10 question rest of practice

[opal wedge]

20/20 rest of practice

[jolly panther]

@hollow sundial I do need help these one s I understand you're tired too

[hollow sundial]

Yeah, it’s kinda late where I am , but if no one answers these, I’ll definitely help tmr 👍

[jolly panther]

<@&286206848099549185>

[jolly panther]

10 question rest of practice

@opal wedge

<@&286206848099549185>

@plush stag may you help me with these questions

[echo saddle]

What q you need help with?

[jolly panther]

All of them I got the question question right on some but some of them I don't know how I got it

This my work

[echo saddle]

For which question

[jolly panther]

I need help with all of them

11-20

[echo saddle]

But what question is that working out for

In fact ignore that^

[quiet timber]

can u show better pic, not dark perhaps

[jolly panther]

This picture is my work I apologize it is unorganized

I'm not sure what I used for each question

I need help with 11-20

[glacial garnet]

For 11

There is 21 numbers

0 counts ad a number

You thought that theres 20 numbers from 0-20

Doing 8/20, 2/5

When its actually just 8/21

12*

[echo saddle]

For 13:
Replace n with 3k and see if you can rearrange it to be in the for 3(x)

Where x is an expression in terms of k

[jolly panther]

Like plug in n with 3

[echo saddle]

3k

[jolly panther]

May you explain this one more

[echo saddle]

Because any integer multiplied by 3 is a multiple of 3

[glacial garnet]

How many prime numbers are between 0-20

[jolly panther]

Where'd the 21 come from

[glacial garnet]

Count from 0 to 4 on one of your hands

See how many fingers you use

[jolly panther]

Oh so you count all the prime numbers

[glacial garnet]

Yes

21 is the amount of numbers in the data set

[jolly panther]

Do you count 0 as prime number

[glacial garnet]

No

The prime numbers are

,2,3,5,7,11,13,17,19

[jolly panther]

So you see the pattern is a multiple of 3 like if the equation equal 3, 6, 9 etc

[glacial garnet]

0 is not divisable by itself so not prime

[jolly panther]

Oh ok where is the 21 coming from I see 8 prime numbers wouldn't it be 8/20

[glacial garnet]

Count from 0-4 on your habd

Hand

Hiw many fingers do you use

[echo saddle]

Let 3k be denote a multiple of 3
2(3k) + 3
6k + 3
3(2k+1)
Since 2k+1 is an integer, 3(2k+1) must be a multiple of 3

[jolly panther]

4

[jolly panther]

Oh ok so I would count (0-20)

[glacial garnet]

Yes

Because it says “in the data set (0…20)

Which means thst it wants 0 to he counted as a number

If it said BETWEEN 0-20 i wouldnt

[jolly panther]

Oh ok got Cha and since out of the 2(3)+ 3=9 it makes it a multiple

[jolly panther]

Oh gotcha omgosh

[glacial garnet]

Any other ones you need help with?

[jolly panther]

Thank for explaining it more

Thank you both for helping me

[glacial garnet]

Good ok you for being able to be taught 2 things at once tbh

I could never 😭

[jolly panther]

Aw thank you no one has ever complimented me before about that ❤️

@echo saddle @glacial garnet The last ones I need help with is 15-20 I should be ok after that. I understand if you both need a break too

[glacial garnet]

For 15

Lets say you had x³+2x²+x

You always want to get to ax²+bx+c if possible

Because that allows you to do the diamond/x game

Or quadratic formula

So what could you factor out of x³+2x²+x

To get to ax²+bx+c

@jolly panther

[jolly panther]

X^3 and the x along with the 2x^2

[glacial garnet]

Show me a factored out version

[jolly panther]

Since there all three GCF with the x

[glacial garnet]

Yes

[jolly panther]

You would break down x(x^2+2+x)

[glacial garnet]

Yes

Good

[jolly panther]

Yay!

[glacial garnet]

Now for this

What is the gcf

[jolly panther]

4? Multiples of 4

[glacial garnet]

Yes

What else

?

Lets say it was 2x³+4x²+2x

What could you take out?

[jolly panther]

The 2

2(x^3+2x^2+x)

[glacial garnet]

Ok

And wirh x³+2x²+x

What could you take out?

[jolly panther]

The x's

[glacial garnet]

So in 2x³+4x²+2x you can take out an 2 and an x

?

[jolly panther]

Yes

[glacial garnet]

So could you say that 2x³+4x²+2x factored out is 2x(x²+2x+1)?

[jolly panther]

Would the 1 be 3x?

[glacial garnet]

What do you mean?

[jolly panther]

I never mind I was adding multipling it would be 2x

[glacial garnet]

Yep

[jolly panther]

That looks good

[glacial garnet]

So take the original question

What could you pull out of this

[jolly panther]

The 4

4x(x^2-6x+9)

[glacial garnet]

Beautiful

And how can you fsctor x²-6x+9?

[jolly panther]

X(x-6+9)

[glacial garnet]

No

There is no x in the 9

Do you know the diamond game

Otherwise known as x method

@jolly panther

[jolly panther]

Would it be x^2-6x+3^2

Do you bring the negatives -6 in the x method

[glacial garnet]

Do you know this

[jolly panther]

It's (x-3)(x-3)

[glacial garnet]

Yep

[jolly panther]

(x+6)(x+7)

[glacial garnet]

Shich is the same as (x-3)²

Rifht?

[jolly panther]

Yes they are both the same but it is simplified

I mean looks more simplified but is still the same