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3 years ago

Please help :) find the area of the regular polygon

Mathematics

1 answer:

viva [34]3 years ago

8 0

9514 1404 393

Answer:

3√3 square units

Step-by-step explanation:

The area of a regular n-sided polygon with radius r is given by the formula ...

A = (n/2)r²·sin(360°/n)

For n=3 and r=2, the area is ...

A = (3/2)(2²)·sin(360°/3) = 6·sin(120°) = 6(√3/2)

A = 3√3 . . . . square units

_____

<em>Alternate solution</em>

The center of this polygon is the centroid, which divides each median into parts with the ratio 2:1. This means the given radius is 2/3 of the height of the triangle. The base of the triangle is 2/√3 times the height, so is ...

b = (2/√3)(3) = 2√3

The area using these dimensions is calculated as ...

A = 1/2bh

A = 1/2(2√3)(3) = 3√3 . . . . square units

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Determine whether each expression is equivalent to 49^2t – 0.5.

vampirchik [111]

Answer:

None of the expression are equivalent to $49^{(2t - 0.5)}$

Step-by-step explanation:

Given

$49^{(2t - 0.5)}$

Required

Find its equivalents

We start by expanding the given expression

$49^{(2t - 0.5)}$

Expand 49

$(7^2)^{(2t - 0.5)}$

$7^2^{(2t - 0.5)}$

Using laws of indices: $(a^m)^n = a^{mn}$

$7^{(2*2t - 2*0.5)}$

$7^{(4t - 1)}$

This implies that; each of the following options A,B and C must be equivalent to $49^{(2t - 0.5)}$ or alternatively, $7^{(4t - 1)}$

A. $\frac{7^{2t}}{49^{0.5}}$

Using law of indices which states;

$a^{mn} = (a^m)^n$

Applying this law to the numerator; we have

$\frac{(7^{2})^{t}}{49^{0.5}}$

Expand expression in bracket

$\frac{(7 * 7)^{t}}{49^{0.5}}$

$\frac{49^{t}}{49^{0.5}}$

Also; Using law of indices which states;

$\frac{a^{m}}{a^n} = a^{m-n}$

$\frac{49^{t}}{49^{0.5}}$ becomes

$49^{t-0.5}}$

This is not equivalent to $49^{(2t - 0.5)}$

B. $\frac{49^{2t}}{7^{0.5}}$

Expand numerator

$\frac{(7*7)^{2t}}{7^{0.5}}$

$\frac{(7^2)^{2t}}{7^{0.5}}$

Using law of indices which states;

$(a^m)^n = a^{mn}$

Applying this law to the numerator; we have

$\frac{7^{2*2t}}{7^{0.5}}$

$\frac{7^{4t}}{7^{0.5}}$

Also; Using law of indices which states;

$\frac{a^{m}}{a^n} = a^{m-n}$

$\frac{7^{4t}}{7^{0.5}}$ = $7^{4t - 0.5}$

This is also not equivalent to $49^{(2t - 0.5)}$

C. $7^{2t}\ *\ 49^{0.5}$

$7^{2t}\ *\ (7^2)^{0.5}$

$7^{2t}\ *\ 7^{2*0.5}$

$7^{2t}\ *\ 7^{1}$

Using law of indices which states;

$a^m*a^n = a^{m+n}$

$7^{2t+ 1}$

This is also not equivalent to $49^{(2t - 0.5)}$

6 0

3 years ago

You would like to join a fitness center. Fit-N-Trim charges $80 per month. Fit-For-Life charges a one tim e membership fee of $7

Y_Kistochka [10]

I don't do good with slope intercept, but I can tell you that Fit n Trim would be $80m and Fit for Life would be $75+55m.

6 0

2 years ago

The function f(x) is given by the set of ordered pairs. {(1,0), (–10,2), (0,6), (3,17), (–2,–1)} Which equation is true? f of ne

Rudik [331]

Answer:

f(0)=6

Step-by-step explanation:

When representing function's values by set of ordered pairs, the first one correspond to the x value and the second to the image or "y" value.

When you read f(0) means "when x is 0" then the 6 is the value of the function or the image.

7 0

3 years ago

Read 2 more answers

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ELEN [110]

Answer:

90°

Step-by-step explanation:

Thales Theorem

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2 years ago

Select the description that is true of the equation y=-5x+5 .

gladu [14]

In y = mx + b form, the slope is in the m position and the y intercept is in the b position.

y = (m)x + (b)
y = -5 x + 5.....slope (m position) = -5....y int (b position) = 5

3 0

3 years ago