Given:
To find:
The simplified expression by factoring.
Solution:
Let us factor the numerator:
31x can be written as 3x + 28x.
Take 3x common in 1st two terms and 7 common in next two terms.
Make sure the remaining terms in the both brackets must be same.
Now, take out common factor (4x + 1).
In the same way, factorize the denominator:
8x can be written as 4x + 4x.
Take 4x common in 1st two terms and 1 common in next two terms.
Make sure the remaining terms in the both brackets must be same.
Now, take out common factor (4x + 1).
Substitute the terms we found for numerator and denominator:
Cancel the common factors.
The simplified expression is 
.
Answer:
Yes, this equation has a solution. According to Intermediate Value Theorem at least one solution for [0,2]
Step-by-step explanation:
Hi there!
1) Remember a definition.
Intermediate Value Theorem:
If 
is continuous on a given closed interval [a,b], and f(a)≠f(b) and f(a)<k<f(b) then there has to be at least one number 'c' between 'a' and 'b', such that f(c)=k
----
(Check the first graph as an example)
2) The Intermediate Value Theorem can be applied to determine whether there is a solution on a given interval.
Let's choose the interval ![[0,2]](https://tex.z-dn.net/?f=%5B0%2C2%5D)
Proceed to the other point: 2
3) Check the 2nd Graph for a the Visual answer, of it. And the 3rd graph for all solutions of this equation.
Answer:
The quotient is 3 and 
.
Step-by-step explanation:
To find the quotient of the division (which is just the solution, really), we have to solve the division itself:
Now that we know the quotient, we can look at the question itself to find it requires from us an answer with a whole number in it.
Therefore, we transform the fraction as thus:
Therefore, the final answer is 3 and .
Hope this helped!
The answer is option E i.e., 1 because we know that there are 3 defective batteries in the case so the probability will never be 1 for this case.
