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Which of the following points is on a circle if its center is (-13,-12) and a point on the circumference is (-17, -12)?

use the distance formula to find the distance between those 2 points, that is the radius.  Call it R

The formula for the circle witll be

$(x+13)^2+(y+12)^2=R^2$

Plug the points in and see which one makes the formula true.

What is the lateral area of a regular pyramid with a square base which has a slant height of 9 units and base side lengths of 7 units?

A) 378

B) 234

C) 189

D) 126

The common ratio is -1.5

To find the number of terms, we have

57875 =  8000 [ 1 - (-1.5)^n ]   / [  1 - (-1.5) ]

57875 = 3200 [ 1 - (-1.5)^n ] 

2315/128 = 1 - (-1.5)^n

(-1.5)^n =  1 - 2315/128

(-1.5)^n = -2187/128       n must be odd.....so....we can solve this

1.5^n =  2187/128     take the log of both sides

n log 1.5 =  log (2187/128)

n =    log(2187/128) / log (1.5)   =  7

So....we are looking for the 7th term which is

8000(-1.5)^(7 - 1)  =   91125

Hello and welcome, WinterPotato!

I'm so glad that you checked out this website. Hope you like it so far! :)

You can post here on the forum page if you have any math questions, or simply if you just want to talk to people, like right now! 

You can also interact with people here to especially help you with homework, and/or concepts that you don't understand. A lot of the people here are so friendly and nice! Oh, and also, if you want, you can help others by answering their questions too!! 

Hope you get to love this website,

NoobieAtMath

p.s. I started here pretty recently, but I've fallen in love with this website! 

p.s.s Also wonderful username. 

JUMBO QUESTION

Using a circle in the complex plane  centered at (0,0) with a radius of 2 , the 6 roots of 64 are

2, 1 + √3 i , -1 + √3 i , -2, -1 - √3 i , 1 - √3 i 

Here's a pic of the solutions

BTW, my favorite season is winter and I like potatoes because they are cool.

That's why my username is WINTER POTATO!

1. Enter the amplitude of the function f(x) .

f(x)=−2sin(3x)−1

In the form  Asin (Bx) + C

The amplitude =  l A l   =  l -2 l  = 2

2. What is the equation of the midline for the function f(x) ?

f(x)=3cos(x)−2.5

Note that the max for the function is 3(1) - 2.5   =  0.5

And the min for the function is    3(-1) - 2.5 =  -5.5

To find the midiine.....add these values and divide the sum by 2

So we have

[ . 5  + - 5.5] / 2 =     -5/2 =  -2.5

So....the equation for the midline is   y = -2.5

$P[\text{at least 2 consecutive tosses have same number}] = \\ 1-P[\text{no consecutive tosses have same number}] = \\ 1-\dfrac{6\cdot 5^4}{6^5} =\\ 1- \dfrac{625}{1296} = \\ \dfrac{671}{1296}$

See if you ideas work by plotting you graph in here

Learn from the answers that i have already given you.

Thanks Tertre.   

Correct, Melody, I forgot. I won't do it next time.

Tertre,

Your LaTex IS nice.  And it is great that you are learning and practicing your skills here.

PLUS

Your answer is nice, I agree, but.....

This person has clearly stated that they want someone to do their homework for them.

Why are you facilitating such blatent cheating?  

It is not like this user can beat you up and take your lunch money if you do not help.

If that were the case I would understand better. 

This is harsh, you are a great member and I don't want you to feel bad.

I'm sure I have at times been guilty of the same 'sin'.

I just don't want this to be known primarily as a free cheat site. 

I want people to learn here, like you and I do.

Perhaps you could have part done it so that the user would at least have to finish the questions on their own.

Thank you! It took a long time to write the Latex! 

I just answered one almost identical to the first question her SO you can do this one yourself!

A sine function has the following key features:

Frequency = 1/8π    I assume you mean  (1/8)pi   ?

Amplitude = 6

Midline: y = 3

y-intercept: (0, 3)

The function is not a reflection of its parent function over the x-axis. Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.

There are 2 answers 

$y=6sin(2x*8)+3$

or

$y=-6sin(2x*8)+3$

Here are the graphs

Nice job, tertre....!!!

(B): We subtract $36$ from both sides, leaving us with $\sqrt{-36}=6i, -\sqrt{-36}=-6i$ . Thus, the two solutions are $\boxed{x=6i,\:x=-6i}.$

(C): There are a few ways to solve this question:

Quadratic Formula:

Use $x = {-b \pm \sqrt{b^2-4ac} \over 2a}$(thanks web2.0calc), and plugging in the values in the form $ax^2+bx+c$, we attain $x=\frac{-\left(-2\right)+\sqrt{\left(-2\right)^2-4\cdot \:1\cdot \:2}}{2\cdot \:1}=1+i$ as one root, and $x=\frac{-\left(-2\right)-\sqrt{\left(-2\right)^2-4\cdot \:1\cdot \:2}}{2\cdot \:1}=1-i$ . Thus, the two roots are $\boxed{1+i, 1-i}.$

Completing The Square:

Our main goal is to get it into the form $x^2+2ax+a^2=\left(x+a\right)^2$, so we have $x^2-2x+\left(-1\right)^2=-2+\left(-1\right)^2$, and simplifying, we get $\left(x-1\right)^2=-1=x=i+1$ and $i-1$ . Thus, the two roots are $\boxed{1+i, 1-i}.$

The greatest possible value of xy will occur when x is most nearly equal to y

We have that

x     y            xy

17   5           85

14  10        140

11   15        165

 8    20        160

So.....xy  is largest when x =  11 and y = 15

Maybe this will help.   

I have not watched it but I would have to learn how to do this befor I could teach you and it is Internet sites, often youtube clips, that I learn from.

I just googled "How do I graph a circle in the complex plane."  And this was the first clip that appeared. 

We have 5x+3y=100, 6x-x+3y=100, 6x+3y=100+x, 3(2x+y)=100+x, 165?

Thanks Tertre but you missed my point. I could do that too. In fact I did do that and then I changed my mind.

If people do not put effort into presenting their questions properly (or at least as good as they are capable of) then perhaps some other people cannot be bothered answering.

Latex is computer code used for displaying mathematics.

The latex box is in the ribbon.  It is the button that say     LaTex.   It is there when you are writing any post.

Click on it to open it.

then copy some of your code and paste it in.  See what happens.

It is easy to learn a little bit of Latex. And when you know a little bit it is easy to learn more. 

You will find it very helpful to become comfortable with very basic coding.

Your post is displaying better now, which is odd because I see no evidence that anyone has edited it. Perhaps it was better than I could see originally and just was not displaying properly.

You can still get rid of the meaningless $ signs though - That would make the question read better.

Here, I'll do it: The equation of the circle centered at $1+2i$ with radius $1$ can be written as $z\overline{z} + pz + q \overline{z} + r = 0.$What is the ordered triple $(p,q,r)$?

2. In triangle ABC, \angle ABC = 90° and AD is an angle bisector. If AB=90, BC=x, and AC=2x-6, then find the area of triangle ABC. Round your answer to the nearest integer. 

Don't see where the angle bisector comes into play, here.....

We have that

BC^2 + AB^2 = AC^2

x^2 + 90^2 =  (2x - 6)^2

x^2 + 90^2 =  4x^2 - 24x + 36

3x^2 - 24x  - 8064 = 0

x^2 - 8x - 2688 = 0    this factors as

(x - 56) (x + 48) = 0

x = 56

So....the area is   (1/2)product of leg lengths  = (1/2)(AB)(BC) = (1/2)(90)(56) = 2520 units^2