Answer:
The least common denominator would be 42.
Step-by-step explanation:
6 and 7 don't share any common multiples with any other number besides 6 or 7.
6 * 7 = 42
Answer:
Yes, The slope of the line k between C and D is constant
Step-by-step explanation:
Lets find the slope of the line K from the points AC and AD
Step1:
Slope of line K from AC (point C)
= 
= 
Step 2:
Slope of line k from AD (point D)
= 
= 
=
The slope of the line K from the points AC and AD are equal
Answer:
71.10
Step-by-step explanation:
![\bf (x-7)(x^2+3x-3)~\hfill \begin{array}{cll} x^2+3x-3\\ \times x\\ \cline{1-1} x^3+3x^2-3x \end{array}~~+~~ \begin{array}{cll} x^2+3x-3\\ \times -7\\ \cline{1-1} -7x^2-21x+21 \end{array}~\hfill \\\\[-0.35em] ~\dotfill\\\\ (x^3+3x^2-3x) +(-7x^2-21x+21)\implies x^3-4x^2-24x+21](https://tex.z-dn.net/?f=%5Cbf%20%28x-7%29%28x%5E2%2B3x-3%29~%5Chfill%20%5Cbegin%7Barray%7D%7Bcll%7D%20x%5E2%2B3x-3%5C%5C%20%5Ctimes%20x%5C%5C%20%5Ccline%7B1-1%7D%20x%5E3%2B3x%5E2-3x%20%5Cend%7Barray%7D~~%2B~~%20%5Cbegin%7Barray%7D%7Bcll%7D%20x%5E2%2B3x-3%5C%5C%20%5Ctimes%20-7%5C%5C%20%5Ccline%7B1-1%7D%20-7x%5E2-21x%2B21%20%5Cend%7Barray%7D~%5Chfill%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%28x%5E3%2B3x%5E2-3x%29%20%2B%28-7x%5E2-21x%2B21%29%5Cimplies%20x%5E3-4x%5E2-24x%2B21)
notice that all you do is simply multiply the terms of either one by the terms of the other sequentially, then add like-terms.
Let x% be the salt concentration of first solution.
Then in 8ml, amount of salt = 
Given that to this 8ml solution, 11ml solution of a 47% salt solution is mixed.
amount of salt in 11ml of 47% salt solution is = 
So, total amount of salt in new mixture = 
But given that this new solution is a 43% salt solution.
Hence amount of salt in new mixture of (8+11)=19ml solution of 43% salt solution is
Hence 
8x+517 = 817
8x=817-517 = 300
x= 300/8 = 37.5
Hence the salt concentration in the first solution is 37.5%