Let a set of
elements.
We can find
(factorial) of the
element.
However, combination of the element lead to less than
possibilities.
(combining like adding or multiplying)
So the proposition is false.
Answer:
Option (D)
Step-by-step explanation:
Given polynomial is,
2x³ - 3x² - 3x + 2
If (x - 2) is the factor of the given polynomial,
By synthetic division we can get the other factor.
2 | 2 -3 -3 2
<u> 4 2 -2 </u>
2 1 -1 0
Therefore, other factor of the given polynomial is (2x² + x - 1)
Now (2x² + x - 1) = 2x² + 2x - x - 1
= 2x(x + 1) -1(x + 1)
= (2x - 1)(x + 1)
Therefore, factors of the given polynomial other than (x - 2) are (2x - 1) and (x + 1)
Option (D) will be the answer.
Answer:
53 teachers
Step-by-step explanation:
Basically, what we need to do here is to find how many teachers there need to be, first. If there are 6,734 students in the school district and if maximum class size is 25, then the number of teachers needed is:
6,734 / 25 = 269.36
Of course, it's obvious that we can't have a decimal number of teachers, so we need to find integer (269 or 270).
If we take 269 teachers and 25 students per class, we get:
269 • 25 = 6,725 students, which is not enough, since there are 6,734 students.
That means that the number of teachers needed is 270.
It is given that there are already 217 teachers, meaning that 270-217=53 teachers have to be supplemented.
Answer:
C. 40
Step-by-step explanation:
Let us say there are x 7's and y 77's.
We have been given that each term in the sum a1+a2+a3+...+an is either 7 or 77 and the sum equals 350. We are asked to find the value of n.
Since the sum of all numbers is 350, so we can represent this information in an equation as:
The only integer solutions for the equation are 10, 20, 30, 40, 50
.
So, there can be these many terms: 10 or 20 or 30 or 40 or 50
.
The given option only contains 40, so 40 would be the answer. For 40 terms to be there, there has to be 39 sevens and 1 seventy-seven.
Let us verify our answer.
Therefore, the total terms (n) could be equal to 40 and option C is the correct choice.
Answer:
Step-by-step explanation:
6 and - 2 are the only two solutions to the required quadratic equation.
So, if the variable is represented by X then (X - 6) and (X + 2) will be the only two factors of the polynomial function.
Therefore, the equation is
(X - 6)(X + 2) = 0
⇒ 
If the leading coefficient of the equation is 3 then we can write the equation as (Answer)
