1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Gala2k [10]
2 years ago
10

Using the factorised trinomial

(n-2)(4n-7)" align="absmiddle" class="latex-formula">, prove that there are only two values of n for which 4 n^{2} - 15n + 14 is a prime number.
Mathematics
1 answer:
andrew-mc [135]2 years ago
5 0
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>
You might be interested in
Which solid figure does this net represent? A) Eliminate B) square pyramid C) triangular prism D) triangular pyramid
vampirchik [111]
It represent a square pyramid
6 0
3 years ago
It takes 5 minutes for 7 people to drink 25 pints of water.At this rate,how long would it take 15 people to drink 160 pints of w
EastWind [94]

Answer:

14.9 min

Step-by-step explanation:

r=rate

r25=5*7

r25=35

r=35/25

r=1.4

substitution

r160=t*15

t=time

r=1.4

1.4*160=t*15

224=t*15/15

224/15=t

14.9 min

4 0
2 years ago
Find the circumference of the circle. Round your answer to two decimal places if necessary <br> 4cm
ratelena [41]

Answer:

I think its 12.56

Step-by-step explanation:

Multiply 4 and 3.14(thats pi)

7 0
2 years ago
A local sports news network publishes its top 11 High School Football Power Rankings each week after the completion of the most
bogdanovich [222]
Yes, being straight is the greatest
4 0
2 years ago
5 out of 8 bags of m and m's had exactly 32 pieces in them. How many bags out of 40 should have exacty 32 pieces
Andre45 [30]

the answer i think is 64

7 0
2 years ago
Other questions:
  • How many times wider is 2ft than the width of 2in
    10·2 answers
  • A triangle has one angle measuring 3x degrees. A second angle measures 2x + 20 degrees and the third angle measures 4x -20 degre
    12·2 answers
  • you forget the last two digits of your password for a website. A what is the probability that you randomly choose the correct di
    5·1 answer
  • rebecca wants to put 544 pennies in a coin collection book. the blue book fits 9 pennies per page. The red book fits 7 pennies p
    5·2 answers
  • What is the equation of a line in slope intercept form, given that the slope of the line is 1 and a point on
    8·1 answer
  • What is the identity of cos 2 θ
    5·1 answer
  • (05.06 LC)
    12·1 answer
  • Find the trig function indicated. Round your answer to the nearest hundredeths place.
    6·1 answer
  • Does somebody know how to find area of a trapizoid???
    10·2 answers
  • 40 boys and 28 girls stand in a circle, hand in hand, all facing inwards. Exactly 18 boys give their right hand to a girl. How m
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!