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Is this Q written correctly?

-5x - 3y = 12y

-5x = 15y

x = -3y         NONE of the options fit this equation.

Here is a bit of computer code that calcultes this kind of question in no time.
a=1000; b=1000; c=(1); n=2; if((a % n)==1,c=(c,n),0); n++; if(n<=b,gotor-2,c);printc; c=sumfor(n, 1, b, (a % n)==1);print"Total =",c
(3, 9, 27, 37, 111, 333, 999) = 7 Numbers.

This is exactly the same as the previous question, except being about rabbit population:

P=220; a=listfor(t, 1, 3, (P =1.15*(P - 20))
Day 1 =230, Day 2 =242, Day 3 =255 - Population of rabbits in 3 days from now.

This is a recursive formula, where the result of the first year is fed back into the formula to get the result for the second year and that back into the formula to get the result for the third year;

P=55000; a=listfor(t, 1, 3, (P =1.03*(P - 800))
Year 1 =55,826, Year 2 =56,677, Year 3 =57,553 - Population of the town 3 years from now.

Log 2^x = log 7

x log 2 = log 7

x = log7/log2 = 2.8074

2^(2x) = 2^(2*2.8074) = 49

Two right triangles with legs   5 and 12       and   9  and 12      Use pythagorean theorem to calculate and add the hypotenuses together.....

Okay, looks like you have to round up. No leftover paper, right? 

Yes, instead of f(x), set it to y! 

Use the right angles, and also you the location where Paul is at.

This is an example of direct proportion, so EP's answer is correct!
 

$9.00/5bulbs = $1.80 / bulb

two right triangles.. you can figure it out

We can set up a ratio: \(5:3\) .

I know... I SAID I CAN’T THINK OF OTHER PLACES TO ASK! :( 

Let W  be the number of workers [ per day ] that we need to make a profit

Total costs  =  500 +  15 * 8  * W      (1)

Total Revenue  =   5 ( 3.10) * 8 *  W    (2)

We want to solve this for W

(2) > (1)

5 ( 3.10) * 8 * W  > 500 + 15 * 8 * W     simplify

124W   > 500 + 120W   subtract  120 W from both sides

4W > 500     divide both sides by  4

W >  125

So...you are correct....we  need 126 workers  [ at a minimum ] to make a profit !!!

2^(3x - 2)  =  5^x      take the ln of both sides

ln  2^(3x - 2)  =  ln 5^x     and we can write

(3x - 2) ln (2)  =  x ln 5    simplify

3x ln 2  -  2ln 2   = x ln 5     rearrange

3x ln 2 - x ln 5   =  2ln 2       factor

x  [ 3 ln 2 - ln 5]  = 2ln 2      divide both sides by  [ 3 ln 2  - ln 5 ]

x  =       2 ln 2

         __________        correct  !!!!

          3ln 2 - ln 5

OK....glad to help....!!!!

Awesome! Thank you for your explanation it has really helped me.   I have been wrtiing down everything so I remember .

Good question  !!!!....note that....

Every point on the graph should check...let's check  ( 4 , -2)

So we have

-2  =  log₂ (4 - 3)  - 2       add to to  both sides

0  =  log₂ (1)     ......  [ Note   log _a (1)  always  = 0   ]  [ proof...check this  log (1) / log (2) ]

0  =  0

True  !!!!

So...we know we have the  correct equation

y  is supplemental to the 131°  angle

So  y  =   180  - 131  = 49°

And this angle is vertical to the bottom left vertex angle of the top triangle  =  49

Tha angle supplemental to the 142° angle at the bottom is 180 - 142  = 38°

So angle  w   = 180  - 38  - 49  = 93°

And by the exterior angle theorem....w =  the sum of 42°  and the angle vertical to the bottom right vertex angle of the top triangle  

So this angle  =    93 - 42   =  51°

So....t  =  180  - 51  - 49  =  180 - 100   =  80°

Yes that all makes sense. I have a question though, when we go to check it we can use any point which in this case would be (7,0) or (4,-2) to check the answer? If not, why would it only be (7,0)?

See my more complete explanation  in the answer to your  latest  post

In   y  = log ( x - a)  + b

The ( x -a) part translates the graph left/right   and the "b" translates it up/down

(x - a)  translates the graph right  by a units

( x + a)  translates the graph left by  a units

+ b   translates the graph up by  b units

- b  translates the graph down by  b units

Notice that it appears the the  parent has been translated to the right by 3  units...

The thing that translates the parent to the right by 3  units must  be  " ( x - 3 ) "

So...it appears that the last answer is correct

To check this....note that  (7,0)  is on the graph...which means that

0  =  log₂ ( 7 - 3)  - 2    must be true....so....

0 =  log ₂ ( 4)  - 2        [  Note that  log₂ (4)  =  log 4 /  log 2   =  2  ]

0  =  2  -  2

Which is true  !!!!

Does this make sense  ???

Not sure about 'standard notation' but

6.856 x 10^6  = (move decimal 6 places to right) = 6 856 000.         or    6856. x 10^3

Is this equation kind of slope intercept form ? but set up a bit different?