Answer:
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Step-by-step explanation:
:[ I do not understand
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>
The top answer is correct.
The values of x and y that will make LMNO a parallelogram are: x = 9, y = 1.5.
<h3>
Properties of a Parallelogram</h3>
- The opposite sides of a parallelogram are parallel to each other and are also of equal lengths.
- Diagonals of a parallelogram are congruent to each other and also bisect each other into equal halves.
Therefore:
ON = LM
Substitute
7x - 5 = 6x + 4
Add like terms
7x - 6x = 5 + 4
x = 9
OL = NM
Substitute
8y + 3 = x + 6
Plug in the value of x
8y + 3 = 9 + 6
8y + 3 = 15
8y = 15 - 3
8y = 12
y = 12/8
y = 1.5
Therefore, the values of x and y that will make LMNO a parallelogram are: x = 9, y = 1.5.
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