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3 years ago

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people are waiting on line for a theater premiere. every 5th person in line will receive a free theater ticket. every 6th person

will recie be a gift card for 40.00. which person is the first person to receive both prizes?

2 answers:

torisob [31]3 years ago

8 0

The line has 'n' number of people. the question says that every 5th person will earn a free ticket while the 6th person will earn a gift card. you must find a appropriate and lowest common factor between the numbers.
the answer is the 30.

oksano4ka [1.4K]3 years ago

4 0

The 30th person will

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Simplify.<br><br> 2x5 - 6x2 + 4x4y<br> -------------------------<br> 2x

Ede4ka [16]

We have the rational expression $\frac{2x^{5}-6x^{2}+4x4y}{2x}$ ; to simplify it, we are going to try to find a common factor in the numerator, and, if we are luckily, that common factor will get rid of the denominator $2x$ .
Notice that in the denominator all the numbers are divisible by two, so 2 is part of our common factor; also, all the terms have the variable $x$ , and the least exponent of that variable is 1, so $x$ will be the other part of our common factor. Lets put the two parts of our common factor together to get $2x$ .
Now that we have our common factor, we can rewrite our numerator as follows:
$\frac{2x(x^{5}-6x+2(2y)}{2x}$
We are luckily, we have $2x$ in both numerator and denominator, so we can cancel those out:
$x^{5}-6x+2(2y)$
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We can conclude that the simplified version of our rational function is $x^{5}-6x+4y$ .

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3 years ago

In a survey of 100 people, 39 preferred ketchup on their hot dogs. What percent did not

Elena-2011 [213]

Answer:

C. 61%

Step-by-step explanation:

out of 100 people, 39 liked ketchup while 61 did not. The ratio and percentage is 61%

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3 years ago

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Point P is located at (−2, 7), and point R is located at (1, 0). Find the y value for the point Q that is located two over three

otez555 [7]

Answer:

$y_Q=\dfrac{21}{5}=4.2$

Step-by-step explanation:

If the point Q that is located two over three the distance from point P to point R, then PQ:QR=2:3.

Use formula to find the coordinates of the point Q:

$x_Q=\dfrac{3x_P+2x_R}{3+2}\\ \\y_Q=\dfrac{3y_P+2y_R}{3+2}$

In your case, P(-2,7) and R(1,0), then

$x_Q=\dfrac{3\cdot (-2)+2\cdot 1}{3+2}=\dfrac{-4}{5}\\ \\y_Q=\dfrac{3\cdot 7+2\cdot 0}{3+2}=\dfrac{21}{5}$

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3 years ago

beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle

Wittaler [7]

Answer:

Step-by-step segment dc bisects segment ab, then point d is equidistant from points a and b because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects. if segment dc bisects segment ab, then point d is equidistant from points a and b because congruent parts of congruent triangles are congruent. if segment ad bisects segment ab, then point d is equidistant from points a and b because a point on a perpendicular bisector is equidistant from:

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2 years ago

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Can somebody explain how these would be done? The selected answer is incorrect, and I was told "Nice try...express the product b

trapecia [35]

Answer:

Solution ( Second Attachment ) : - 2.017 + 0.656i

Solution ( First Attachment ) : 16.140 - 5.244i

Step-by-step explanation:

Second Attachment : The quotient of the two expressions would be the following,

$6\left[\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi \:}{5}\right)\right]$ ÷ $2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right]$

So if we want to determine this expression in standard complex form, we can first convert it into trigonometric form, then apply trivial identities. Either that, or we can straight away apply the following identities and substitute,

( 1 ) cos(x) = sin(π / 2 - x)

( 2 ) sin(x) = cos(π / 2 - x)

If cos(x) = sin(π / 2 - x), then cos(2π / 5) = sin(π / 2 - 2π / 5) = sin(π / 10). Respectively sin(2π / 5) = cos(π / 2 - 2π / 5) = cos(π / 10). Let's simplify sin(π / 10) and cos(π / 10) with two more identities,

( 1 ) $\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos \left(x\right)}{2}}$

( 2 ) $\sin \left(\frac{x}{2}\right)=\sqrt{\frac{1-\cos \left(x\right)}{2}}$

These two identities makes sin(π / 10) = $\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}$ , and cos(π / 10) = $\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}$ .

Therefore cos(2π / 5) = $\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}$ , and sin(2π / 5) = $\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}$ . Substitute,

$6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right]$ ÷ $2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right]$

Remember that cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting those values,

$6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right]$ ÷ $2\sqrt{2}\left[0-i\right]$

And now simplify this expression to receive our answer,

$6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right]$ ÷ $2\sqrt{2}\left[0-i\right]$ = $-\frac{3\sqrt{5+\sqrt{5}}}{4}+\frac{3\sqrt{3-\sqrt{5}}}{4}i$ ,

$-\frac{3\sqrt{5+\sqrt{5}}}{4}$ = $-2.01749\dots$ and $\:\frac{3\sqrt{3-\sqrt{5}}}{4}$ = $0.65552\dots$

= $-2.01749+0.65552i$

As you can see our solution is option c. - 2.01749 was rounded to - 2.017, and 0.65552 was rounded to 0.656.

________________________________________

First Attachment : We know from the previous problem that cos(2π / 5) = $\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}$ , sin(2π / 5) = $\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}$ , cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting we receive a simplified expression,

$6\sqrt{5+\sqrt{5}}-6i\sqrt{3-\sqrt{5}}$

We know that $6\sqrt{5+\sqrt{5}} = 16.13996\dots$ and $-\:6\sqrt{3-\sqrt{5}} = -5.24419\dots$ . Therefore,

Solution : $16.13996 - 5.24419i$

Which rounds to about option b.

7 0

3 years ago