maths plz.....help!!!! i'll giv full stars to the best answer plzzz help?

Question

if a^2+b^2+c^2=16 nd ab+bc+ca=10 thn find the value ofa+b+c
2] convert the folowing decimal no in the form of p/q bust5.2......,23.43......,o.32......,o.123,0.235
3] if 27^x=9/3^x then find the value of x
4] show that x^a [b-c]/x^b [a-c]divided [x^b/x^a]^c=1
5] simplyfy underroot 5+under root 3/under root 5-under root 3+under root 5-under root 3
6] show that [x^a x^bx^c]^4

Answer 1

Well, your no. 6 is incomplete.
No.2, what do you mean by "p/q bust"??
Let's do these one at a time, leaving out the "bust"
in no.2.
1). (a+b+c)² = a²+b²+c² + 2(ab+ac+bc).
(Just multiply out to get this!)
So (a+b+c)² = 16+2(10) = 36
and a + b + c = 6.
or a + b + c = -6.

2). 5.2 = 5 2/10 = 27/10
23.43 = 23 43/100 = 2343/100
0.32 = 32/100 = 8/25.
I'll let you do the rest!

3). 27^x = 3^(3x)
So
3^(3x)* 3^x = 9 = 3².
3^(4x) = 3^2
4x = 2
x = 1/2

4). I think I figured out what you want.
Let's simplify the numerator of your
fraction(i.e., the part before the "divided").
We get
x^(ab-ac) / x^(ba-bc)=
x^(ab-ac)/x^(ab-bc)=
x^(-ac)/x^(-bc) =
(x^b/x^a)^c,
which is your denominator.
So the quotient is 1.

5). It's not entirely clear what you want, but I'll
assume you want to simplify
(√5 + √3)/(√5 - √3) + (√5 - √3).
The secret is to multiply top and bottom of the
fraction by √5 + √3 to get rid of the radicals
in the denominator.
This gives
(√5 + √3)(√5 + √3)/2 + √5 - √3.
Now multiply out the radicals and simplify to get
(8 + 2√15)/2 + √5 - √3.
= 4 - √3 + √5 + √15=
4 - √3 + √5(1 + √3).
Hope that helped a bit!
BTW Are you using a Windows machine?
If so, instead of writing "underroot 5",
type left Alt 251 to get the radical sign and √5.
The 251 is on the number pad part of the keyboard.

Answer 2

1) (a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ac) = 36
a + b + c = +/- 6

2) 5.2 = 52/10 = 26/5, 2343/100, 0.32 = 32/100 = 8/25
You just need to multiply the numerator by a number such that the decimal is removed. The number with which you multiply becomes the denominator.

3) 27^x = 9 / 3^x
27^x * 3^x = 9
81^x = 9
(9^2)^x = 9
9^2x = 9
2x = 1
x = 0.5

4) Just solve the numerator first and try to make it equal to the denominator -
x^a(b - c) / x^b(a - c)
Open the brackets :
x^ab - ac / x^ ab - bc
Use the laws of exponents :
x^ab - ac - ab + bc = x^(b - a)c = [x^(b - c)]^c = [x^b/x^a]^c = Denominator
Thus the given expression is equal tp 1.

5) [(sqrt. 5 + sqrt.3) / (sqrt.5 - sqrt.3)] + (sqrt.5 - sqrt.3)
Rationalize the denominator of the first term by multiplying the numerator and the denominator by sqrt. 5 + sqrt. 3 :
(sqrt. 5 + sqrt.3)^2 / 2 (Use the identity a^2 - b^2 = (a + b)(a - b))
8 + 2 * sqrt. 15 / 2
Take 2 common from the numerator and cancel with the denominator :
2 + sqrt. 15

Now take the 2nd term into consideration. The expression becomes :
2 + sqrt. 15 + sqrt.5 - sqrt. 3
I don't think it can be solved further.

6) The question is incomplete.

Hope this helps.

[e-mail]

Answer 3

I'm soo happy you joined! I'm going to warn you though, It's super addicting and crazily fun! Lol, all my questions have plenty of answers that I can choose from! I love it :) I hope you have tons and tons of fun with it. Haha- best answer please?I gave you a star! I'd give you 100s if I could! :) :) :)

Answer 4

i'll do #1.

(a+b+c)^2 = a^2 + b^2 + c^2 + 2*(ab+ac+bc)
= 16 + 2*10 = 36
so a+b+c = sqrt(36) = 6

Answer 5

Dr. D has #1 correct

5.2 = 5 2/10 = 5 1/5 = 26/5
23.43 = 23 43/100 = 2343/100
.32 = 32/100 = 16/50 =8/25

27^x = 9/3^x
3^3x *3^x = 3^2
3^4x = 3^2
4x = 2
x = 1/2

x^a [b-c]/x^b [a-c]divided [x^b/x^a]^c=1
x^a(b-c)/[x^b(a-c)] * x^ac/x^bc =1
x^ac(x^ab-x^ac)/[x^bc(x^ab-x^bc)] =1
(x^(ac+ab) - x^(2ac))/(x^(ab+bc) - x^(2bc)) =1
The identity does not seem to be true or I am nott understanding your [ ] terms.

Answer 6

here's 3:
27^x = 9/3^x ==>
81^x = 9
x = .5

Answer 7

I'm really sorry I don't know. but try searching it on Google. That's what I did once. type in math answers. if this doesn't work I'm really REALLY sorry!

Answer 8

uuuuhhhh.never mind