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3 years ago

Choose all of the sums that are RATIONAL.

Mathematics

1 answer:

S_A_V [24]3 years ago

6 0

Answers:

Rational
Rational
Rational
Irrational
Rational
Irrational

In short, 4 and 6 are irrational. Everything else is rational.

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Explanation:

A rational number is one in the form p/q where p,q are integers and q is nonzero. In the case of something like 3/5, we have p = 3 and q = 5.

Any terminating decimal can be converted to a rational number. Eg: 0.125 = 125/1000.

Any whole number is a rational number. Eg: 5 = 5/1.

Adding any two rational numbers leads to some other rational number.

Based on what is mentioned above so far, this means choices 1 through 3 are rational sums.

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Choice 4 is not rational because sqrt(2) is irrational. The rule is

irrational+rational = irrational

Choice 5 is a rational sum because sqrt(4) = 2 = 2/1

Choice 6 is irrational for similar reasons as choice 4. Here pi = 3.14... is irrational.

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3 years ago

If the square of a number is added to 8 times the number, the result is 100.

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$\huge \boxed{\mathbb{QUESTION} \downarrow}$

If the square of a number is added to 8 times the number, the result is 100. Find x.

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

Let's take the number as 'x'.

Square of x = x²
8 times x = 8x

We are given that, 8x + x² = 100

Now, let's solve for x.

__________________

$8 x + x ^ { 2 } = 100$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x²+bx=c.

$x^{2}+8x=100$

Divide 8, the coefficient of the x term, by 2 to get 4. Then add the square of 4 to both sides of the equation. This step makes the left-hand side of the equation a perfect square.

$x^{2}+8x+4^{2}=100+4^{2}$