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1 year ago

Is the expression below a perfect square trinomial or the difference of two squares?

Mathematics

1 answer:

DanielleElmas [232]1 year ago

7 0

The expression shown below is a difference of two squares.

<h3>Is a given expression a perfect square trinomial or a difference of two squares?</h3>

In this problem we have an algebraic expression that has to be checked by algebraic procedures. The complete procedure is shown below:

(x² + 8 · x + 16) · (x² - 8 · x + 16) Given

(x + 4)² · (x - 4)² Perfect square trinomial

[(x + 4) · (x - 4)] · [(x + 4) · (x - 4)] Definition of power / Associative and commutative property

(x² - 16)² Difference of squares / Definition of power / Result

The expression shown below is a difference of two squares.

To learn more on differences of squares: brainly.com/question/11801811

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Answer:

A. The length of the third side is approximately 5 feet.

B. A = $88^{o}$ , B = $60^{o}$ and C = $32^{o}$ .

Step-by-step explanation:

Let the triangle be ABC. Given two sides and an included angle, let us apply the cosine rule to determine the third length.

A. Let side a = 6 feet and c = 3 feet, thus;

$b^{2}$ = $a^{2}$ + $c^{2}$ - 2ac Cos B

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B. Given that B = $60^{o}$ , then let us apply the Sine rule to determined the measure of A.

$\frac{a}{SinA}$ = $\frac{b}{SinB}$

So that,

$\frac{6}{Sin A}$ = $\frac{5.2}{Sin60^{o} }$

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Since the sum of angle in a triangle = $180^{o}$ .

Then,

A + B + C = $180^{o}$

$88^{o}$ + $60^{o}$ + C = $180^{o}$

$148^{o}$ + C = $180^{o}$

C = $180^{o}$ - $148^{o}$

= $32^{o}$

C = $32^{o}$

Thus,

A = $88^{o}$ , B = $60^{o}$ and C = $32^{o}$ .

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