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3 years ago

Which expression is equivalent to 27 + 45? 8(3 + 6) 8(19 + 37) 9(3 + 5) 9(18 + 36)

Mathematics

2 answers:

Sladkaya [172]3 years ago

4 0

9(3+5) is equivalent because factoring a 9 out of both 27 and 45 leaves us with 9(3+5).

dlinn [17]3 years ago

3 0

It may be easier to just do the work until you find a result equal to 27+45.
You must do the work inside parentheses first:

8(3+6) = 8(9) = 72 It just happens that this is equal to 72.

8(19+37) = 8(56) This is much greater than 72 and is not the correct answer.

And so on.

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Answer: 6s-3.3

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a. There are 0 or 2 real positive roots for the equation and

b. There are 0 or 2 real negative roots for the equation.

<h3>What is the Descartes'rule of sign?</h3>

Descartes' rule of sign states that

The number of real positive zero of a polynomial f(x) is the number of sign changes of the coefficients of f(x) or an even number less than the number of sign changes of the coefficients of f(x)
The number of real negative zero of a polynomial f(x) is the number of sign changes of the coefficients of f(-x) or an even number less than the number of sign changes of the coefficients of f(-x)

<h3>How to find the number of possible positive and negative roots are there for the equation?</h3>

Given the equation 0 = −8x¹⁰ − 2x⁷ + 8x⁴ − 4x² − 1, writing it as a polynomial function, we have f(x) = −8x¹⁰ − 2x⁷ + 8x⁴ − 4x² − 1

<h3>a. The number of positive roots</h3>

So, to find the number of positive roots, we find the number of sign changes of the polynomial f(x).

So, f(x) = −8x¹⁰ − 2x⁷ + 8x⁴ − 4x² − 1

Since f(x) has coefficients -8, -2, + 8, -4, -1, there are two sign changes from -2 to + 8 and from + 8 to -4.

So, there are 2 or 2 - 2 = 0 real positive roots.

So, there are 0 or 2 real positive roots for the equation.

<h3>b. The number of negative roots</h3>

So, to find the number of negative roots, we find the number of sign changes of the polynomial f(-x).

So, f(-x) = −8(-x)¹⁰ − 2(-x)⁷ + 8(-x)⁴ − 4(-x)² − 1

= −8x¹⁰ + 2x⁷ + 8x⁴ − 4x² − 1

Since f(x) has coefficients -8, +2, + 8, -4, -1, there are two sign changes from -8 to + 2 and from + 8 to -4.

So, there are 2 or 2 - 2 = 0 real negative roots.

So, there are 0 or 2 real negative roots for the equation.

So,

There are 0 or 2 real positive roots for the equation and
There are 0 or 2 real negative roots for the equation.

Learn more about Descartes' rule of sign here:

brainly.com/question/28487633

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1 year ago

Radium-226 is a metal with a half-life of 1600 years. If you start with 1 kilogram of radium-226, how much will remain after 20,

erica [24]

Ending Amount = Beginning Amount / 2^n
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Ending Amount = 1 kg / 2^12.5
Ending Amount = 1 kg / <span> <span> <span> 5,792.6
</span></span></span>Ending Amount = <span> <span> <span> 0.00017263 kilograms = </span></span></span><span>0.17263 grams

</span>

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