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IrinaK [193]
2 years ago
9

A regular hexagon rotates counterclockwise around its center. It turns through angles greater than 0° and less or equal to 360°.

At how many different angles of a hexagon map onto itself?
Mathematics
1 answer:
Sonja [21]2 years ago
6 0

there are 6 sides to a hexagon

360/6 = 60 degrees

 so it will map onto itself at 60, 120, 180, 240, 300 & 360

 there are 6 different angles



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Carlie runs two different business. She needs to pay $100 for materials, and pay her associates $12 per hour for her childcare b
V125BC [204]

Answer:

C(x) = 100 + 12x

L(x) = 275 + 10x

Step-by-step explanation:

Let x = no. of hours

C(x) = 100 + 12x

L(x) = 275 + 10x

8 0
2 years ago
A sample of tritium-3 decayed to 94.5% of its original amount after a year.
Zolol [24]
(a) If y(t) is the mass after t days and y(0) = A then y(t) = Ae^{kt}.

y(1) = Ae^k = 0.945A \implies e^k = 0.945 \implies k = \ln 0.945

\text{Then } Ae^{(\ln 0.945)t} = \frac{1}{2}A\ \Leftrightarrow\ \ln e^{(\ln 0.945)t} = \ln \frac{1}{2}\ \Leftrightarrow\  ( \ln 0.945) t = \ln \frac{1}{2} \Leftrightarrow \\ \\
t = - \frac{\ln 5}{\ln 0.945} \approx 12.25 \text{ years}

(b)
Ae^{(\ln 0.945) t} = 0.20 A \ \Leftrightarrow\ (\ln 0.945) t \ln \frac{1}{5}\ \implies \\ \\
t = - \frac{\ln 5}{\ln 0.945} \approx 28.45\text{ years}
3 0
2 years ago
Rewrite in simplest radical form! Show your work.
vazorg [7]

x^{\frac{1}{\frac{-3}{6} }}

First, let's deal with the fraction in the denominator of the exponent. Multiply the top and bottom of the exponent by 6.

x^{\frac{6}{-3} }

Now that the fraction in the denominator is taken care of, we can reduce the denominator.

x^{-2}. Some professors might accept this as simplest form, but others might ask you to get rid of the negative.

x^{-2} = \frac{1}{x^{2} }

7 0
2 years ago
Read 2 more answers
The total cost of a shirt and a tie was $75.62. if the price of the shirt was $4.02 less than the tie, what was the price of the
kifflom [539]
--------------------------------------------
Define x:
--------------------------------------------
Let the tie be x
Tie = x
Shirt = x - 4.02

--------------------------------------------
Construct equation :
 --------------------------------------------
The sum of the shirt and tie is $75.62
x + x -4.02 = 75.62
2x - 4.02 = 75.62
2x = 79.64
x = $39.82

--------------------------------------------
Find the cost of tie and shirt :
--------------------------------------------
Tie = x = $39.82
Shirt = x - $4.02 = $39.82 - $4.02 = $35.80

----------------------------------------------------------------------------------------
Answer: The price of the short is $35.80
----------------------------------------------------------------------------------------
5 0
2 years ago
The initial temperature of a cup of tea is 200ºF. The surrounding temperature is 70ºF, and the value of the constant k is 0.6.
Nezavi [6.7K]

Newton's Law of Cooling states that the change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature over time.

Therefore when expressed mathematically, this is equivalent to:

dT = - k (T – Ts) dt

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Integrating:

ln [(T2– Ts) / (T1– Ts)] = - k (t2 – t1)

Before we plug in the values, let us first convert the temperatures into absolute values R (rankine) by adding 460.

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ln [(T2– 530) / (660 – 530)] = - 0.6 (2 - 0)

T2 = 569.16 R

T2 = 109 ºF

Answer: After 2 hours, it will be 109 ºF

6 0
2 years ago
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