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3 years ago

Classify each number as rational or irrational

Mathematics

2 answers:

padilas [110]3 years ago

5 0

1. R
2. Ir
3. R
4. R
5. R
6. Ir
7. R
8. Ir

Keith_Richards [23]3 years ago

4 0

11/3....this is rational because it is a fraction
sqrt 48.....irrrational because it cant be made into a fraction
6.25....rational
0.01045....if this terminates(ends), it is rational
sqrt 16/81....rational because it equals 4/9
sqrt 3/16....irrational
0.42...rational
16pi....irrational

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Step-by-step explanation:

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A bottle of nail Polish holds 0.8 ounce, A bottle of perfume holds 0.45. How many more of nail Polish hold?

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When solving for x, what is x squared plus 15 equals -8x

VLD [36.1K]

Answer:

x = - 5, x = - 3

Step-by-step explanation:

Given

x² + 15 = - 8x ( add 8x to both sides )

x² + 8x + 15 = 0 ← in standard form

Consider the factors of the constant term (+ 15) which sum to give the coefficient of the x- term (+ 8)

The factors are 5 and 3, since

5 × 3 = 15 and 5 + 3= 8, thus

(x + 5)(x + 3) = 0 ← in factored form

Equate each factor to zero and solve for x

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3 years ago

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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3 years ago

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ira [324]

Answer:

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