you can see the distance between the intervals in the graph more easily because you can see how far the plots are away from each other by connecting the w/ lines. Ex you had 5 on a graph and you had 12 after it there is an interval of 8 in between so you can visually see how far apart the numbers area simple 2d xy line graph has only the possibility for 2 different variables (x and y).. for a 3 variable graph you would have to go into a 3d xyz graph with each variable as x, y and z. it is possible to fit a line to this but for an easier analysis it is better to analyse the variables in pairs. Hope this helps.
Simplify the ration expression
![\frac{3x-6}{x-2}](https://tex.z-dn.net/?f=%5Cfrac%7B3x-6%7D%7Bx-2%7D)
start by seeing if anything in the numerator or denominator can be factored,
you should notice that you can factor out a 3 from 3x-6 in the numerator
when you do so, the result is
![\frac{3 *(x-2)}{x-2}](https://tex.z-dn.net/?f=%5Cfrac%7B3%20%2A%28x-2%29%7D%7Bx-2%7D)
now, since there is an x-2 in the numerator and denominator, they "cancel" out since
![\frac{x-2}{x-2} =1](https://tex.z-dn.net/?f=%5Cfrac%7Bx-2%7D%7Bx-2%7D%20%3D1)
however, only when
![x \neq 2](https://tex.z-dn.net/?f=x%20%5Cneq%202)
since
![\frac{0}{0} \neq 1](https://tex.z-dn.net/?f=%5Cfrac%7B0%7D%7B0%7D%20%5Cneq%201)
when you cancel out the x-2, you're left with 3
hence, your answer is C
For this case we must solve the following questions:
Question 1:
We should simplify the following expression:
![\frac {\frac {m ^ 2 * n ^ 3} {p ^ 3}} {\frac {mp} {n ^ 2}} =](https://tex.z-dn.net/?f=%5Cfrac%20%7B%5Cfrac%20%7Bm%20%5E%202%20%2A%20n%20%5E%203%7D%20%7Bp%20%5E%203%7D%7D%20%7B%5Cfrac%20%7Bmp%7D%20%7Bn%20%5E%202%7D%7D%20%3D)
Applying double C we have:
![\frac {m ^ 2 * n ^ 3 * n ^ 2} {mp * p ^ 3} =](https://tex.z-dn.net/?f=%5Cfrac%20%7Bm%20%5E%202%20%2A%20n%20%5E%203%20%2A%20n%20%5E%202%7D%20%7Bmp%20%2A%20p%20%5E%203%7D%20%3D)
By definition of multiplication of powers of the same base we have to place the same base and add the exponents:![\frac {m ^ 2 * n ^ 5} {m * p ^ 4} =](https://tex.z-dn.net/?f=%5Cfrac%20%7Bm%20%5E%202%20%2A%20n%20%5E%205%7D%20%7Bm%20%2A%20p%20%5E%204%7D%20%3D)
Canceling common terms:
![\frac {mn ^ 5} {p ^ 4}](https://tex.z-dn.net/?f=%5Cfrac%20%7Bmn%20%5E%205%7D%20%7Bp%20%5E%204%7D)
Answer:
Option A
Question 2:
We should simplify the following expression:
![\frac {3xyz ^ 2} {6y ^ 4} * \frac {2y} {xz ^ 4}](https://tex.z-dn.net/?f=%5Cfrac%20%7B3xyz%20%5E%202%7D%20%7B6y%20%5E%204%7D%20%2A%20%5Cfrac%20%7B2y%7D%20%7Bxz%20%5E%204%7D)
So, we have:
![\frac {3xyz ^ 2 * 2y} {6y ^ 4 * xz ^ 4} =\\\frac {6xy ^ 2z ^ 2} {6y ^ 4xz ^ 4} =](https://tex.z-dn.net/?f=%5Cfrac%20%7B3xyz%20%5E%202%20%2A%202y%7D%20%7B6y%20%5E%204%20%2A%20xz%20%5E%204%7D%20%3D%5C%5C%5Cfrac%20%7B6xy%20%5E%202z%20%5E%202%7D%20%7B6y%20%5E%204xz%20%5E%204%7D%20%3D)
Simplifying common terms:
![\frac {1} {y ^ 2z ^ 2}](https://tex.z-dn.net/?f=%5Cfrac%20%7B1%7D%20%7By%20%5E%202z%20%5E%202%7D)
Answer:
Option D
Question 3:
We factor the following expressions to rewrite the experience:
<em>
: </em>We look for two numbers that multiplied give 10 and added 7:
![(r + 5) (r + 2)](https://tex.z-dn.net/?f=%28r%20%2B%205%29%20%28r%20%2B%202%29)
<em>
</em> We look for two numbers that multiplied give -50 and added -5:
![(r-10) (r + 5)](https://tex.z-dn.net/?f=%28r-10%29%20%28r%20%2B%205%29)
<em>
</em>
Rewriting the given expression we have:
![\frac {(r + 5) (r + 2) * 3 (r-10)} {3 (r-10) (r + 5)} =](https://tex.z-dn.net/?f=%5Cfrac%20%7B%28r%20%2B%205%29%20%28r%20%2B%202%29%20%2A%203%20%28r-10%29%7D%20%7B3%20%28r-10%29%20%28r%20%2B%205%29%7D%20%3D)
We simplify common terms in the numerator and denominator we have:
![(r + 2)](https://tex.z-dn.net/?f=%28r%20%2B%202%29)
Answer:
Option D
Answer:
is rational number.......
Answer:10,800
Step-by-step explanation:
im not sure but what i did was 90x120=10800