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]
3 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]3 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
Draw a mapping diagram (1,0) (3,0) (5,4) (7,4) (9,4)​
Anton [14]

Answer:

See attachment

Step-by-step explanation:

In other to draw a mapping diagram for the ordered pairs (1,0) (3,0) (5,4) (7,4) (9,4).

We identify the domain and range:

The domain is the set of the first coordinates of the ordered pairs.

Domain={1,3,5,7,9}

The range is the set of all the second coordinates.

Range: {0,4}

3 0
3 years ago
onah’s sister is 10 years old. Jonah is 8 years younger than twice his sister’s age. Write an expression for Jonah’s age.
Serga [27]

Answer:

Step-by-step explanation:

Jonah sister is 10 years old. Jonah is 8 years younger than twice hos sister age

j = 2s - 8

this is the equation.

You can solve it by substituting in 10 for s, because sister is 10 years old.

5 0
2 years ago
Read 2 more answers
Using the sine rule, calculate the length y. Give your answer to 2 s.f.​
Tpy6a [65]

Answer:

y = 9.84 mm

Step-by-step explanation:

<h2>Sine rule:</h2>

Law of sine:

   \sf \boxed{\bf \dfrac{a}{Sin \ A}=\dfrac{b}{Sin \ B}= \dfrac{c}{Sin \ C}}

    a = y

    A = 31°

   b  = 17 mm

    B = 117°

\sf \dfrac{y}{Sin \ 31^\circ}=\dfrac{17}{Sin \ 117^\circ}\\\\

          \sf y = \dfrac{17}{Sin \ 117^\circ}*Sin \ 31^\circ\\\\  y = \dfrac{17}{0.89}*0.515\\\\y = 9.84 \ mm

8 0
2 years ago
Which equation represents the horizontal line passing through (5, 3)?
Viktor [21]

Step-by-step explanation:

General equation for horizontal line: y = a

Since the point (5, 3) has y-value 3,

the equation of the horizontal line is y = 3.

7 0
2 years ago
The sum of a number and five is seventeen what is the number?​
RoseWind [281]
The number would be 12
4 0
3 years ago
Read 2 more answers
Other questions:
  • Sophia's vegetable garden is is divided into 12 equal sections. She plans carrots in 8 of the sections. Write two factions that
    8·2 answers
  • 24 ten thousands equals
    9·1 answer
  • Katrina paid $24.30 for a backpack that was marked down 10%. Find the original
    14·1 answer
  • Please help quick!!
    13·2 answers
  • There are four hundred twenty-three people attending luncheon. If a table can hold 6 people, how many tables do they need?
    7·1 answer
  • What is half of one inch?
    5·2 answers
  • Math problem. I need help plz.
    14·2 answers
  • Please help I don't understand i'm in the lowest class.
    14·2 answers
  • Ava owns a small business selling clothing. She knows that in the last week 34
    13·1 answer
  • What is the first step in constructing an incenter to triangle xyz?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!