Identify which of the following statement(s) is always true?

Mathematics

1 answer:

julia-pushkina [17]3 years ago

8 0

Answer:

Statement 3

Step-by-step explanation:

Statement 1: For any positive integer n, the square root of n is irrational.

Suppose n = 25 (25 is positive integer), then

$\sqrt{n}=\sqrt{25}=5$

Since 5 is rational number, this statement is false.

Statement 2: If n is a positive integer, the square root of n is rational.

Suppose n = 8 (8 is positive integer), then

$\sqrt{n}=\sqrt{8}=2\sqrt{2}$

Since $2\sqrt{2}$ is irrational number, this statement is false.

Statement 3: If n is a positive integer, the square root of n is rational if and only if n is a perfect square.

If n is a positive integer and square root of n is rational, then n is a perfect square.

If n is a positive integer and n is a perfect square, then square root of n is a rational number.

This statement is true.

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3 years ago

Find the value of x to the nearest tenth. a. 11.3 b. 12.5 c. 12.9 d. 13.1

Scorpion4ik [409]

Answer:

Step-by-step explanation:

We have perpendicular bisector through a chord of the circle. We know the length, so either side of the chord is 11 due to the bisector cutting it directly in half. Since the radius is a fixed distance from the center to any point on the edge of the circle, we can draw the radius x from the circle to the end of the chord to form a right triangle.

We can use Pythagorean Theorem $a^{2} +b^{2} =c^{2}$ to find the missing side length x. a=6, b=11 and c=x.