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I have already figured it out, thank you though. I will show you my thought process in a second after I finish one step of this problem

the answer would be 18, right?

If it is given that two triangles are similar, then it also means that the sides are proportional. Does this detail help you make progress here?

Listing all the possible arrangements is one way to approach this problem; however, if I told you that this number has 10  or 100 digits, would you be as willing to write out all of them? I doubt it.

The first digit has two possibilities; it can either be a 2 or a 5. 

The second digit has two possibilities; it can either be a 2 or a 5.

The third digit has two possibilities; it can either be a 2 or a 5.

\(2*2*2=8 \text{ integers}\)

The question never specifies which coefficient I am matching. Am I matching the coefficient of the "x" or the coefficient of the "y?"

I guess I will answer both questions. 

The first equation \(5x-2y=16\), the coefficient of x is 5. The coefficient of x in the second equation is 15. Therefore, the constant necessary to multiply the first equation is 3. 

The first equation \(5x-2y=16\) , the coefficient of y is -2. The coefficient of y in the second equation is -7. Therefore, the constant necessary to multiply the first equation is 7/2 or 3.5. 

Thank you CPhill, I was working with you while you were composing an answer and I was going over my thought process and you proved it to me that I was right, once again Thank You

Thank you so much

Thank you so much CPhill, you helped me solve my homework in time

1.  Heres the graph : https://www.desmos.com/calculator/rdw0easlxd

2.  In the form  y  = mx  ...... the slope  =  m  = 3.5

This means that as  x changes by 1, y changes by 3.5

3. Suppose  that it costs 3.50 to rent a canoe for  1 hour

Then...the cost of renting a canoe for  x hours =  y = 3.5x     where y is the total cost 

HAHAHA!!!!!....I'm probably the only person in LA  that doesn't eat crawfish...!!!

(a)   angle XBC  = 55°  because it is a corresponding angle  to angle AXY

(b) Since XB = XC   ....then the angles opposite these sides are equal

So  angle XBC  =  55° =  angle XCB

So...angle BXC  =  180  -  m angle XBC  - m angle XCB  =

180   - 55   -55   =

180 - 110   =

70°

(b) 55+55=110, 180-110=70 degrees..If you look at the two lines!

a)  Unit rate  =  24 oz / 10lb   = 2.4 oz /  lb

This means that we  need 2.4 oz of seasoning for every pound of crawfish

b) For  30 lbs....we need    30 * 2.4 =  72 oz of seasoning

c)  With 36 oz of seasoning...we can cook      36 / 2.4  =  15 lbs of crawfish

....and Basic /advanced/particle/theoretical/astro Physics, Chemistry, Statics, Dynamics, Electricity and circuits, Mechanics of Materials, Electromagnetics and maybe a smidge of Thermodynamics.....

HaHa  .... JK     

Ok, that's a lot buddy pal

Yes. You will need a Masters Degree in Mathematics, which must include: Trigonometry, Algebra, Geometry, Calculus, Statistics, Probability Theory, Number Theory, Combinatorics and many many other branches which I have not listed!.

I believe the answer is C. Feel free to correct me if i'm wrong.

sorry dude we cant 

idk if you can see the image 

C. Factor

1.  ln 216x^4  ...this is a single  natural log 

We could write this as 

 ln 216 + ln x^4   = 

ln 216 + 4 ln x 

2.  ln 72x  ..this is a single natural log expression

We  could write this  as

ln 72  + ln x

3. ln (216 + x^4)   ....cannot be simplified any further

4.  ln 18x^4  ....this is a single natural log expression

We could write this as

ln 18  +  ln x^4  =

ln 18 + 4 ln x

Well there's a short and fantastic explanation. Thanks!!

Basically, in a few short words, the explanation is:

Since the numbers in this set are part of an arithmetic sequence, every number that comes after the first term is increasing at a constant value. In our case, the numbers are increasing by 2.

Since the numbers are are in this arithmetic sequence, the difference between any two consecutive numbers is going to be 2.

Therefore, \(\boxed 2\) is our first integer.

We can get the next integer using a similar method. Since this is an arithmetic sequence as stated before, every other number that comes after the first term also increases at a constant value.

To make this easier to understand, lets take 1 and 5, 3 and 7, 5 and 9, 7 and 11, as well as 9 and 13. The positive difference between all of these pairs is 4.

Therefore, the difference between -any two integers that are split apart by one number in this sequence- , is 4.

So \(\boxed 4\) is our second integer.

Now if we were to continue on in the same fashion, we would get the positive integers of 2, 4, 6, 8, 10, and 12. Therefore, we would have \(\boxed {\boxed {6}}\) integers.

Now I know my explanation is confusing, I do have some flaws that may not be too easy to understand. If anyone could explain it better, that would be awesome!