Question

http://prntscr.com/o0x5ab

Answer 1

@Ultrilliam @Tranquility

Answer 2

Do you know the formula?

Since the angle's vertex is at the center of the circle

Answer 3

yees but where do we plug in the 312

Answer 4

oh wait would the answer be 312?

Answer 5

Here in your question, we know ADB is 312

We need to find the arc of AB

Since it's a circle, we know the total is 360

So a simple subtraction can help us
360 - 312 = ?

Answer 6

thats 48

Answer 7

Perfect!
\( \ m\angle ACB = m \overset{\LARGE{\frown}}{AB} = 48^o \)

Answer 8

Got itt
What about this one?
http://prntscr.com/o0xpr5

Answer 9

(-3x - 6)=(-4x) ?

Answer 10

This is an inscribed angle

The formula for inscribed angles are
inscribed angle = 1/2 (intercepted arc)

In our case, that would be

\(\ m\angle ACB = \frac{1}{2} \left ( m \overset{\LARGE{\frown}}{AB} \right)\)

Answer 11

Plug in the values that they gave you. Also, you'll need to memorize these formulas for your exams or at the very least write it down to make it easier to find the formula when you encounter similar questions. With enough practice, you'll eventually remember the formulas

Answer 12

I see okay, so what would m∠ACB be? like how do we know what numbers to plug in

Answer 13

m∠ACB is the same as m∠C

Just follow the points A C B and see what angle that forms, it's angle C. I write it as ACB because it removes any vagueness about which side of the angle it could be

Answer 14

They told you
m∠C = -3x-6
arc AB = - 4x

Answer 15

You have to solve for x

Answer 16

-3x-6=1/2(- 4x) ?

or the other way around?

Answer 17

@Tranquility

Answer 18

That's correct! Now solve for 'x'

Answer 19

-6

Answer 20

how about this one?

http://prntscr.com/o0y3v4

Answer 21

@Tranquility u there?

Answer 22

-6 is correct

Answer 23

Okay what about the other question I posted?

Answer 24

Congruent means that they are the same length, so set them equal to each other and solve

2x + 1 = 3x - 7

Answer 25

You solve for x, and then you have to plug it into either 2x+1 or 3x-7 and find the length. It doesn't matter which one you plug it into since both of them are of the same length

Answer 26

17 is the answer correct?

Answer 27

http://prntscr.com/o0y87x

this one @Tranquility ?^

Answer 28

Correct

Now set this one up just like we did the previous one.
QR = LN
OP = VW

I think we're going to have to solve a system of equations here

Answer 29

so 3y+16=y+8 ?

Answer 30

thats -4

Answer 31

is that the answer?

Answer 32

No

You set WV = LN

Your question states that LN is congruent to QR
And OP is congruent to WV

Answer 33

oh so I have to do the opposite? y+8=3y+16 ?

Answer 34

wait no thats still -4

Answer 35

im not sure

Answer 36

Flipping sides of the equation won't change anything

For example

Apple = Banana

and

Banana = Apple

are going to be the same thing

Answer 37

We know that QR = LN
We know this because the question says that they are congruent.

We also know VW = OP

You have to look at the values that are given for these line segments in the image.

So for QR = LN
in the image, we can see that QR = -x
and that LN = y + 8

so QR = LN
we plug in what we just got
\(\Large -x = y+8\)

That's one of our equations.

Can you do the same for VW = OP?
(Also VW is the same thing as WV, it doesn't matter which way you write the letters because the line will still stay the same.)

Answer 38

3y+16=-x

Answer 39

Perfect!

Answer 40

So we have

-x = y + 8
3y + 16 = -x

There are multiple ways to solve this. Do you know how to solve systems of equations? If so we can just "cheat" and just use a calculator or graph it. Otherwise, we can work it out because knowing how to solve systems of equations is really important

Up to you

Answer 41

y=-x-8

y=-x/3-16/3

Answer 42

Yes, now you can subtract the equations so that the y cancels out and we're left with x

However, the substitution method is much more easier in this case than doing this elimination method

If you know, we have
-x = y + 8
3y + 16 = -x

Plug in -x = y + 8 into the second equation
So in place of that -x, we can replace it with y + 8
That way, we'll be able to solve for y

Does that make sense?

Answer 43

so first subtract the two equations?

Answer 44

If you want to go that route, it would be messier and longer since you're dealing with fractions and then you solve for x and then you have to solve for y

Let's use the substitution method
\(\color{red}{-x}\) = y + 8
3y + 16 = \(\color{red}{-x}\)

We have a \(\color{red}{-x}\) in both of the equations
This is basically like
a = b
c = a

We can then say that b = c

Does that make sense?

Answer 45

so y+8=3y+16 ?

Answer 46

Right on! Now solve for y

Answer 47

-4

Answer 48

Correct

Answer 49

http://prntscr.com/o0yqb1

Answer 50

Let's make a new post for questions as this post is getting quite cluttered