hectictar

a)

I don't know what kind of diagram it wants.....but we can calculate the percenteges like this:

We can replace the  %  sign with  / 100

And we can replace the word "of" with *

So.....

Can you finish those?

After you get the answers for these, you might notice the pattern that they are talking about in part b.

.

Yes!

The sum of the measures of all the arcs in a circle is  360°

So... looking at the circle in problem #9....we can make the following equation:

61°   +   (5x - 7)°   +   34°   +   (9x - 22)°   =   360°

                                                                                Remove the degree sign from every term.

61   +   5x - 7   +   34   +   9x - 22   =   360

                                                                                Combine like terms.

14x   +  66   =  360

                                   Subtract  66  from both sides of the equation.

14x   =   294

                                   Divide both sides of the equation by  14

x   =   21

Now that we know what  x  is, we can find the measures of all the arcs.

\(\begin{array}{ccccccc} m\stackrel{\large\frown}{GK}& =& (9x-22)^{\circ}& =&(9(21)-22)^\circ&=&167^\circ\\~\\ m\stackrel{\large\frown}{HJ}& =& (5x-7)^{\circ}& =&(5(21)-7)^\circ&=&98^\circ\\~\\ m\stackrel{\large\frown}{HGJ}& =& m\stackrel{\large\frown}{HG}+m\stackrel{\large\frown}{GK}+m\stackrel{\large\frown}{KJ} & =& 61^\circ+167^\circ+34^\circ&=&262^\circ\\~\\ m\stackrel{\large\frown}{GKJ}&=&m\stackrel{\large\frown}{GK}+m\stackrel{\large\frown}{KJ} &=&167^\circ+34^\circ&=&201^\circ \end{array}\)

To get a number into scientific notation, we want to write it in such a way that the decimal point immediately follows the most significant digit.

In other words, we want to move the decimal point all the way up to right before the most significant (leftmost) digit.

Notice that

4.5  *  10   =   45

So  45  could be expressed as  4.5 * 10

Also...

3.25 * 10 * 10   =   325

So  325  could be expressed as  3.25  *  10²

In the same way.....

1 trillion   =   1 000 000 000 000     =     1  *  10¹²

1 million   =   1 000 000   =   1 * 10^?

Can you fill in the blank? 

Since  Y  is the midpoint of  XZ,  it must be that

the length of  XY   =   the length of  YZ

which means

3a + 1   =   a + 9        Let's solve this equation for a.

                                  Subtract  a  from both sides of the equation.

2a + 1   =   9

                                  Subtract  1  from both sides of the equation.

2a   =   8

                                  Divide both sides of the equation by  2

a   =   4

Now that we know what  a  is,  we can find the length of  XZ.

the length of  XZ   =   3a + 1  +  a + 9

the length of  XZ   =   3(4) + 1  +  4 + 9

the length of  XZ   =   12 + 1  +  4 + 9

the length of  XZ   =   ?

To find the mean, add up all the numbers and divide by the number of numbers in the list.

mean   =   (  5  +  -7  +  12  +  -10  +  15  )  /  5

Just type that into a calculator (such as the one on this website) to get your answer 

_

We are given:

A  =  (4, 1)

B  =  (6, 2)

C  =  (-1, 2)

And we can let:

P  =  (x, y)

By the Pythagorean Theorem/distance formula we can say:

PA²  =   (x - 4)²  +  (y - 1)²

PB²  =   (x - 6)²  +  (y - 2)²

PC²  =   (x + 1)²  +  (y - 2)²

Then....

PA² + PB² + PC²   =   (x - 4)²  +  (y - 1)²   +   (x - 6)²  +  (y - 2)²   +   (x + 1)²  +  (y - 2)²

Expand each term, then combine like terms to get:

PA² + PB² + PC²   =   3x²  -  18x  +  3y²  -  10y  +  62

I don't think so. At least I don't know of any way to delete a post. I think only Admin can delete posts, although moderators can hide posts.