First, some defintions
reciprocals are like a/b and b/a or 5/1 and 1/5
remember,
![\frac{\frac{a}{b}}{\frac{c}{d}}=(\frac{a}{b})(\frac{d}{c})=\frac{ad}{bc}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7Ba%7D%7Bb%7D%7D%7B%5Cfrac%7Bc%7D%7Bd%7D%7D%3D%28%5Cfrac%7Ba%7D%7Bb%7D%29%28%5Cfrac%7Bd%7D%7Bc%7D%29%3D%5Cfrac%7Bad%7D%7Bbc%7D)
john's fraction is reciprocal of sarah's
john=a/b
sarah=b/a
david multiplies his by sarah and gets 12/35
(b/a)(david)=12/35
multplies his number by john and gets 12/35
(a/b)(david)=15/7
hmmm
(b/a)(david)=12/35 and
(a/b)(david)=15/7
if we divide them then we do
![\frac{(\frac{b}{a})(david)}{(\frac{a}{b})(david)}=\frac{\frac{12}{35}}{\frac{15}{7}}=](https://tex.z-dn.net/?f=%5Cfrac%7B%28%5Cfrac%7Bb%7D%7Ba%7D%29%28david%29%7D%7B%28%5Cfrac%7Ba%7D%7Bb%7D%29%28david%29%7D%3D%5Cfrac%7B%5Cfrac%7B12%7D%7B35%7D%7D%7B%5Cfrac%7B15%7D%7B7%7D%7D%3D)
![\frac{\frac{b}{a}}{\frac{a}{b}}=\frac{\frac{12}{35}}{\frac{15}{7}}=](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7Bb%7D%7Ba%7D%7D%7B%5Cfrac%7Ba%7D%7Bb%7D%7D%3D%5Cfrac%7B%5Cfrac%7B12%7D%7B35%7D%7D%7B%5Cfrac%7B15%7D%7B7%7D%7D%3D)
![(\frac{b}{a})(\frac{b}{a})=(\frac{12}{35})(\frac{7}{15})=](https://tex.z-dn.net/?f=%28%5Cfrac%7Bb%7D%7Ba%7D%29%28%5Cfrac%7Bb%7D%7Ba%7D%29%3D%28%5Cfrac%7B12%7D%7B35%7D%29%28%5Cfrac%7B7%7D%7B15%7D%29%3D)
![\frac{b^2}{a^2}=\frac{84}{525}=](https://tex.z-dn.net/?f=%5Cfrac%7Bb%5E2%7D%7Ba%5E2%7D%3D%5Cfrac%7B84%7D%7B525%7D%3D)
![\frac{b^2}{a^2}=\frac{4}{25}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%5E2%7D%7Ba%5E2%7D%3D%5Cfrac%7B4%7D%7B25%7D)
square root both sides
![\frac{b}{a}=\frac{2}{5}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7Ba%7D%3D%5Cfrac%7B2%7D%7B5%7D)
therefor
b=2 and a=5
john's number is a/b=5/2
sarah's number is 2/5
david, hmm
sarah times david=12/35
2/5 times david=12/35
times both sides by 5/2
david=60/70
david=6/7
check other
john times david=15/7
5/2 times 6/7=15/7
30/14=15/7
15/7=15/7
true
sarah's favorite number is 2/5
john's favorite number is 5/2
david's favorite number is 6/7
60 oz
Step-by-step explanation:
Although 60 is the correct answer, you might want to double check because you just used two different systems of measurement in one problem.
Hello from MrBillDoesMath!
Answer:
x = 0, 7
Discussion:
f(g(x)) =
f ( x^2-7x) =
1/ ( x^2 - 7x)
The points NOT in the domain are those where the denominator, x^2 - 7x = 0.
x^2 - 7x = 0 => factor x from each term
x(x-7) = 0 => one or both terms must each 0
x = 0 or x =7
Thank you,
MrB
Answer:
Positive
Step-by-step explanation:
As height is increasing, shoe size is also increasing (positive slope)
Negative correlation is when one variable increases and the other decreases (negative slope)
13-5=8
8+7=15 answer is 15