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Thank you so much LuckyDucky! Really appreciate it! 

THANK YOU AGAIN CPHILL!  UR THE BEST!

Well.....two great minds couldn't be wrong  ( could we  ???  )

LOL!!!!

Yep I just did the question myself and I reached the same answer as CPhill

Here to help

:D

My ¢LORD that would be intriguing

Amount financed  =  cost of car - down payment =  11578 - 4100   = 7478

Amt repaid  = monthly payment x months  = 251.34 x 36   =  9048.24

Finance charge =  amt repaid - amt financed  = 9048.24 - 7478  = 1570.24

Cost of car =  down payment  + amt repaid =  4100 + 9048.24  = 13,148.24

z  = -3 + 3i

To find the value of r:  r  =  sqrt( (-3)² + (3)² )  =  sqrt( 9 + 9 )  =  sqrt(18)  =  3sqrt(2)

To find the angle:  tan^-1( 3 / -3 )  =  tan^-1( -1 )  =  3pi / 4       [remember that it is in the second quadrant]

3sqrt(2) cis( 3pi/4)    

To find the three cube roots of  -2 - 2i

find the radius:  sqrt( (-2)² + (-2)² )  =  sqrt( 4 + 4 )  =  sqrt(8)

and the angle:  tan^-1( -2 / -2 )  =  5pi/4     [remember that it is in the third quadrant]

We now have:  8^1/2cis( 5pi / 4 )

To find the first cube root, we need to find the cube root of  8^1/2  which is  (8^1/2)^1/3  =  8^1/6                            

and to divide the angle by 3, giving us  5pi /12.

So, for our first answer, we have  8^1/6 cis ( 5pi / 12 )

To find the next answer, we need to add 1/3 (or 2pi / 3 ) of the circle to our previous answer:   8^1/6 cis ( 13pi / 12 )

and to get our last answer we need to add another  2pi / 3 to this answer:   8^1/6 cis ( 21pi / 12 )  =  8^1/6 cis ( 7pi / 4 )

Thanks for answering 

however

Please can you stop posting your answers in boldface. 

It makes them harder to read.

z = r cis  θ

r = √[ (-3)^2 + 3^2 ]  =  √18  =  3√2

θ  =  arctan (  3/-3)  =  arctan (-1)  =  3pi/4

So

z = 3√2 cis  ( 3pi/4)

You are getting a lot of practice posting pic, learn to do them the right way around!

If it comes out the wrong way, delete it, and try again. (rotate your file on your computer or phone)

You might as well learn something by posting here!

thank u sooo much!

I'm a little confused  here.....the "colorings"  look the same

If we're  just  counting the blocks the progression  is  6, 8 ,10

The albebraic rule for  this  is

b = 4 + 2n

Where  n =  the figure number  and b  is the number of blocks in that figure

I do not know intersecting cord theorum.

I was just going to use distance XB=distance XE and solve the equation for k

X(1,k)  k is the radius.

At least post it the right way around!

Thanks, Melody....nice graphic    !!!!

We can use the intersecting chord theorem here

Let 1/2 the side of the square  = 1

Let  the  diameter of the  circle be  2  +  x

We have that

1 * 1   =   2 * x

1  = 2 *  x

x =1/2

The diameter  =    2 + 1/2  =   5/2

The radius is 1/2 of this =   5/4

I do not think that is correct asinus.  

My image is below.

I was going to give you teaching instruction but CPhill is answering so I am sure he will give you the whole lot.

I hope you have the sense to learn from it.

Look here: https://web2.0calc.com/questions/help-thanks-in-advance_4

Slope  =   [ 1 - - 5]  / [ 6 - -3]  =   6/9  = 2/3

Using  (6, 1)   we have that

y = (2/3) ( x - 6) + 1       multiply through by 3

3y  = 2( x - 6)  + 3

3y  = 2x - 12 +  3

3y = 2x   -  9       rearrange as

2x - 3y  =  9

A = 2     B  =  - 3     C   = 9

A + B + C   =    8

𝐅𝐢𝐫𝐬𝐭, 𝐲𝐨𝐮 𝐬𝐡𝐨𝐮𝐥𝐝 𝐠𝐞𝐧𝐞𝐫𝐚𝐭𝐞 𝐚𝐛𝐨𝐮𝐭 𝟏𝟎 𝐭𝐞𝐫𝐦𝐬 𝐨𝐟 𝐭𝐡𝐞 𝐟𝐢𝐫𝐬𝐭 𝐬𝐞𝐪𝐮𝐞𝐧𝐜𝐞 𝐚𝐬 𝐟𝐨𝐥𝐥𝐨𝐰𝐬:

𝐥𝐢𝐬𝐭𝐟𝐨𝐫𝐞𝐚𝐜𝐡(𝐧, 𝐝=(𝟎.𝟓, 𝟎.𝟕𝟓 , 𝟏.𝟑𝟏𝟐𝟓 , 𝟑.𝟎𝟑𝟓𝟏𝟓𝟔𝟐𝟓 , 𝟏𝟐.𝟐𝟒𝟕𝟑𝟐𝟗𝟕𝟏 , 𝟏𝟔𝟐.𝟐𝟒𝟒𝟒𝟏𝟒𝟖 , 𝟐𝟔𝟒𝟖𝟓.𝟒𝟗𝟒𝟓𝟒 , 𝟕𝟎𝟏𝟓𝟎𝟕𝟗𝟎𝟔.𝟕 , 𝟒𝟗𝟐𝟏𝟏𝟑𝟑𝟒𝟑𝟖𝟕𝟑𝟑𝟑𝟔𝟔𝟐𝟎 , 𝟐𝟒𝟐𝟏𝟕𝟓𝟓𝟒𝟑𝟐𝟏𝟖𝟏𝟗𝟔𝟖𝟓𝟕𝟑𝟓𝟓𝟔𝟔𝟔𝟗𝟖𝟐𝟎𝟑𝟑𝟑𝟐𝟑𝟕𝟎𝟎 , 𝟓.𝟖𝟔𝟒𝟖𝟗𝟗𝟑𝟕𝟑 𝐄+𝟕𝟎 , 𝟑.𝟒𝟑𝟗𝟕𝟎𝟒𝟒𝟔𝟔 𝐄+𝟏𝟒𝟏), 𝐜=𝟏 / (𝐧+𝟏))

𝐒𝐞𝐜𝐨𝐧𝐝, 𝐲𝐨𝐮  would 𝐠𝐞𝐧𝐞𝐫𝐚𝐭𝐞 𝐭𝐡𝐞 𝟐𝐧𝐝 𝐬𝐞𝐪𝐮𝐞𝐧𝐜𝐞 𝐛𝐲 𝐚𝐝𝐝𝐢𝐧𝐠 𝟏 𝐭𝐨 𝐞𝐚𝐜𝐡 𝐭𝐞𝐫𝐦 𝐚𝐧𝐝 𝐭𝐚𝐤𝐢𝐧𝐠 𝐢𝐭𝐬 𝐫𝐞𝐜𝐢𝐩𝐫𝐨𝐜𝐚𝐥 𝐚𝐧𝐝 𝐬𝐮𝐦 𝐭𝐡𝐞𝐦 𝐚𝐥𝐥 𝐮𝐩. 𝐀𝐧𝐝 𝐭𝐡𝐢𝐬 𝐢𝐬 𝐰𝐡𝐚𝐭 𝐲𝐨𝐮 𝐬𝐡𝐨𝐮𝐥𝐝 𝐠𝐞𝐭:

(𝟎.𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟕, 𝟎.𝟓𝟕𝟏𝟒𝟐𝟖𝟓𝟕𝟏𝟒, 𝟎.𝟒𝟑𝟐𝟒𝟑𝟐𝟒𝟑𝟐𝟒, 𝟎.𝟐𝟒𝟕𝟖𝟐𝟏𝟖𝟕𝟖, 𝟎.𝟎𝟕𝟓𝟒𝟖𝟔𝟗𝟏𝟏𝟎𝟗, 𝟎.𝟎𝟎𝟔𝟏𝟐𝟓𝟕𝟖𝟑𝟖𝟓𝟏, 𝟎.𝟎𝟎𝟎𝟎𝟑𝟕𝟕𝟓𝟓𝟎𝟗𝟎𝟓𝟔, 𝟎.𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟏𝟒𝟐𝟓𝟓𝟎𝟎𝟔𝟖𝟏, 𝟎.𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟐𝟎𝟑𝟐𝟎𝟓𝟐𝟏 𝟗𝟒, 𝟒.𝟏𝟐𝟗𝟐𝟑𝟔𝟏𝟏𝟖 𝐄-𝟑𝟔, 𝟏.𝟕𝟎𝟓𝟎𝟓𝟗𝟎𝟗𝟐 𝐄-𝟕𝟏, 𝟐.𝟗𝟎𝟕𝟐𝟐𝟔𝟓𝟎𝟕 𝐄-𝟏𝟒𝟐)=𝟏.𝟗𝟗𝟗𝟗𝟗𝟗𝟗𝟗𝟗𝟗𝟓𝟕𝟎𝟔𝟎𝟔𝟖𝟑𝟎𝟑𝟐𝟎𝟓𝟐.

𝐀𝐬 𝐲𝐨𝐮 𝐜𝐚𝐧 𝐞𝐚𝐬𝐢𝐥𝐲 𝐬𝐞𝐞 𝐭𝐡𝐚𝐭 𝐭𝐡𝐞 𝐬𝐮𝐦 𝐨𝐟 𝐭𝐡𝐞 𝟐𝐧𝐝 𝐬𝐞𝐪𝐮𝐞𝐧𝐜𝐞 𝐠𝐞𝐭𝐬 𝐜𝐥𝐨𝐬𝐞𝐫 𝐚𝐧𝐝 𝐜𝐥𝐨𝐬𝐞 𝐭𝐨 𝟐 𝐛𝐮𝐭 𝐍𝐄𝐕𝐄𝐑 𝐪𝐮𝐢𝐭𝐞 𝐫𝐞𝐚𝐜𝐡𝐢𝐧𝐠 𝐢𝐭. 𝐓𝐡𝐢𝐬 𝐢𝐬 𝐍𝐎𝐓 𝐚 𝐦𝐚𝐭𝐡𝐞𝐦𝐚𝐭𝐢𝐜𝐚𝐥 𝐩𝐫𝐨𝐨𝐟 𝐛𝐮𝐭 𝐜𝐨𝐦𝐩𝐮𝐭𝐚𝐭𝐢𝐨𝐧𝐚𝐥 𝐢𝐧𝐝𝐢𝐜𝐚𝐭𝐢𝐨𝐧 𝐭𝐡𝐚𝐭 𝐭𝐡𝐞 𝐬𝐭𝐚𝐭𝐞𝐦𝐞𝐧𝐭 𝐢𝐬 𝐭𝐫𝐮𝐞!.

I’m failing geometry:(

Hello guest!

\(r^2=(\frac{a}{2})^2+(\frac{a}{2})^2\\ r^2=(\frac{2cm}{2})^2+(\frac{2cm}{2})^2\\ r^2=2\cdot 1cm^2\\ r=\sqrt{2cm^2}\)

\(r=1.414cm\)

  !

We  only need two points  to  write the equation

(0, -3)   and (-2,1)  are on the graph

The slope  between these points is :

[ 1 - - 3 ]   / [ -2 - 0 ]   =    [ 4] / [ -2 ]   =   -2

Using the point   (0, -3)   we  have that

y =  -2x  - 3

In standard form we have :

2x + y + 3  =  0