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stich3 [128]
4 years ago
9

Find the equation for each problem.

Mathematics
1 answer:
IRINA_888 [86]4 years ago
4 0

Answer:

-2, 3

Step-by-step explanation:

slope=-4

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The longest side in the triangle is opposite to the largest angle of this triangle. If triangle is acute, then all angles are acute. Acute angle has cosine that is positive.

Use cosine theorem to determine the cosine of the largest angle:

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Then

225=x^2+4x^2-4x^2\cos \alpha,\\ \\\cos \alpha=\dfrac{225-5x^2}{-4x^2}=\dfrac{5x^2-225}{4x^2}.

Since \cos \alpha>0, then

\dfrac{5x^2-225}{4x^2}>0\Rightarrow 5x^2-225>0.

Divide this inequality by 5:

x^2-45>0,\\ \\(x-3\sqrt{5})(x+3\sqrt{5})>0,\\ \\x\in (-\infty,-3\sqrt{5})\cup (3\sqrt{5},\infty).

Note that 3\sqrt{5}\approx 6.71, then the smallest possible whole-number value of x is 7.

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3 years ago
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Answer:

Always

Step-by-step explanation:

Some people might mistaken it for sometimes, but the part that makes it always is when it says "regular" hexagons.

Similarity is defined by having congruent angles and proportional sides. Regular hexagons will always have internal angles of 60°, meaning that any two regular hexagons will always be similar.

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