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swat32
3 years ago
9

Express answer in exact form. Show all work for full credit.

Mathematics
1 answer:
Ipatiy [6.2K]3 years ago
6 0

Answer:

Area = 23.38 square"

Step-by-step explanation:

It is given that a regular hexagon is having a side = 3"

Since hexagon is inscribed in a circle therefore all the triangles formed by the radii and the sides of hexagon will be equilateral triangles.

In a hexagon number of triangles formed = 6

Area of an equilateral triangle = 1/4s²√3

By putting the value of s = 3"

Area of one triangle = 1/4×3²√3 = (9√3)/4

and we know number of triangles formed inside the hexagon = 6

Therefore area of hexagon = 6×(9√3)/4 = 23.38 square"

Answer is 23.38 square"

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butalik [34]
We know for the problem that the performer earned $120 at a performance where 8 people attend. We also know that he u<span>ses 43% of the money earned to pay the costs involved in putting on each performance, so we need to find the 43% of $120. To do that, we are going to divide 43% by 100%, and then multiply it by $120:
</span>\frac{43}{100}*120=51.6
Now we know that the performer uses $51.6 of $120 to pay the costs involved in putting on each performance. The only thing left to find his profits is subtract $51.6 from $120:
120-51.6=68.4

We can conclude that the performer makes a profit of $68.4 when 8 people attend his performance.
 
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3 years ago
PLS HELP!!!!What are the sine, cosine and tangent ratios of<br>angle W in the triangle below​
Ksju [112]

Step-by-step explanation:

Remember SOH-CAH-TOA:

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

The side adjacent to W is 4.  The side opposite of W is 3.  The hypotenuse is 5.

Therefore:

Sine = 3 / 5

Cosine = 4 / 5

Tangent = 3 / 4

7 0
3 years ago
What is the value of x?​
Kazeer [188]

Answer:

Step-by-step explanation:

The volume of a sphere is

V=\frac{4}{3}\pi r^3

We are told our volume is 500pi/3, so we fill that in and solve for r:

\frac{500\pi}{3}=\frac{4}{3}\pi r^3

Start by multiplying both sides by 3 over 4 pi:

(\frac{3}{4\pi})\frac{500\pi}{3}=(\frac{3}{4\pi})\frac{4\pi}{3}r^3

Simplifying gives us

125=r^3

Take the cubed root of both sides to get that

r = 5

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3 years ago
PLEASE HELP!! Dee bought 6 dolls and 2 toy trains for $55. At the same prices, Joy bought 4 dolls and 7 toy trains for $65. What
GuDViN [60]

Answer:

The cost of 1 doll   =  $ 7.5

and The  Cost of 1 toy train =   $ 5

Step-by-step explanation:

Let the price of 1 doll  = $ x

The price of  1 toy train  = $ y

Now, according to the question:

6 x + 2 y  = $ 55

and  4 x   + 7 y = $ 65

Solving the given system of equation,

From (1), we get

x= \frac{55 - 2y}{6}

4 ({\frac{55 - 2y}{6}} )  + 7y = 65

or, solving for y , we get

110y - 4y + 21 y = 195

or, 17 y = 85

⇒ y= 85/17 = 5

This implies :  6 x + 2 (5)   =55

or, 6x = 55 - 10 = 45

or, x =  45/ 6 = 15/2

Hence, the cost of 1 doll  = x = $ 7.5

and the Cost of 1 toy train =  y = $ 5

5 0
3 years ago
A quadratic rule for a particular parabola is of the form y = ax^2 + bx. The parabola passes through with the coordinates (-1, 4
Scilla [17]

Answer:

y = (4/7)x² - (24/7)(x)

Step-by-step explanation:

4 = a(-1)² + b(-1)

4 = a - b

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36a + 6b = 0

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a = 4/7

b = -24/7

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6 0
3 years ago
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