5. Without living the following equations decide whether there will be one solution, no solutions or Infinitely many solutions and explain why you think so.
3x-2=3x-2
2x-4=2x-7
3x-5=6x-5

3x-2=3x-2 ->Infinite potential answer for x because they are same function

2x-4=2x-7 ->No answer because there is no x value that satisfy the equation

3x-5=6x-6 -> 3x=1 -> x=1/3 ->only 1 answer

answer is the third choice:

3x^5+4x^4+x^3+2x^2-10x-7=0

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for