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Answered.  

You are just putting up your homework and asking people to do it for you.

This is certainly not encouraged.

Since you have asked more than one question on each of your posts, and you have made numerous posts in the past few hours, your questions have been blanked out.

Make one post.  Ask one question on that post.

If you have ideas of your own then say what you have tried or what you have thought about.

Wait for an answer.

Learn from the answer ...  interact with the answerer  ...  Say thanks, give points, etc.

If you do not understand ask for clarification.

If you think it is wrong then politely say so but also say why you believe it to be wrong.

Then, try answering other similar questions on you own.

https://web2.0calc.com/questions/prime-sum

The sum of all x that work is 540 degrees.

Answer: \(22.5\pi + 30\), or rounded as \(\approx 100.686\)

Solution:

Pretend that the shaded region is a full circle with radius of 15. The circumference of that circle would be \(2\pi r\), or since r = 15, \(30\pi\).

Because a circle has 360 degrees, and there is 90 degrees being taken out of it, one quarter of the circle has been 'unshaded'. So you have to take away 1/4 of the \(30\pi\), which just leaves \(\frac 3 4 \cdot 30\pi\) which equals \(22.5\pi\) left. There is still one thing left. When one quarter of the circle was taken away, OQ and OP were left exposed as perimeter, which means you have to add 15 x 2 = 30 to the answer. This leads to the final answer being \(22.5\pi + 30\), or rounded as \(\approx 100.686\).

Simply use factorials.

4! = 4*3*2*1

= 12*2*1

=24

So, there are 24 ways to distribute.

By the Euclidean Algorithm, the sum of all the possible values of h(x) is 16.

x+y = 15       y = 15 -x

10y + x  = 27 + 10x + y       sub in red equation for y

10(15-x) + x = 27 + 10x + 15-x

150-10x+x     = 27 +10x+15-x

108 = 18x       x = 6     then y =9

Here is a Venn diagram:     Looks like 11    ( as P4 found ! ) 

Straightforward:   1950 boxes / 30 days = 65 boxes/day

would it not just be 26-3-7-5

=11

oh oops wow i mess that up lol

nice solution!!

28 m x 3.2808 ft/m *  2.75 dollars/ft =        (28* 3.2802)* 2.75   dollars =___________ dollars

ohhhhhhh oops lol

from 9 to -84   is  27 more of the common diference , d , of the sequence

(-84 - 9 )/27 =  -93/27 = -31 / 9

from 5 th tem to 23 is addition of 18  d's

  9 + 18 ( -31/9) = -53

you can't always jump to conclusions like that just by looking at the graph. :)

anyway

the distance from the graph to the origin can be represented like this (by the Pythagorean theorem):

\(\sqrt{x^2+(\frac{1}{\sqrt{2}}(x^2-3))^2}\\=\sqrt{x^2+\frac{(x^2-3)^2}{2}}\\= \sqrt{x^2+\frac{x^4-6x^2+9}{2}}\\=\sqrt{\frac{x^4-4x^2+9}{2}}\\ =\sqrt{\frac{x^4-4x^2+4+9-4}{2}}\\=\sqrt{\frac{(x^2-2)^2+5}{2}}\)

Since \((x^2-2)^2\) will always be nonnegative for real numbers, the best you can do to minimize it is to set it equal to 0, and you will obtain your final answer:

\(\sqrt{\frac{0+5}{2}}=\boxed{\sqrt{\frac{5}{2}}}\)

for completeness, if you want to know the x value for which this minimum distance occurs, you can just solve an equation:

\((x^2-2)^2=0\\x^2-2=0\\x=\pm\sqrt{2}\)

1. The smallest possible area of triangle OAB is 60.

2. The minimum value of f(1) is 88.

If the first term is x, second is x + y, and so on,

The fifth term would be \(x + 4y = 9\) and 32nd would be \(x + 31y = -84\). Subtract and solve for x and y,

\(x + 4y = 9 \\ x+ 31y = -84 \\ 27y = -93 \\ y = -\frac{31}{9} \\ x + 4(-\frac{31}{9})=9 \\ x - 13 \frac{7}{9} = 9 \\ x = 22 \frac{7}{9}\)

Equation for 23nd term would be \(x + 22y\).

\(22 \frac{7}{9} + 4(-\frac{31}{9}) \\ 22 \frac{7}{9} + - 13\frac{7}{9} = 9\)

So the 23rd term is 9.

Multiply all 4 equations together,

\(m^3a^3t^3h^3= 27 \\ math=3\)

Divide by each equation,

\(h = 24 \\ t = \frac{3}{32} \\ a = 9 \\ m = \frac{4}{27}\)

Equation: y = -3x + 91
\(91 + 17 = 108 \\ 108 / 3 = 36 \\ y = -3(36) + 91 = -108 + 91 = -17\)

So 35 terms will come before -17 appers.

Similar problem: https://web2.0calc.com/questions/trapezoid-amp-circle

For the 1st one I was looking for the 50th term not the 15th sorry, but thanks anyways! 

(2) Sorry I don't know why the numbers did not work.

The pages of a book are numbered 1 through n. When the page numbers of the book were added, one of the page numbers was mistakenly added twice, resulting in an incorrect sum of 1986. What was the number of the page that was added twice?

Equation of line,

\(y = 2x + b\)

Plugging in (8, 0),

\(0 = 2(8) + b \\ 0 = 16 + b \\ b = -16\)

So the y-intercept has y-coordinate -16, so it is at point, (0, -16)

If we graph it on desmos, just to get a visual,

We can see that the x intercepts are the closest point. Plugging in y = 0,

\(0=\frac{1}{\sqrt{2}}\left(x^{2}-3\right) \\ \frac{x^2}{\sqrt{2}} - \frac{3}{\sqrt{2}} = 0 \\ x^2 - 3 = 0 \\ x^2 = 3 \\ x = \pm\sqrt{3}\)

So the smallest distance is $\sqrt{3}$