Melody

Thanks Guest,

(-1/4)^2+1/9=

\((\frac{-1}{4})^2+\frac{1}{9}\\ =(\frac{-1*-1}{4*4})+\frac{1}{9}\\ =(\frac{1}{16})+\frac{1}{9}\\ =\frac{1}{16}+\frac{1}{9}\\ =\frac{1}{16}\times\frac{9}{9}+\frac{1}{9}\times \frac{16}{16}\\ =\frac{1*9}{16*9}+\frac{1*16}{9*16}\\ =\frac{9}{144}+\frac{16}{144}\\ =\frac{9+16}{144}\\ =\frac{25}{144}\\\)

Hello birthdaygirl, welcome to the forum.   :)

I am curious, is it your birthday everyday ??

x^2+y^2-8x-6y+24=0

\(\mbox{We have to rearrange it into this form}\\ (x-h)^2+(y-k)^2=r^2 \qquad \\centre\;(h,k) \qquad radius=r\\~\\ x^2+y^2-8x-6y+24=0\\ x^2-8x\qquad+y^2-6y=-24\\ x^2-8x+(\frac{8}{2})^2\qquad+y^2-6y+(\frac{6}{2})^2=-24+(\frac{8}{2})^2+(\frac{6}{2})^2\\ x^2-8x+16\qquad+y^2-6y+9=-24+16+9\\ (x-4)^2\qquad+(y-3)^2=1\\ \mbox{Circle centre (4,3) radius=1} \)

What is pi times 1 1/2 to the second power??

\(\pi\times (1.5)^2 = 2.25\pi\\ or\\ (pi\times 1.5)^2 = 2.25\pi^2\)

- (5𝑖+2)         - ( - 12𝑖+18)     - ( - 16𝑖+11)

=  -5𝑖-2               +12𝑖-18          +16𝑖 - 11

=  -5𝑖      +12𝑖    +16𝑖    -2     -18       - 11

=    23i                                  -31

=    23i  - 31

Mmm thanks  Heureka,

most kids here have not ever dealt with imaginary numbers so I think the question refers only to real numbers.

Lets see.

why is there no pair of linear functions that can multiply together to result f(x)= x^2+1

I am just thinking here....

Let the 2 linear functions be  f(x)=ax+k      and     g(x)=mx+b    where a,k,m, and b are all real numbers.

\((ax+k)(mx+b) = amx^2 + abx  + kmx  + kx\\ (ax+k)(mx+b) = amx^2 + (ab+km)x  + kb\)

Now we want this to equal x^2+1

\(amx^2 + (ab+km)x  + kb =x^2+1\\ \)

Equating coefficients

am=1     a=1/m

bk=1      b=1/k

ab+km=0    1/(mk) +km=0          1/(mk) = -mk      

This is impossible becaus one side will be negative and the other will be positive.

Neither m nor k can be zero becasue you cannot divide by 0.

Hence 2 linear functions cannot multiply to give   x^2+1   

(not in the real number system anyway )     :))

While the outline of what I have done should be correct my layout is very poor.

Perhaps someone can present it better ??

ab+cd-ac-bd=

You cannotr simplify this

But

you can factorise it

ab+cd-ac-bd

=ab-ac+cd-bd

=a(b-c)+d(c-b)

=a(b-c)-d(b-c)

= (a-d)(b-c)

how to solve (65000/10000)1/4

\( (\frac{65000}{10000})^{1/4}=(\frac{6.5*10000}{10000})^{1/4}= 6.5^{0.25}\quad or \quad \sqrt[4]{6.5}\)

You couls estimate this on the calculator if you wanted to. ://

6.5^0.25 = 1.5967184337873702

There is only one real solution

Yes, I agree with that answer.

The first person can be seated anywhere.

Then there are 3 people of that gender left and they can be seated in 3! ways.

Then the 4 others can be sat in 4! ways.

That is   3!*4! ways altogether :)