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Ira Lisetskai [31]
2 years ago
10

A student concludes that for all values of x,x^2+x+1 produces a prime number. Which value of x serves as counterexample to prove

this conclusion false?

Mathematics
1 answer:
Dafna11 [192]2 years ago
5 0

Answer:

j

Step-by-step explanation:

Substitute the given values into x² + x + 1 and check if result is prime

x = - 4

(- 4)² - 4 + 1 = 16 - 4 + 1 = 13 ← prime

(- 2)² - 2 + 1 = 4 - 2 + 1 = 3 ← prime

(- 3)² - 3 + 1 = 9 - 3 + 1 = 7 ← prime

4² + 4 + 1 = 16 + 4 + 1 = 21 ← not prime

x = 4 serves as a counterexample to disprove this conclusion

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jeyben [28]

An expression is defined as a set of numbers, variables, and mathematical operations. The value of the expression (√2)π/(√5) is 2.

<h3>What is an Expression?</h3>

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The value of the expression (√2)π/(√5) can be written as,

\dfrac{\sqrt2 \pi}{\sqrt5}\\\\= \sqrt{\dfrac25}\pi\\\\=\sqrt{0.4} \times \pi\\\\

= 0.6324 × π

= 1.9869 ≈ 2

Hence, The value of the expression (√2)π/(√5) is 2.

Learn more about Expression:

brainly.com/question/13947055

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Now solve for x

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The ratio of fiction to nonfiction books in a classroom library is 2 to 3 . If there are 24 books nonfiction books in the classr
worty [1.4K]

Answer:

<h2>16</h2>

Step-by-step explanation:

Given the ratio of fiction to nonfiction books in a classroom library is 2 to 3, then the total ratio of both books will be 2+3 = 5. If there are 24 books non fiction books in the library, to get the amount of fictionbooks that are there we will follow the following steps.

First we will calculate the total number of books in the shelf;

3/5 * Total number of books = total non fiction books

3/5 * Total number of books = 24

3*Total number of books = 5*24

3*Total number of books = 120

Total number of books = 120/3

Total number of books = 40

Therefore there are 40 total of books on the shelf.

Total number of fiction books = 2/5 * 40

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Total number of fiction books = 16 books

<em>Hence there are 16 fiction books on the shelf.</em>

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Answer:

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Step-by-step explanation:

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