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It's nice...........................

Here's a system for you:

\(-4x+y-2z=-14\)

\(8x-2y+4z=7\)\(2x-4y+z=3\)

The second one:

2*[1-(-3)^n] / [1 -(-3)]=-29,524
Solve for n:
1/2 (1 - (-3)^n) = -29524

Multiply both sides by 2:
1 - (-3)^n = -59048

Subtract 1 from both sides:
-(-3)^n = -59049

Multiply both sides by -1:
(-3)^n = 59049

Take the logarithm of both sides, ignoring the - sign:
Log(59,049)/ Log(3)

Answer: n = 10
P.S. Regarless of -3, you can still take the positive log of both sides. It will still give you an accurate n. 

The first one:

I shall consider the 16th term as the 1st. term =543

53 - 16 + 1 =38 number of terms.

Common difference =-12

Sum =n/2[2a + (n -1)d]

Sum =38/2[2*543 + (38 - 1)*(-12)]

Sum = 19[1,086 + (-444)]

Sum = 19[642]

Sum =12,198

We have the following system

a(1)  + b(1)  + 2  =  5

a(2)  + b(2)  + 2  = 8      simplify

a   + b   =   3      

2a + 2b  =  6     →   a + b  = 3    

Since  we have  two equal equations, we have infinite answers  for a and b

For instance...if   a  = 1, then b  = 2

And  our function becomes

f(x) =  x  + 2x  + 2    =    3x + 2

Then  f(3)   =  3(3) + 2   =  11

Maybe you meant that   f(x)  = ax^2 + bx + c        ???

BTUs per cubic foot = total number of BTUs / total number of cubic feet

750 BTUs/person  *  15 people   =   11,250  BTUs   total

38 ft * 8.5 ft * 6.25 ft   =   2018.75   cubic feet   total

11,250 BTUs / 2018.75 cubic feet  ≈    5.573    BTUs per cubic foot

I'm not cheating, I call it using my resources wisely, and I've only done that a couple times.

It's a basic quadratic function.

step1:  ax²+bx+c = 0

It takes a while, but you eventually get to the quadratic formula, x=(-b ± sqrt(b²-4ac)/2a

Also, is there a plus/minus button? I just copied the symbol I used off Google.

Wow really! Hey it's a good thing to know how to do! 

Whenever the focus lies above the directrix, the parabola turns "upward"

The  vertex  is  

( x coordinate of the focus, [sum of y coordinate of the focus + numerical value of the directrix]/ 2 )  =   ( 4,  [6 + 2] / 2 )  =  ( 4, 8/2)  =  (4, 4)

And we have the following form :

4p ( y - k)  =  (x - h)^2      where   (h, k)  is the vertex  and  "p"  =  y coordinate of the focus - y coordinate of the vertex  =  6 - 4  =   2

So we have

4(2) ( y - 4)  =  ( x - 4)^2

8 (y - 4)  =  ( x - 4)^2

See the graph, here ;

https://www.desmos.com/calculator/o8jsbrmpgz

I was going to ask the exact same question! I almost typed it out and realized that someone beat me to it. :(

It's correct!

Hmmm...how about...

Solve for x.

ax² + bx + c = 0

You will need to "complete the square" to get the answer.

I think this is probably algebra II level, but I'm not sure.

Or maybe you've done this already...

Midpoint formula  =   (  sum of x coordinates / 2 ,  sum of y coordinates / 2 )

Example  ....midpoint of   (5,4)  ( 7, 8)

(  [ 5 + 7]/ 2 , [4 + 8] / 2  )   =   ( 12 / 2 , 12 / 2)  =  (6 , 6)

x+y+z+t=number of students at Oddville Academy

(Also I noticed that the languages' first letters spell "odd")

I need help with same question but the website you gave didn't make any sense to me or show me how to solve..?

Did you ever get this answer?

of a segment: hypotenuse of the right triangle created divided by two

I think you want the measure of the arc DF 

\(\angle{DEF}=\frac12\,\cdot\,\overset{ \frown}{DF} \\~\\ 72^{\circ}=\frac12\,\cdot\,\overset{\frown}{DF} \qquad \text{ Multiply both sides of the equation by 2.} \\~\\ 144^{\circ}=\overset{\frown}{DF}\)

I'll think and then edit this.

Also...

1/9=.111111111111111111...

2/9=.2222222222222222...

...

24/99=.242424242424242424...

123/999=.123123123123123...

123456789/999999999=.123456789123456789123456789123456789...

That is pretty cool Z !!!!  👍

Also, you might have seen that trick about how to remember the multiples of 9 before....

One time I wondered what would it do if I just continued the list past 90.

The first column counts up, the second column counts down. Whenever you reach zero in the second column, repeat the number in the first column.

0    9

1    8

2    7

3    6

4    5

5    4

6    3

7    2

8    1

9    0

9    9

10  8

11  7

12  6

13  5

14  4

15  3

16  2

17  1

18  0

18  9

19  8

20  7

21  6

22  5

23  4

...

Let's fast forward to " 909 "

...

90  9

91  8

92  7

93  6

94  5

95  4

96  3

97  2

98  1

99  0

99   9

100 8

101 7

102 6

103 5

...It still works !!  I don't know why, but for some reason I find this neat LOL 

Notice that  in each hundred....we have  [ 10 + 9 ]  =   19  integers that contain at least one zero

And there are  9 "blocks" of  "hundreds"   from  100 - 999

So.....the probability  is :

[ 19 * 9 ]  / [ 999 - 100 + 1 ]  =   171 / 900    =  [ 19/ 100 ]

900 possible outcomes, 

ones that have at least 1 zero: every ten and 100-109,200-209,300-309,...900-909

900/10 = 90

90+90=180

would this be right?

do this

First one

t₁₆   =  543 - 12 (15)   =  363

t₅₃  =    543  - 12(52)  =  -81

Sum  of the terms  =  [ first term in series  +  last term in series] [ number of terms] / 2

**The number of terms is figured as   [ 53 - 16 + 1 ]   =  [ 38] 

So....the sum is : [ 363  +  - 81 ] [ 38 ] / 2  =  [282] [38] / 2  =   5358

Second one

The nth term of series can be  expressed  as  :

a_n   =   2 (-3)^n-1

So

-29524   =  2 (-3) ^n-1       

Notice here that - 29524  is not a term in this series :

https://www.wolframalpha.com/input/?i=2(-3)%5E(n+-+1)++++from+n++%3D+1++to+n+%3D+10