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Bess [88]
3 years ago
14

Josh walks 18 dogs each week. Today, he is walking 1/3 of the dogs. How many dogs is he walking today?

Mathematics
1 answer:
Amiraneli [1.4K]3 years ago
4 0
18*(1/3)  (or one third of eighteen) = 6 dogs
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Simplify this expression:<br> i ^257
Katarina [22]
Okay! 
What is i? 
i = <span>√(-1)

What is i^2? 
i^2 = </span>√(-1) * <span>√(-1) 

Note: Whenever you multiply two square roots with the same numbers you get this: 

</span><span>√(a^2)
</span>
Or in this case: 

√(-1 * -1) = -<span>√(1) = -1
</span>
So, 
i^2 = -1

What does i^3 equal? 
i^3 = √(-1) * √(-1) * √(-1) = 1 * √(-1) = <span>√(-1) which is... -i
</span>
What does i^4 equal? 
i^4 = √(-1) * √(-1) * √(-1) * √(-1) =  √(-1 * -1 * -1 * -1) = 1

After that the cycle does it thing and cycles back. 
So, with this information we can figure out what i^157 equals. 

Knowing long division here helps a lot!
Take 157 and divide it by 4 using long division. If you don't know it, I'll show you how to do it to the best of my abilities. (Refer to the picture. If you have any questions about it then ask. Even if the question is... what does this say?) 

After using long division we see that we get: 
39 with a remainder of 1. 

What that means is: 
(i^4)^39 is what we have. The remainder of 1 means that we have 1 i left. So our answer is i. 

The reason we divided by 4 and not some other term is because i^4 = 1, so it is easy to work with. In this case (i^4)^39 still just equals 1. Which leaves our remainder as our answer. 

So once again the final answer is: 
i

As for i^257. I'll show you the answer, but I won't give the work for this one. I'd recommend you try it out for yourself. 

i^257 = (i^4)^64 * i = i.

I hope that I helped, and if you have any further questions then ask away! 


8 0
3 years ago
A geographer found that the land area of Aruba is 75 square miles and the land area of Bermuda is 19 square miles. Based on thes
MakcuM [25]

The interpretation of<em> </em><em>x</em> in the equation 75•x + 19•y = T, used by the geographer, based on the land area of Aruba, 75 m², and Bermuda, 19 m², is the population in a square mile of Aruba

<h3>Which method can be used to find the interpretation of <em>x </em>in the equation?</h3>

The land area of Aruba = 75 m²

Land area of Bermuda = 19 m²

The total number of residents is given in the question by the equation;

75•x + 19•y = T

Therefore;

x = The number of people in a square mile in Aruba

y = The number of people in a square mile in Bermuda

Which gives;

  • The interpretation of the variable, <em>x </em>in the context is the population of Aruba per square mile.

Learn more about variables here:

brainly.com/question/11451813

#SPJ1

6 0
1 year ago
X=6<br> y=2x-3<br><br> i’m doing Solve Systems of Equations by Substitution.
Oksana_A [137]

y=9

Step-by-step explanation:

y=2(6)-3

y=12-3

y=9

4 0
2 years ago
Read 2 more answers
Find the correct linear equation: y is the quotient of thrice a number and ten.
Anarel [89]

Answer:

y = (3x)/10

Step-by-step explanation:

quotient  = divide

7 0
2 years ago
EXPAND:
Sladkaya [172]

Answer:

\displaystyle  A) 5\log( {x}^{}   )  +   2 \log( {y}^{} )

Step-by-step explanation:

we would like to expand the following logarithmic expression:

\displaystyle   \log( {x}^{5}  {y}^{2} )

remember the multiplication logarithmic indentity given by:

\displaystyle \rm  \log( \alpha  \times  \beta ) \iff  \log( \alpha ) +  \log( \beta )

so our given expression should be

\displaystyle   \log( {x}^{5}   )  +    \log( {y}^{2} )

by exponent logarithmic property we acquire:

\displaystyle   5\log( {x}^{}   )  +   2 \log( {y}^{} )

hence, our answer is A

5 0
3 years ago
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