help-13

[kindred storm]

OK, so x = 0 tells us exactly what x is if that part is the right one.

That's already solved for x.

But 6x - 7 = 0 doesn't tell us what x is yet.

So, we have to solve for x.

What do you get for x?

[left hound]

x=0

x=x*

6x-7=0

^^^

that 1

[kindred storm]

Well, you know how in some movies there are different universes where history was different in the different universes?

[left hound]

6x-7= 0

ye

[kindred storm]

OK, so the different or things are like different universes.

Like in one universe, x = 0, and in another universe, 6x - 7 = 0.

In the x = 0 universe, x is exactly the same number as 0.

Because that's what = means.

[left hound]

ye

[kindred storm]

In the 6x - 7 = 0 universe, we don't know x yet.

So, what's x in that universe?

[left hound]

don't know yet

because 6x-7= 0

[kindred storm]

Right, so let's use algebra to solve for x.

[left hound]

it equals to 0 because it isn't solved

[kindred storm]

Or isolate x.

How did you get that?

[left hound]

continue

[kindred storm]

Oh, I mean that you should solve 6x - 7 = 0 for x.

6x - 7 = 0

What's the next line?

[left hound]

6x -7 =0
6x= +7
x=7/6
x=1 1/6

[kindred storm]

Good, except they say to leave it as an improper fraction.

So, x = 7/6 is the last line.

[left hound]

k

that's my answer??

[kindred storm]

Almost.

[left hound]

oh

[kindred storm]

So, if this was on a paper test, you'd write x = 0 or x = 7/6.

[left hound]

ye

[kindred storm]

Now it wants you to write the answers separated by a comma.

So, it's just 0,7/6

[left hound]

alr

lemme try that

it worked

now I gotta do more questions similar to it

[kindred storm]

I have time for one more if you want.

Or if you want, you can try them on your own.

[left hound]

ye

can I do 1 with you

[kindred storm]

Sure.

[kindred storm]

What do they want you to do with that?

[left hound]

factor

[kindred storm]

OK, do you know the quadratic formula?

If not, there's another way.

@left hound

[left hound]

wait lemme try reading my notes from class

[wraith dagger]

Chai T. Rex

[kindred storm]

If you don't remember seeing that, we'll use the other way.

[umbral jackal]

by factoring huh.

do you know the factor theorem

[left hound]

I'm just reading my notes rn

my buddy showed me how to solve this 1 but I don't understand how to get these numbers

[kindred storm]

Oh, I'll show you a way.

[kindred storm]

No, that's incorrect.

If you multiply that out, you don't get what you started with.

[umbral jackal]

it's -37p+15p**^2** not -37p+15p

[left hound]

hb this 1?

[kindred storm]

Right.

[left hound]

good

[kindred storm]

That's a good one.

[left hound]

I understand this 1

[left hound]

this 1 I don't understand lol

[kindred storm]

So, you take the ² coefficient and the constant term.

[left hound]

I was trying to figure it out

[kindred storm]

The coefficient on y² is 1, right?

[left hound]

can I show something and you tell me if I did it right?

[kindred storm]

OK.

[left hound]

this setup look alr?

[kindred storm]

Yes.

A times C is 300.

The times part is always A times C.

[left hound]

ye

now I need to find the factors of the 300

[kindred storm]

Right, the factor pairs.

[left hound]

which is hard for me

lol

[kindred storm]

OK, so start with this:

1 × 300
-1 × -300

Those are two factor pairs.

[left hound]

ye

[kindred storm]

Then, go up through the numbers.

Does 2 divide 300 evenly?

[left hound]

ye

[kindred storm]

So,

2 × 150
-2 × -150

[left hound]

no good

[kindred storm]

Right, way too big.

So, we go up to 3.

[left hound]

still no good

[kindred storm]

Right, what about 4?

[left hound]

nope

[kindred storm]

Right, still too big.

What about 5?

[left hound]

nope

[kindred storm]

What about 6?

[left hound]

nope

[kindred storm]

What about 7?

[left hound]

nope

[kindred storm]

It doesn't divide 300.

What about 8?

[left hound]

ye

no

nope

[kindred storm]

What about 9?

[left hound]

nope

[kindred storm]

What about 10?

[left hound]

nopw

[kindred storm]

Getting close, though.

[left hound]

yup

[kindred storm]

-10 + -30

What about 11?

[left hound]

nope

[kindred storm]

Not a divisor.

What about 12?

[left hound]

ye

ye sirrrr

[kindred storm]

OK, so we have -12 + -25 = -37.

Now, we try two things.

[left hound]

ye

(p-12)(p-25)

[kindred storm]

15p² - 12p - 25p + 20
15p² - 25p - 12p + 20

No, that's not correct.

We have to write it out with the p term separated into two.

We don't know which order is right.

Does it make sense how I wrote them?

[left hound]

oh oki oki

yeye

[kindred storm]

OK, so, the first one:

(15p² - 12p) + (-25p + 20)

We take out the largest common factor of both parentheses.

[left hound]

3

[kindred storm]

Almost.

What about the p part?

p to the what power?

Which power is the smallest?

[left hound]

3p(5p-4)

[kindred storm]

Almost.

Don't forget to divide the 12 by 3.

OK, (-25p + 20)

[left hound]

5(-5p+4)

[kindred storm]

Right, and the smallest p is p to the zero power.

Which means no ps.

OK, are the parenthesized parts the same yet?

3p(5p - 4) + 5(-5p + 4)

[left hound]

ye

[kindred storm]

Almost.

You just have to take the negative out of the last one.

15?

See how one has (5p - 4) and one has (-5p + 4)?

[left hound]

how do I do that?

ye

[kindred storm]

They're the negatives of each other.

Because all the signs are opposites.

5p and -5p, -4 and 4.

So, you can pull the negative out of the second one.

[left hound]

how

[kindred storm]

3p(5p - 4) + 5(-5p + 4)
3p(5p - 4) - 5(5p - 4)

[left hound]

oohhhh

oki oki I get it

[kindred storm]

Now the parentheses are the same.

[left hound]

yeh

[kindred storm]

Now, you know the distributive property?

a(b + c) = ab + ac?

[left hound]

oki

[kindred storm]

Or (b + c)a = ba + ca

[left hound]

ye

ikr that ofc

[kindred storm]

So, we have 3p**(5p - 4)** - 5**(5p - 4)**

[left hound]

yup

[kindred storm]

Those parentheses are the same.

So, we have the (b + c)a = ba + ca

That side.

[left hound]

ye

[kindred storm]

We can get the (b + c)a = ba + ca side from that.

(3p - 5)(5p - 4)

3p(5p - 4) - 5(5p - 4)

Sorry?

[left hound]

nth keep going

[kindred storm]

So,

3p(5p - 4) - 5(5p - 4)
(3p - 5)(5p - 4)

See how I undistributed it?

[left hound]

ye

[kindred storm]

I did the distributed property backwards.

That's a way to factor.

OK, so that should be the answer.

We just have to check it.

The way to check it is to multiply it out.

See if it's what we started with.

(3p - 5)(5p - 4)

What does that expand to?

[left hound]

foil

15p^2 + 12p + 15p^2 + 20

[kindred storm]

Almost. The signs are off and the exponents are off.

Try again.

[left hound]

15p^2 - 12p - 25p +20

[kindred storm]

OK, now combine like terms.

[left hound]

15p^2 -37p +20

[kindred storm]

And that's what we started with, so that's the right answer.

[left hound]

omg that's so cool

any chance you can summarize what we did

like the steps

I need to write this down to practice

[kindred storm]

OK, so we get it in standard form, where the exponents go from highest to lowest.

Then we multiply together A and C.

[left hound]

ye

[kindred storm]

Then we try the factor pairs to see which add together to get B.

Then we don't know which order they come in, so we try one order. If it doesn't work, we try the other order.

So, like:

15p² - 12p - 25p + 20
15p² - 25p - 12p + 20

We separate that old -37p.

It separates two different ways.

So we try both.

When we try one, we put parentheses like this:

(15p² - 12p) + (-25p + 20)

Then we factor the GCF out of each parentheses.

3p(5p - 4) + 5(-5p + 4)

And we see if the parenthesized parts are the same or negatives of each other.

If so, we continue. If not, we go to the other way of separating them.

But these are negatives of each other.

So, we just take the negative out of one of them.

3p(5p - 4) - 5(5p - 4)

Now the parentheses are the same.

Then you put the parts in front of the parentheses together.

(3p - 5)(5p - 4)

And then you check your work with FOIL.

See if you get what you started with.

If you want to get good at doing this, do a lot of problems.

If you run out of problems and you want to do more, here's how to make a new problem:

Fill two sets of parentheses with a number times a variable plus a number. Same variable in both:

(10p + 6)(8p - 7)

Use FOIL and combine like terms:

80p² - 70p + 48p - 42
80p² - 22p - 42

Now, start with 80p² - 22p - 42 and see if you get the parentheses you started with.

[left hound]

gimme like 5-10 min

[kindred storm]

OK.

[left hound]

I'ma go get a drink

and relax my brain

[kindred storm]

Breaks are good.

[cedar kiln]

@left hound Has your question been resolved?

[left hound]

ok

I'm back

r u here?

[kindred storm]

@left hound Yes.

[left hound]

alr I'm going to copy down what I wrote for the other question

real quick

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[kindred storm]

.reopen

[cedar kiln]

✅

[left hound]

back

[kindred storm]

Hello.

[left hound]

hb dis 1

is this right?

I don't seem to understand how he pulled all these numbers from

unless he's wrong again

[kindred storm]

It's mostly right.

Line 5 is wrong.

Notice how all the terms have a factor of -4x²y².

You can undistribute it.

-4x²y²(2x⁵y⁶) - 4x²y²(x⁴y) - 4x²y²(-3)

-4x²y²(2x⁵y⁶ + x⁴y - 3)

[left hound]

alr

starting from the question

he changed the format

then he divide everything by 2?

[kindred storm]

It's put into standard form on the second line.

-4x²y² is factored out of the first two terms on the third line.

-4x²y² is factored out of the third term on the fourth line.

Then you can just undistribute from there.

[left hound]

yeh I'm not understanding the third line

chai

[kindred storm]

Well, it goes like this.

What's the GCD of the first two terms?

[left hound]

wait

I understand the third line

could you explain the 4th line

[kindred storm]

OK, they have + 12x²y² on the end.

They change that to - 4x²y²(-3) by factoring out -4x²y².

[left hound]

oh oki oki

hb 5th line?

collect like terms?

how he write line 5?

looks weird at the end of line 5

[kindred storm]

The fifth line is wrong.

[left hound]

alr

[kindred storm]

It should just undistribute.

-4x²y²(three terms here)

[left hound]

what should the 5th line look like?

[kindred storm]

Well, you have:

-4x²y²(2x⁵y⁶) - 4x²y²(x⁴y) - 4x²y²(-3)

Notice how the part in front of the parentheses is the same on all three.

So, how would it look undistributed?

[left hound]

what does undistributed mean?

[kindred storm]

Well, the distributive property is a(b + c + d) = ab + ac + ad

Notice how you have the right side.

You have the same thing times three different things, just like the distributive law has the same thing times three different things.

[left hound]

ye

[kindred storm]

a(b + c + d) = ab + ac + ad

So, we want to start on the right side and get to the left side.

So, a is the thing attached to all three.

And -4x²y² is the thing attached to all three in your problem.

And it's in front of the parentheses on the left.

-4x²y²(…)

[left hound]

ye

[kindred storm]

And then, inside the parentheses, you have the three things -4x²y² was attached to.

Just like in the distributive law, you have the three things that were attached to a.

-4x²y²(2x⁵y⁶) - 4x²y²(x⁴y) - 4x²y²(-3)

-4x²y²(2x⁵y⁶ + x⁴y - 3)

Another way to see it is that the things in parentheses get added together in new parentheses.

5x(2y) + 5x(-6) + 5x(7x)
5x(2y - 6 + 7x)

Does that make sense?

[left hound]

yes

I see that

[kindred storm]

So, this is the factored form:

-4x²y²(2x⁵y⁶ + x⁴y - 3)

It has the GCD of the three original terms in front.

And then it has what the GCD was multiplied by on each term in parentheses.

So, like if I have 20 + 60 + 12.

[left hound]

I get it now

[kindred storm]

Oh, OK.

[left hound]

I see the resemblance

dis 1 look oki?

[kindred storm]

Yes, and check it by expanding it.

See if you get what you started with.

[left hound]

I have question

how he write that last line?

[kindred storm]

Well, he factored this part 2**(-x - 6 + x²)**.

The 2 is done.

It's a coefficient or a linear factor.

But the part in parentheses isn't linear (degree 1), it's quadratic (degree 2), so it can probably be factored into two linear factors.

And that's what he did.

[left hound]

yes but how did he do it

[kindred storm]

With that method from before.

-x - 6 + x²

Put it in standard form.

x² - x - 6

Multiply A and C.

[left hound]

I mean from the second last line to the last line

[kindred storm]

Right, that's how that was done.

[left hound]

Ohhh

he used the ac methoc

method*

[kindred storm]

Yes, that's right.

One trick, though.

It's -1 for B, right?

[left hound]

ye

[kindred storm]

So, the factors have to be two numbers that are right next to each other.

[left hound]

oki

[kindred storm]

Like -20 and 19.

Because that's the only way to get -1.

And AC = -6

So, it can't be 1 and -6 or -1 and 6.

But 2 times 3 makes 6.

[left hound]

true

that's why I didn't see that

he didn't write down that step

2 & -3

make 6

dis 1?

[kindred storm]

That looks fine, but check it by expanding to make sure.

[left hound]

alr

Hey I have question

when I was doing the AC

he didn't get the right number I don't think

should be 3 and 6

[kindred storm]

Right, 3 and -6.

[left hound]

-3 and 6*

no?

[kindred storm]

Oh, right.

Because it's +3x.

[left hound]

ye

but his final answer is wrong no?

[kindred storm]

So, we have either:

(9x² - 3x) + (6x - 2)
(9x² + 6x) + (-3x - 2)

Depending on whether -3x or 6x comes first.

[left hound]

bigger number goes first

so 6x

[kindred storm]

OK, so:

(9x² + 6x) + (-3x - 2)

[left hound]

ye

[kindred storm]

So, take out the GCD of both.

[left hound]

3(3x^2 + 2x)

[kindred storm]

Don't forget to take out the lowest power of x.

[left hound]

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

[kindred storm]

That's part of the GCD too.

[left hound]

3x(3x+2)

like this?

[kindred storm]

Yes, that's right.

And then you have (3x + 2) and (-3x - 2), which are negatives of each other.

So, you take the negative out of one of them.

[left hound]

3(3x+2) -(3x+2)

[kindred storm]

Almost.

3x(3x + 2) - (3x + 2)

[left hound]

alr

this my answer?

[kindred storm]

No, you have to undistribute.

[left hound]

how I do that part again?

[kindred storm]

Right now, you have subtraction as your main operation.

[left hound]

ye

[kindred storm]

Factors are things you multiply together, so you should get multiplication as your main operation.

A bunch of things multiplied together.

So, you have 3x(3x + 2) - (3x + 2)

The parts outside the parentheses are 3x and -1.

Do you see why the -1?

[left hound]

ye

[kindred storm]

OK, you just put the parts outside the parentheses in their own parentheses.

(3x - 1)(3x + 2)

So, you have

-3(9x² + 3x - 2)
-3(3x - 1)(3x + 2)

And notice how you have three things multiplied together.

Factoring gives you a bunch of things multiplied together.

And that's what we have.

We also have a number and two degree-1 polynomials.

So, we're done factoring once everything is below degree 2.

[left hound]

isn't it

hmm

[kindred storm]

Some degree 2 and above can't be factored nicely.

Like x² + 5.

So if they can't be done, you just leave them.

But try to get everything below degree 2 if you can.

[left hound]

tell me if this is right

3(3x+2x)(-3x-2)
-3(3x-1x)(3x+2)

[kindred storm]

From the problem we just did, no.

[left hound]

hmm

which part is wrong?

[kindred storm]

You dropped the +

You also forgot the x.

3(3x + 2)(-3x - 2)

should be

3x(3x + 2) + (-3x - 2)
3x(3x + 2) - (3x + 2)

If you can, have a piece of paper you work on.

When you go to the next line, change one thing only about the previous line.

Like if you have

(9x² + 6x) + (-3x - 2)

You can factor the first parentheses

3x(3x + 2) + (-3x - 2)

Only one thing was done and everything else is exactly the same.

That way the + doesn't disappear.

[left hound]

what do I do from there?

3x(3x + 2)+(-3x - 2)

[kindred storm]

Well, then you factor the second parentheses, but that's done already.

You forgot the + again.

If that happens a lot, when you're done writing a line, make sure it's exactly the same as the previous line except for just one change.

That will make the paper keep track of everything correctly instead of your head.

Which can make it easier to get the correct answer.

[left hound]

where do I go from here tho

[kindred storm]

The second parentheses is factored.

So, you check whether the parentheses are the same or negatives of each other.

If it's either one, that's good.

If they're negatives of each other, take the negative out of one of them.

So, do that.

[left hound]

3x(3x+2) - (3x+2)

[kindred storm]

Good, now take the parts outside the equal parenthesized parts into their own parentheses.

[left hound]

-3x(3x-2)+(3x+2)

?

[kindred storm]

Nope.

3x(3x + 2) - (3x + 2)

The parts before each parentheses are 3x and -1.

So, you add them together in their own parentheses.

(3x - 1)(3x + 2)

[left hound]

-3(3x-1)(3x+2)

[kindred storm]

Right.

And everything is below degree 2, so you're done except for checking it.

Just expand to check.

See if you get what you started with.

[left hound]

ye

how he right the last 2 lines?

[kindred storm]

It's the difference of squares technique.

(a + b)(a - b) = a² - b²

Notice how the right side is two squared numbers subtracted.

Called the difference of two squares.

So, whenever you see that, you take the square root of both of them.

In one parentheses, you put them added. In another, you put them subtracted.

a² - b²
(a + b)(a - b)

Does that make sense?

[left hound]

ye

but can't you just go from
3(x^2 - (5y)^2)
3(x+5y) (x-5y)?

[kindred storm]

Yes.

The fourth line wasn't needed.

[left hound]

would this work too just curious

3(x-5y) (X+5y)

just switch the minus and + sign

[kindred storm]

Yes, that would work because it doesn't matter what order you multiply things in.

So, like 3 × 5 × 6 = 3 × 6 × 5

You can rearrange them.

So, you're just rearranging the two parenthesized parts.

[left hound]

does this look good?

[kindred storm]

Yes, but put the Ts in order of the subscript.

h = 100T₁ - 100T₂

Like variables are alphabetical order and then if they're the same letter, you do what's attached to them in order.

[left hound]

oki doki

hb this 1?

[kindred storm]

Looks good.

[left hound]

he fliped it when he moved it over

5/7

[kindred storm]

Fill in -15/7 in the original equation for z and see if the sides are equal.

That's how you check solving.

Yeah, a fraction times its reciprocal is 1, so it gets rid of the fraction.

[left hound]

hmm alr

where did the 6 go?

in the 2nd to third line

[kindred storm]

Subtracted 3 from both sides.

[left hound]

alr

[kindred storm]

-7z/5 + 3 = 6
-7z/5 + 3 - 3 = 6 - 3
-7z/5 = 3

[left hound]

hb this

I don't know whats going on X_X

numbers are everywhere

[kindred storm]

Yeah, it's not well-written.

[wraith dagger]

Chai T. Rex

[kindred storm]

Does that make sense?

[left hound]

tryna think

so

theres no answer tho

[kindred storm]

The answer is at the bottom: -5/7

[left hound]

ik but how he get that

[kindred storm]

Do you understand why they multiply by both denominators?

[left hound]

where he get the 7x?

[kindred storm]

That's later on.

But do you understand why they multiply by both denominators?

[left hound]

I understand the 4x(3x+1) part

[kindred storm]

Why do they do that?

[left hound]

common demominator

[kindred storm]

It gets rid of both denominators.

[left hound]

ye

alr

got it

[wraith dagger]

Chai T. Rex

[kindred storm]

Do you understand these steps?

[left hound]

cross multiply

[kindred storm]

Well, distribute.

The 4x(3x + 1) gets distributed to both fractions.

And then the denominator cancels one of the factors in 4x(3x + 1).

For the first fraction, the 4x is cancelled, leaving 3x + 1 multiplied by the 5.

For the second fraction, the 3x + 1 is cancelled, leaving 4x multiplied by the -2.

[left hound]

uhh

how you get 5?

[kindred storm]

It's in the numerator of the second fraction.

Sorry, the first fraction.

[wraith dagger]

Chai T. Rex

[left hound]

ok umm

I'm talking about

the 7x and the +5 on the left side

how he get that?

[kindred storm]

Well, I have 5(3x + 1) - 2(4x), right?

[left hound]

ye

[kindred storm]

What does that expand to?

[left hound]

15x+5 - 8x

[kindred storm]

Combine like terms.

[left hound]

7x+5

dis 1?

how did he get 60?

where did that come from?

[kindred storm]

It's incorrect.

[left hound]

from where is it wrong?

[kindred storm]

Line 6 should be -5/(2y) = -29/24. It's missing the - on the right.

And then they multiply both sides by 24y.

So, the left side becomes -60.

The right side becomes -29y

I have to go in five minutes.

[left hound]

Question

shouldn't the 60 have the y?

and 29 be just the number?

[kindred storm]

I don't know what you mean.

What does it mean for 60 to have the y?

[left hound]

-60y

and 29

[kindred storm]

Yes, -60 = -29y is correct.

[left hound]

should be -60y= 29

right?

[kindred storm]

They forgot a minus sign on the sixth line.

Other than that, it's correct.

The 24y line is a bit misleading, since it's not an equation. It just tells what they're multiplying both sides by.

[left hound]

ye so it should be -60y=29?

then y= 29/60

[kindred storm]

-60y = -29

Then y = 29/60.

[left hound]

alr

[kindred storm]

-5/(2y) = 29/24

should be

-5/(2y) = -29/24

Make sure you don't just review how someone else did them.

That'll help you to understand a little, sure, but you need practice to really get it.

[left hound]

y= -9/20

[kindred storm]

Like people can tell you how to ride a bike, but you don't really get it until you ride it a while and learn how to stay upright.

[left hound]

is the right answer

he didn't reduce

[kindred storm]

No, 29 is prime and 60 isn't a multiple of it, so it's a reduced fraction already.

[left hound]

oh yeh

sorry my head is everywher e

I woke up at 8:00 for work and it's like 5:33am rn

tryna study before the test

[kindred storm]

Oh, OK. I'd recommend sleep.

[left hound]

I will

after I got Q 16 17 18 and 19

4 more to go!

[kindred storm]

It'll help on the test and you solidify what you were just learning before sleep when you sleep.

[left hound]

my test is at 3:00 pm

so like 9 hours

9-10

[kindred storm]

Unfortunately, I have to go.

Let me check something.

[left hound]

aww fr?

alrr

wait a sec

nvm

I understand how to do #17 18 and 19 lol

only #16 if that's ok with you

[kindred storm]

Yeah, my room is dirty and I have to have it clean in about 2.5 hours.

OK, I can do one more.

[left hound]

yayyy 😄

what happen here?

I got confused on the third line

[kindred storm]

They skipped some steps.

They multiply both sides by 8x(5x - 3).

[\frac1{8(5x - 3)} + \frac1{2x} = -\frac5{5x - 3}]
[8x(5x - 3)\qty(\frac1{8(5x - 3)} + \frac1{2x}) = 8x(5x - 3)\qty(-\frac5{5x - 3})]

[wraith dagger]

Chai T. Rex

[kindred storm]

Try the expansions on both sides.

Don't expand the small parentheses.

Distribute 8x(5x - 3) to the things inside the big parentheses.

[left hound]

on the left side it would just cancel out

[kindred storm]

Then cancel if you can.

Then expand some more.

[left hound]

left with 1/2x = 40x-24

[kindred storm]

On the left side, yes it does somewhat.

No, it can't cancel out that way.

Distribute 8x(5x - 3) to 1/(8(5x - 3)) and to 1/(2x).

What do you get for both of them?

[left hound]

not too sure

[kindred storm]

Well, just multiply.

[left hound]

oh oki

[wraith dagger]

Chai T. Rex

[kindred storm]

See, we distribute.

Then we can cancel some things.

[left hound]

ye

[kindred storm]

So, what do you get for the first term after cancelling?

[left hound]

first fraction ends up with 0

[kindred storm]

No.

It can only be zero if the numerator is zero.

Turn it into a fraction.

[left hound]

left with just 1

[kindred storm]

Almost.

The part on the left has an extra x in it.

[left hound]

oh yeh

I didn't see that

[kindred storm]

So, we have x for the first term.

What about the second term?

[left hound]

wait how come it had extra x in it?

oh

ok

nvm

I got it

[kindred storm]

What about the second term?

[left hound]

how do I multiply that?

the brackets n stuff are confusing me

[kindred storm]

Well, you just multiply the part in front into the top.

[left hound]

8x(5x-3)/2x

[wraith dagger]

Chai T. Rex

[kindred storm]

Right, now cancel.

What does it simplify to?

[left hound]

4x(5x-3)

[kindred storm]

Almost.

Don't forget to cancel the xs.

[wraith dagger]

Chai T. Rex

[kindred storm]

The 8 cancels the 2 leaving 4 in the top.

[left hound]

oh

[kindred storm]

The x cancels the x getting rid of both.

[left hound]

4(5x-3)

like that

[kindred storm]

Good, so x + 4(5x - 3).

What does that expand and combine like terms into?

[left hound]

20x -20

[kindred storm]

Almost.

What do you get before combining like terms just after you expand?

No, that's further off.

x + 4(5x - 3)

What does 4(5x - 3) expand to?

[left hound]

x + 20x -3

21x-3

[kindred storm]

Not quite.

Do the expansion explicitly.

4(5x - 3)
4·5x - 4·3

[left hound]

oh

21x-12

[kindred storm]

No.

Right.

Now, lets do the right side of the equal sign.

[left hound]

k

[wraith dagger]

Chai T. Rex

[kindred storm]

What cancels?

[left hound]

this 1 more tricky

[kindred storm]

Well, you can first multiply the part in front onto the numerator.

What do you get from that?

[left hound]

40x^2 -24

[kindred storm]

No, I mentioned a numerator.

Multiply the part in front onto the numerator.

[left hound]

40x

[kindred storm]

What is that referring to?

[left hound]

8x times 5? you mean?

[kindred storm]

What about the (5x - 3) in front?

[left hound]

oh

40x(25x-15)

[kindred storm]

No.

Why did the (5x - 3) change?

[left hound]

sorry

just confused rn

please forgive me

[kindred storm]

It's not a bad thing, I just think you're tired.

It's hard to learn when you're tired.

[left hound]

40x(5x-3) then 200x^2 -120

[kindred storm]

No, but you don't want to expand.

Notice how you have (5x - 3) on the top and bottom.

Leave things factored.

[left hound]

alr

would just be 40

[kindred storm]

That makes it easy to spot opportunities to cancel.

Almost.

[left hound]

40x^2

[kindred storm]

Almost.

[wraith dagger]

Chai T. Rex

[left hound]

ohhhh

yes yes yes

oki oki

[kindred storm]

So, we have 21x - 12 = -40x.

[left hound]

alr

any chance you have the pictures for that to show it

I wanna write it down

[kindred storm]

For the steps we've done?

[left hound]

ye

[kindred storm]

It'll take a few minutes.

[left hound]

yes please

once I wake up I'll review all of this

lol

will be much clear

[wraith dagger]

Chai T. Rex

[kindred storm]

@left hound

[left hound]

ye

lemme write dis down

thx

[kindred storm]

You're welcome.

[left hound]

hey

1 quick question before you go

How come we multiplyed both sides by 8x(5x-3) ?

[kindred storm]

Because that's the GCD of all the denominators.

Multiplying both sides by the GCD of all denominators gets rid of the denominators.

[left hound]

question.....

why not do greatest common denominator first

like uhh

8x(5x-3) / 8(5x-3) = 8x

then 8x multiply the top would be 8

first the first fraction

etc

[kindred storm]

I don't understand what you mean.

[left hound]

I send you picture

[kindred storm]

That's essentially what we did.

But it equals x instead of 8x.

And that's what we got for the first term.

[left hound]

like this

can't we do that?

the just multiply they tops with those?

[kindred storm]

I don't understand what's going on there.

[left hound]

I did the GCD

the first divide is the first fraction demoninator

2nd divide is the second fraction demininator

3rd divide is third fraction demoninator

[kindred storm]

OK, but you also need to put their numerators.

[left hound]

yup

[kindred storm]

The numerators aren't all the same.

[left hound]

oki

1 times x = X
1 times 4x(5x-3) = 4x(5x-3)
5 times 8x= -40x

so it would be x + 4x(5x-3) = -40x

yk?

[kindred storm]

Yeah, but that's still not quite right.

I mean, if you can do the cancellation in your head, that's fine.

But it's easy to make mistakes.

[left hound]

will it give me same answer?

if I do this waY?

[kindred storm]

Yes, if you do it correctly, but the second term is wrong.

You're essentially doing the cancelling in your head rather than on paper.

But it's easy to make a mistake that way.

[left hound]

whats wrong with the 2nd?

[kindred storm]

It has an extra x.

[left hound]

ohhh

[kindred storm]

4x(5x - 3) should be 4(5x - 3).

[left hound]

ok I get it

4(5x-3)

you right mb

[kindred storm]

When I was learning this, I had a way to avoid errors.

Just change one thing from the previous line, and make sure everything else is exactly the same.

That way, you can focus on getting the step you're doing on that line correct.

[left hound]

alr Chai I'ma let you go now lol

thanks for the help

took like what

[kindred storm]

OK, have a good rest and test.

[left hound]

6 hours lol

[kindred storm]

You're welcome.

[left hound]

Thankss!!

[kindred storm]

No problem.

[left hound]

.close

[cedar kiln]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[crimson sedge]

Can someone double check this for me?

Or if i did something wrong (dont wanna lose points cuz teacher grades hw harshly)

[ember python]

Looks good

[dense hornet]

uhh this homework is graded?

[crimson sedge]

yeah waler

so i always double check

[crimson sedge]

thank you

cuz i want to do well in this class

[dense hornet]

ok then you shouldn't be asking for help then

[crimson sedge]

am i not allowed to?

[ember python]

Oh yeah

[dense hornet]

yes you aren't

well no

[crimson sedge]

i thought as long as im not asking people to do it its fine?

[ember python]

Depends

Does your teacher forbid asking for help, i.e do they want you to do it by yourself

[crimson sedge]

okay well, im going to be studying for this calc exam very soon, i plan on doing a ton of practice problems on my own

in that case is it fine if i ask to double check

[dense hornet]

academic dishonesty is not highly encouraged, since homework are being graded for a reason

[ember python]

It’s common sense

[dense hornet]

oh well, dont know, will let the <@&268886789983436800> deal with this

[ember python]

If you’re supposed to do it by yourself, you can’t get help

[crimson sedge]

okay i'll avoid asking homework questions here

but i'll ask for help for my own personal studying

[umbral jackal]

give him a chance first

[ember python]

If you’re allowed to consult other people, it’s okay

[crimson sedge]

he said we are allowed to discuss with classmates

but no copying

idk if he grades homework for completion or for every problem

and correctness

[ember python]

That sounds like it’s not that bad

If you can discuss it with others

[cedar kiln]

Channel closed

Closed due to the original message being deleted

[ember python]

The sort of thing that’s banned if when you can’t discuss it with anyone, i.e it’s for you and you only

[crimson sedge]

that seems much more like a test

online exam or something

thats definitely not what this is

definitely have received a lot of help when doing even problems in the book that dont have answers in the back

so i'll mainly utilize this discord for that use then

thank you :)

.close

[ember python]

Yea np

(Channel was already closed because you deleted the original message)

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[remote dust]

<@&286206848099549185>

[remote dust]

hello

?

[sharp harness]

use one channel for question, dont ping helpers from the beginning and ask your question

[remote dust]

are you a helper?

[ember python]

It doesn’t matter they’re right

1 channel, and don’t ping helpers immediately be patient

[spring wharf]

close one of the open channels

[ember python]

Choose one to close

If not we’ll just close one randomly

[remote dust]

chose one

i closed help 9

[ember python]

Okay good

Next time wait at least 15 minutes before you ping helpers

(once)

[remote dust]

why does it matter

[quick geode]

bro

someone usually answers quickly

[ember python]

Read the message above yours…

[quick geode]

can i become helper?

[spring wharf]

Read the rules maybe

[remote dust]

shush peasent

[ember python]

So helpers know where to look for people who’ve actually been waiting a long time

[ember python]

Contact a moderator

[quick geode]

how did you become?

[ember python]

I contacted a moderator lmao

[quick geode]

sorry @remote dust for using your channel but we are here

[quick geode]

ok lol

[ember python]

Just be patient

[cedar kiln]

@remote dust Has your question been resolved?

[cedar kiln]

Channel closed

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[cedar kiln]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[left hound]

.reopen

[left hound]

is this right?

[reef venture]

yes

[left hound]

alr

I got question about that 1

when it comes to this type of question

I ignore the outside 4x and just use the bracketed number?

[reef whale]

If the product of two things are zero, then either the left one or the right one must be zero
Then you can essentially split the problem into two

[left hound]

alr

hb this 1?

this 1 looks confusing

[reef whale]

Looks right to me

[left hound]

can you explain how they got this

the 3rd line

[still sequoia]

using the quadratic roots formula

[left hound]

can you guild me on how

[still sequoia]

if you have an equation that cannot be easily factored and is in the form ax^2 + bx +c = 0
Then you can use the formula and substitute the values of a, b and c in it to get the answer

[left hound]

I looked it up and it's still confusing me

A= 2
B= 4
C=-1

I understand that part

but idk what to do from there

ye

fr?

[heady grotto]

yeah

[left hound]

calculator sounds better lol

how do I do it?

[heady grotto]

look for the "equations" section on the calculator and choose the one where the function has the form of ax^2 + bx + c = 0

its usually from menu, and option 3 on a casio calculator

[left hound]

I found the EQN button

it's asking for 2 unknown or 3

[heady grotto]

could u send a picture of your calculator lol

[left hound]

y

e

ye

I can

rn

I see

Mcl, Mode, All

ok

"Reset All"

[heady grotto]

@left hound choose unknowns as 2

[left hound]

oki

I did 2 unknowns

now it said a1?

[heady grotto]

u put in the a value

which is 2

for ur question

[left hound]

b1?

4

[heady grotto]

4

c1 = -1

[left hound]

alr

now what's a2?

[heady grotto]

oh nvm i think its the wrong type of mode @left hound

cancel it

[left hound]

alr

[heady grotto]

and uh go to the place where it said unknowns

and

press right on the big menu thing

so that it says "degree"

and then choose 2

and do the same thing

[left hound]

oki

how do I type it tho

wait

I got x1= 0.22474

-2.2247

so what's my answer?

they want it in p= something

[heady grotto]

ur x1 and x2 is ur p

its just a dummy variable lol

[left hound]

how do I change that lol

change it to like this

alr thanks

[cedar kiln]

@left hound Has your question been resolved?

[cedar kiln]

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[ripe hamlet]

This is a hexagon in an isosceles triangle.
Can anyone give me a hint to solve the area of the hexagon myself?

[ripe hamlet]

Sure it's really obvious that it's not solvable without that!

[upper garnet]

maybe split the hexa into triangles

[ripe hamlet]

How can I find the side of it?

[upper abyss]

Doesn't look doable. You can grow the hexagon and just make the triangle taller to fit

However you can relate area to height, that'd be cool

[cedar kiln]

@ripe hamlet Has your question been resolved?

[ripe hamlet]

.close

[cedar kiln]

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[crimson sedge]

Hello, I have that type of expression and I need to find n, is there any way to actually calculate it instead of just guessing numbers which will fit in? (I'm asking in general, for instance, with higher numbers it would be impossible to guess that number) Thanks.

[quartz vale]

2^(n/3) = 2^(5)
n/3 = 5

[dull anchor]

yea

[crimson sedge]

okay, and how would you get the factorise (5) if there would be bigger number

i don't know how it's called in english

[quartz vale]

factorise

[crimson sedge]

okay

[dull anchor]

$\left(\sqrt[3]{2}\right)^n=\left(2^{\frac{1}{3}}\right)^n$

[wraith dagger]

Big xdddd

[dull anchor]

$log_{2}(32)=5$

[wraith dagger]

Big xdddd

[crimson sedge]

oh

[dull anchor]

if you exponent both sides you get $32=2^5$

[wraith dagger]

Big xdddd

[crimson sedge]

i haven't learnt logarithms yet, but I understand the principle

thanks for help 🙂

[dull anchor]

no problem

[crimson sedge]

should i close it now?

[dull anchor]

if you dont have any other questions sure

[crimson sedge]

okay

.close

[cedar kiln]

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[empty parrot]

is time the derivative of distance with respect to speed?

[upper garnet]

wha

[bold hinge]

t = dx/dv
Seconds = meters/(meters/second)

Yeah checks out

[cedar kiln]

@empty parrot Has your question been resolved?

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[maiden osprey]

hello i need some help getting the volume and surface area of this triangular prism