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3 years ago

I need help simplifying both of these. thank you!

Mathematics

1 answer:

4vir4ik [10]3 years ago

5 0

<h3>Answer:</h3>

-100x +100; 3
5x +81; 162

<h3>Step-by-step explanation:</h3>

The distributive property is your friend. It tells you ...

a(b + c) = ab + ac

It can also be used to simplify the product of binomials (or other polynomials).

(a +b)^2 = (a +b)(a +b) = a(a +b) + b(a +b) = a^2 +ab +ab +b^2

(a +b)^2 = a^2 +2ab + b^2 . . . . . . . worth remembering

1. (x -10)^2 -x(x +80) = (x^2 -20x +100) +(-x^2 -80x)

= -100x +100 . . . . . . simplified form

For the purposes of calculation, it can be easier to factor out 100:

= 100 (1 -x)

Then for x = 0.97

= 100(1 -0.97) = 100(0.03) = 3

___

2. (2x +9)^2 -x(4x +31) = (4x^2 +36x +81) -4x^2 -31x = 5x +81

For x = 16.2, this is ...

5(16.2) +81 = 81 +81 = 162

_____

The purpose of the attachment is to show the evaluation is correct.

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Answer:

$\frac{\frac{4}{5}}{\frac{1}{3}+\frac{1}{5}-\frac{3}{5}}=-12$

Step-by-step explanation:

Considering the expression

$\frac{\frac{4}{5}}{\frac{1}{3}+\frac{1}{5}-\frac{3}{5}}$

Solution Steps:

$\frac{\frac{4}{5}}{\frac{1}{3}+\frac{1}{5}-\frac{3}{5}}$

$\mathrm{Combine\:the\:fractions\:}\frac{1}{5}-\frac{3}{5}:\quad -\frac{2}{5}$

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$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{\frac{b}{c}}{a}=\frac{b}{c\:\cdot \:a}$

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$=-\frac{4}{5\cdot \frac{1}{15}}$

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We can set this equal to 0 and factor by using the quadratic formula which is:

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So, let's do just that:

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Note that the 6 goes away if you divide both sides by 6. In this case, a = 1, b = -1, and c = -2. Let's plug that into the quadratic equation:

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So, we can write this as:

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