an alcoholic? How old was you suster? Is this abusive behavior why your sister never laughs?

Im just going to guess that ur supposed to multiply them

https://web2.0calc.com/questions/prime-one-less-than-a-square

here it says that it is a square

The second rectangle would have dimensions of 7.5 each, since it is a square. We double that because the sides have been folded in half for each side to get a 15 by 15 square. 15*15 is 225.

AGREED! And good answer CPhill! :D

-Grace

WOW DewdropDancer  you are very good at catching copied problems! :D

-Grace

Lol, use a calculator. But if you want me to answer it here, as we know 25 * 3 = 75. so 94 - 75 = 19. After that, we can use long division to find that the answer to that is 19 ÷ 25 = 0.76. So then 3 + 0.76 = 3.76. That is the one that makes the most sense to me but if you would like a more simple way to do it, Use long division to divide 94 by 25. 94 ÷ 25 = 3.76. (Correct me if I'm wrong).

It's not a yes or no answer it's telling to prove how, and I should add that it's supposed to use factoring.

I am very sorry. I am a bit rusty on my elementary math... it has been about a year since I've had a refresher for it.  Let me fix that mistake and take a bit of time into that. I would say it is the only perfect square that is one above a prime number I went all the way to 263.

8 is not a perfect square.