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:
x ≤ -9
Step-by-step explanation:
to solve this equation you must subtract 5 from both sides
you get
x ≤ -9
that is your answer
Answer:
-2
Step-by-step explanation:
The leading coefficient in a polynomial is the coefficient that corresponds with the highest degree term. In this case, -2 is the leading coefficient since its term has x² as the highest degree of the quadratic.
Let’s put these into one fraction each:
Biking:
= (12*5)/8 miles
= 60/8 miles
This can be reduced to,
= 15/2 miles
Swimming:
= (5*2)/3 miles
= 10/3 miles
Running:
= (6*3)/8 miles
= 18/8 miles
This can be reduced to,
= 9/4
Now we add all the distances up:
= (15/2) + (10/3) + (9/4)
Now we just can add the numerators and the denominators. We must find the lowest common factor (LCF) for our 3 denominators (2,3,4). Our LCF turns out to be 12. *Remember what we do to the denominator we must do to the numerator. So:
= (15/2) + (10/3) + (9/4)
= [(15*6)/12] + [(10*4)/12] + [(9*3)/12]
= (90/12) + (40/12) + (27/12)
= (157/12)
Therefore Aaron Ran 157/12 miles or 13.08 miles.
Hope this helps!
Answer:26
Step-by-step explanation:
