Haven’t done this in a while but the first is rational, second is irrational, third is rational, fourth is irrational, fifth is rational, sixth is rational, seventh is irrational
8 can go into 71 seven times
Answer:

Step-by-step explanation:

Start by factoring out a 5:

We need to find two integers that have a product of 12, and a sum of -7:
(-3)(-4)=12
-3-4=-7
We can split -7x into -3x and -4x

Factor each half separately:
![5[x(x-3)-4(x-3)]](https://tex.z-dn.net/?f=5%5Bx%28x-3%29-4%28x-3%29%5D)
Since x and -4 are both being multiplied by x-3, we can combine them:

Answer:
Step-by-step explanation:
Hello, this is a geometric sequence so we are looking for a multiplicative factor.

So, the explicit formula is for n

Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:

Step-by-step explanation:
<u>Complete Question:</u>
A monkey is swinging from a tree. On the first swing, she passes through an arc whose length is 24 m. With each swing, she travels along an arc that is half as long as the arc of the previous swing. Which expression gives the total length the monkey swings in her first n swings?
<u>Solution:</u>
First Swing:
24 m
Second Swing:
Half of first, so
24(1/2)
Third Swing:
Half of second, so:
24(1/2)(1/2)
Fourth Swing:
24(1/2)(1/2)(1/2)
So we see the general formula as:

<u>Note:</u> n -1 because (1/2) plays a role from second swing, which is n - 1
where n is the number of swings