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Anestetic [448]
3 years ago
12

WILL MARK BRANLIEST A graph is shown below: Dotted line joining negative 1, negative 2 and 5,0 and the region above the line is

shaded. Which of the following inequalities is best represented by this graph? x − 3y > 5 x − 3y < 5 x − 2y > 5 x − 2y < 5
Mathematics
1 answer:
s2008m [1.1K]3 years ago
4 0
Hello there!

<span>A graph is shown below: Dotted line joining negative 1, negative 2 and 5,0 and the region above the line is shaded. Which of the following inequalities is best represented by this graph? x − 3y > 5 x − 3y < 5 x − 2y > 5 x − 2y < 5

Answer: 
</span><span>x – 3y < 5</span>
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42

Step-by-step explanation:

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HEEEELPPPPPPPPP Which properties describe the graph of (x + 5)2 + (y – 10)2 &lt; 169?
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The perimeter of equilateral triangle ABC is 81/3 centimeters, find the length of the radius and apothem.
MAXImum [283]

There is a typo error, the perimeter of equilateral triangle ABC is 81/√3 centimeters.

Answer:

Radius = OB= 27 cm

Apothem = 13.5 cm

A diagram is attached for reference.

Step-by-step explanation:

Given,

The perimeter of equilateral triangle ABC is 81/√3 centimeters.

Substituting this in the formula of perimeter of equilateral triangle =3\times\ side

3\times\ side =[tex]81\sqrt{3}

Side = \frac{81\sqrt{3} }{3} =27\sqrt{3} \ cm

Thus from the diagram , Side AB=BC=AC= 27\sqrt{3} \ cm

We know each angle of an equilateral triangle is 60°.

From the diagram, OB is an angle bisector.

Thus \angle OBC = 30°

Apothem is the line segment from the mid point of any side to the center the equilateral triangle.

Therefore considering ΔOBE, and applying tan function.

tan\theta =\frac{perpendicular}{base} \\tan\theta=\frac{OE}{BE} \\tan\theta=\frac{OE}{\frac{27\sqrt{3}}{2}  } \\tan30\times {\frac{27\sqrt{3} }{2} }= OE\\\frac{1}{\sqrt{3} } \times\frac{27\sqrt{3} }{2} =OE\\

Thus ,apothem  OE= 13.5 cm

Now for radius,

We consider ΔOBE

cos\theta=\frac{base}{hypotenuse} \\cos30= \frac{BE}{OB} \\Cos30 = \frac{\frac{27\sqrt{3} }{2}}{OB}  \\OB= \frac{\frac{27\sqrt{3} }{2}}{cos30} \\OB= \frac{\frac{27\sqrt{3} }{2}}{\frac{\sqrt{3} }{2} } \\OB =27 \ cm

Thus for

Perimeter of equilateral triangle ABC is 81/√3 centimeters,

The radius of equilateral triangle ABC is 27 cm

The apothem of equilateral triangle ABC is 13.5 cm

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Step-by-step explanation:

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