4n² - 15n + 14<span> is always the product of two numbers, for it to be prime number, one of these factors must be either 1 or -1.
Case n - 2 = 1
That would be n = 3
Then </span>4n² - 15n + 14<span> = 5 , which is prime.
Case n - 2 = -1
That would be n = 1
Then </span>4n<span>² - 15n + 14 = 3, which is also prime.
Case 4n - 7 = 1
That would be n = 2 and that makes other factor (n-2) zero so it's not prime
Case 4n-7 = -1
That would be n = 3/2 which is not integer, so </span>4n<span>² - 15n + 14 will not be interger.
For any other n values, </span>4n<span>² - 15n + 14 will be composite number since it is product of two factors.
Therefore we are left with n = 1 and n = 3; only two values of n.</span>
Answer:
Step-by-step explanation:
AS we can see the lines are parallel so
2 ( 4x - 3) + 7(x + 3) = 180° ( being so - interior angles)
8x - 6° + 7x + 21° = 180°
15x + 15° = 180°
15x = 180° - 15°
15x = 165°
x = 165° / 15
Therefore x = 11°
Now
2 ( 4x - 3) = 2 ( 4 * 11° - 3°) = 2 ( 44 - 3)° = 2* 41 = 82°
7(x + 3 ) = 7 ( 11° + 3°) = 7 * 14 = 98°
Answer:
1
4
9
16
25
36
49
64
81
100
Step-by-step explanation:
1 = 1²
4 = 2 x 2 = 2²
9 = 3 x 3 = 3²
16 = 4 x 4 = 4²
25 = 5 x 5 = 5²
36 = 6 x 6 = 6²
49 = 7 x 7 = 7²
64 = 8 x 8 = 8²
81 = 9 x 9 = 9²
100 = 10 x 10 = 10²
To answer this problem, the utilization of the provided formula is of utmost importance.
The formula to be used would be for the combination with no repetition since it is what is asked and possibly happens when involving the products mentioned in the problem. The formula would be
n! where in
------------- n = number of things to choose from
(n - r)! r! r = number of things needed to form
the symbol ! is called a factorial function which replaces the sequence of multiplying a number in a descending order.
lets substitute and solve
13!
--------------
(13 - 6)! 6!
13!
-------------
(7!) 6!
6,227,020,800
-------------------
5,040 x 720
6,227,020,800
-------------------
3,628,800
1,716
The answer would be 1,716.
The only factors are 1 and 29
