Answer:
no
Step-by-step explanation:
Step-by-step explanation:
∴ Addition is associative. ∴ Subtraction is not associative. ∴ Multiplication is associative. ∴ Division is not associative.
...
Associativity for Integers.
Operation Commutative True / False
Addition a + (b + c) = (a + b) + c True
Subtraction a − (b − c) = (a − b) − c False
Answer:
a. no real root
Step-by-step explanation:
sqrt(-9/16) has no real roots because negative numbers do not have two real numbers that are the same that multiply together to give a negative
-a * -a = a^2
a*a = a^2
There is no real number that gives -a^2
<h3>
<u>Explanation</u></h3>
![{12x}^{4} + {39x}^{3} + {9x}^{2}](https://tex.z-dn.net/?f=%20%7B12x%7D%5E%7B4%7D%20%20%2B%20%20%7B39x%7D%5E%7B3%7D%20%20%2B%20%20%7B9x%7D%5E%7B2%7D%20)
- Factor the expression by using common factor.
We csn pull out 3x² out of the expression.
![{3x}^{2} (4 {x}^{2} + 13x + 3)](https://tex.z-dn.net/?f=%20%7B3x%7D%5E%7B2%7D%20%284%20%7Bx%7D%5E%7B2%7D%20%20%2B%2013x%20%2B%203%29)
We simply pull out the x-term with lowest degree and 3 out of the expression. If another expression cannot be factored after first factoring then that's the final answer.
- The expression can still be factored. Factor the expression by using two brackets.
![{4x}^{2} + 13x + 3 \\ (4x + 1)(x + 3)](https://tex.z-dn.net/?f=%20%7B4x%7D%5E%7B2%7D%20%20%2B%2013x%20%2B%203%20%5C%5C%20%284x%20%2B%201%29%28x%20%2B%203%29)
![3 {x}^{2} (4x + 1)(x + 3)](https://tex.z-dn.net/?f=3%20%7Bx%7D%5E%7B2%7D%20%284x%20%2B%201%29%28x%20%2B%203%29)
<h3>
<u>Answer</u></h3>
![\large \boxed { {3x}^{2} (4x + 1)(x + 3)}](https://tex.z-dn.net/?f=%20%5Clarge%20%5Cboxed%20%7B%20%7B3x%7D%5E%7B2%7D%20%284x%20%2B%201%29%28x%20%2B%203%29%7D)
Out of a sample of 80 books, 6 were historical books. So the percentage of books in the sample will be:
![\frac{6}{80}*100= 7.5](https://tex.z-dn.net/?f=%20%5Cfrac%7B6%7D%7B80%7D%2A100%3D%207.5%20)
%
We can use this sample to represent the entire collection of books in the library. So the best estimate of total number of historical books in the library is 7.5% of 21360 , which comes out to be:
7.5 % of 21360 =
![0.075(21360)=1602](https://tex.z-dn.net/?f=0.075%2821360%29%3D1602)
Therefore, roughly 1602 books out of 21360 book of library are historical books.