5. (6 marks) use mathematical induction to prove that for each integer n ≥ 4, 5^n ≥ 2^2n+1 + 100.
( take +100 into considersation since previous solution didnt )

Step-by-step explanation:

We will prove by mathematical induction that, for every natural ,  

We will prove our base case, when n=4, to be true.

Base case:

Inductive hypothesis:  

Given a natural ,  

Now, we will assume the induction hypothesis and then use this assumption, involving n, to prove the statement for n + 1.

Inductive step:

With this we have proved our statement to be true for n+1.  

In conlusion, for every natural .

answer:

3 bags of apples and 2 bags of oranges.

step-by-step explanation:

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is