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3 years ago

The expression 12x+15x-11x can be combined because of which property

Mathematics

2 answers:

Kazeer [188]3 years ago

7 0

The answer would be A. Commutative property of addition

Lisa [10]3 years ago

7 0

Answer:

Option A.

Step-by-step explanation:

Commutative property of addition says that if we add two or many numbers, order doesn't matter.

Let there are three numbers a, b, and c.

When we add them by commutative property, result will remain same.

If we add [(a + b)+ c] or [a + (b + c)], result will be same.

Therefore, 12x + 15x - 11x = (12 + 15 - 11)x

= (27 - 11)x

= 16x

Option A. Commutative property will be the answer.

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Could someplease explain the whole problem? For the first part my the answer I got was x= .618, -.618, and <img src="https://tex

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Answer:

a) x = (√5 -1)/2 ≈ 0.618034

b) 1/x = (√5 +1)/2 ≈ 1.618034

Step-by-step explanation:

Given:

x/(1 -x) = 1/x

Find:

Exactly, and as a decimal approximation, ...

a) x, using the quadratic formula

b) 1/x

Solution:

a) We can multiply the given equation by x(1 -x) to obtain ...

x² = 1 -x

x² +x -1 = 0 . . . . . . add x-1

The coefficients for use in the quadratic formula are a=1, b=1, c=-1. The solution using the quadratic formula is ...

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-1\pm\sqrt{1^2-4\cdot1\cdot(-1)}}{2\cdot1}=\dfrac{-1\pm\sqrt{5}}{2}$

We are only interested in the positive solution, which is ...

$\boxed{x=\dfrac{\sqrt{5}-1}{2}\approx0.618034}$

b) The quadratic we developed in the first part can be rearranged like this:

x² +x = 1 . . . . . . add 1 to both sides

x(x +1) = 1 . . . . . factor out x

x +1 = 1/x . . . . . .divide by x

Then to find the value of 1/x, we simply need to add 1 to the value of x we have:

$\dfrac{1}{x}=\dfrac{\sqrt{5}-1}{2}+1=\dfrac{\sqrt{5}-1}{2}+\dfrac{2}{2}=\dfrac{\sqrt{5}-1+2}{2}\\\\\boxed{\dfrac{1}{x}=\dfrac{\sqrt{5}+1}{2}\approx1.618034}$

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