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4 years ago

15

Triangle ABC has side lengths 8, 15, and 17. Do the side lengths from a Pythagorean triple? Yes or no?

2 answers:

nasty-shy [4]4 years ago

6 0

Yes, they form a Pythagorean triple.

hjlf4 years ago

5 0

Use the Pythagorean Theorem, substituting 8, 15, and 17 for a, b, and c respectively. Then, simplify to determine whether the equation is true.

$8^2+15^2=17^2$

$64+225=289$

$289=289$

As any number is clearly equal to itself, this statement is true, so 8, 15, and 17 is a valid Pythagorean Triple.

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Given a term in an arithmetic sequence and the common difference, find the first five terms

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Step-by-step explanation:

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3 years ago

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4 years ago

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Are the equations 2x - y = - 4 and 3x + y = -1 dependent, independent or neither

steposvetlana [31]

Answer:

From the above calculations, it is clear that the consistent system has exactly one solution i.e. x = -1, y =2, therefore, it is independent.

Step-by-step explanation:

Given the system of equations

$\begin{bmatrix}2x-y=-4\\ 3x+y=-1\end{bmatrix}$

$\mathrm{Multiply\:}2x-y=-4\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:6x-3y=-12$

$\mathrm{Multiply\:}3x+y=-1\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:6x+2y=-2$

$\begin{bmatrix}6x-3y=-12\\ 6x+2y=-2\end{bmatrix}$

$6x+2y=-2$

$-$

$\underline{6x-3y=-12}$

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so the system of equations becomes

$\begin{bmatrix}6x-3y=-12\\ 5y=10\end{bmatrix}$

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$5y=10$

Divide both sides by 5

$\frac{5y}{5}=\frac{10}{5}$

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Adding 6 to both sides

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Therefore, the solution to the system of equations be:

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From the above calculations, it is clear that the consistent system has exactly one solution i.e. x = -1, y =2, therefore, it is independent.

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3 years ago