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Nimfa-mama [501]
3 years ago
5

last night, julie's pet hamster zoe kept julie awake for at least an hour running on her exercise wheel and scratching at the co

rner of her cage. zoe ran on the wheel at lease twice as long as she scratched at the corners of her cage, and she spent more than 1/4 hour running on her wheel. Which system of inequalities represents the time zoe kept juile awake last night if x is the number of hours zoe spent running on her wheel and y is the nu=umber of hours spent scratching her cage

Mathematics
1 answer:
borishaifa [10]3 years ago
6 0

Answer: x+y\geq 1, x>\frac{1}{4} ,  x\geq 2y and y\geq 0

Step-by-step explanation:

Here,  x represents the number of hours Zoe spent running on her wheel and y represents the number of hours spent scratching her cage.

Julie was awoke for at least an hour running on her exercise wheel and scratching the of her cage.

⇒ x+y\geq 1

She ran on her wheel at least twice as long as she scratched at the corners of her cage.

⇒ x\geq 2y

Also, She spent more than 1/4 hour running on her wheel.

⇒ x>\frac{1}{4}

And, we know that number of hours can not be negative.

⇒  y\geq 0

Therefore, the complete system of inequality which shows the given situation is,

x+y\geq 1, x>\frac{1}{4} and x\geq 2y, y\geq 0

Note: the feasible region ( covered by the given system) is shown in the below graph.


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Answer:

Diameter: 14

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Step-by-step explanation:

To find the diameter, you do 43.96 divided by 3.14 and that equals 14

To find the radius, you just divide 14 by 2 and that equals 7.

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3 years ago
No body helped me the last time so I’m posting it again I really need help with this
PIT_PIT [208]
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3 years ago
What term is 1/1024 in the geometric sequence,-1,1/4,-1/6..?
Trava [24]

Answer:

\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}

Step-by-step explanation:

The explicit formula for a geometric sequence:

a_n=a_1r^{n-1}

a_n - n-th term

a_1 - first term

r - common ratio

r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}

We have

a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...

The common ratio:

r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}

<h2>It's not a geometric sequence.</h2>

If a_3=-\dfrac{1}{16} then the common ratio is r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}

Put to the explicit formula:

a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}

Put a_n=\dfrac{1}{1024} and solve for <em>n </em>:

-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1

\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6

5 0
3 years ago
Which equation, when solved, results in a different value of x than the other three?
kicyunya [14]
I would have to say -7(1/8)x-4/3=20.


The first and the second one both result in
-23 5/7

The last one results in -24 8/21

but the third one is -22 3/8.

So your answer is either the third of the last one. I assumed the third because, it is lower than all others and the first two are closer to 24 than they are to 22. It’s your choice on how to judge it.
5 0
2 years ago
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