Question

If P(x+1)=3x^2-2x-5, Find P(4).

Answer 1

@waterineyes may answer is P= 12x-20 am I right?

Answer 2

No..

Answer 3

u should get a full value with no variables.
since, x + 1 = 4
hence, x = 3. sub this in the eq.

Answer 4

Thanks alot

Answer 5

In place of x you have to substitute 3:

See, P(x+1)

Here we have to find P(4)

so,

x + 1 = 4

or x = 3

Now put this x = 3 in the given function:

\[3(3)^2 - 2(3) - 5\]

Calculate its values..

Answer 6

16

Answer 7

Yes you are absolutely right..

Answer 8

what i did was i factor it so I get 12x-20

Answer 9

After factoring you can put the value also:

12x - 20 = 12*3 - 20 = 36 - 20 = 16..

The main thing is to put the values of x here..

Answer 10

Thanks a lot guys!

Answer 11

Welcome dear..

Answer 12

@waterineyes can you please help me in my attached files. My teacher said it has an answer but my mom said It doesn't have

Answer 13

My internet speed is slow so it is taking time in opening so wait please.

Answer 14

it is ok dear

Answer 15

Line I is parallel to what??

And Line II is perpendicular to what??

Answer 16

That is what I told to my teacher too and he send me this email Problem 1 (a) is not as confusing as you think. All you have to do is rearrange both equations to solve for y in each case and see what the slopes, the coefficient of x are. You can then figure out what A1/B1 is in terms of A2 and B2, if the lines are assumed to be parallel or perpendicular to each other.
@waterineyes

Answer 17

Yes I got it now:

Write here your first equation..

Answer 18

It is in attached file cause dont know how to use drawing here

Answer 19

Okay I will do it for you..

Answer 20

Thanks a lot. This is in my review paper for finals.Thanks a lot @waterineyes

Answer 21

\[A_1x + B_1y = C_1\]

Evaluate y from here:

\[y = \frac{C_1 - A_1x}{B_1}\]

Or we can write it as:

\[y = \frac{-A_1}{B_1}x + \frac{C_1}{B_1}\]

Now can you tell me coefficient of x here??

Answer 22

I dont understand still

Answer 23

I show you step by step but do you know about coefficient??

Answer 24

is a multiplicative factor in some term of an expression @waterineyes

Answer 25

Yes..
Suppose you are given with -5x..

So, -5 is the coefficient here..

Answer 26

is it -A,B and C?

Answer 27

I will come to it later..

See, you are given with:

\(A_1x + B_1y = C_1\)

Subtract both the sides by \(A_1x\)

You will get:

\[B_1y = C_1 - A_1x\]

For simplicity write the x terms in front:

So,

\[B_1y = -A_1x + C_1x\]

Divide by \(B_1\) both the sides:

\[y = \frac{-A_1}{B_1} + \frac{C_1}{B_1}\]

Till here any difficulty??

Answer 28

There will not come \(C_1x\) it is simply \(C_1\) in the second last step..

Answer 29

so this is the answer for parallel in what number and perpendicular?

Answer 30

This is only 25 % complete..

Answer 31

so there is a lot of steps to get the answers?

Answer 32

Have you got the steps tell me honestly...

Answer 33

the one you teach me yes

Answer 34

So, we got:

\[y = \frac{-A_1}{B_1}x + \frac{C_1}{B_1}\]

Now tell me what is the term attached to x here??

Answer 35

the A2?

Answer 36

In the equation I have just written above..

i think there is \(\frac{-A}{B}\) attached to the x.. right??

Answer 37

Sorry..
\[\frac{-A_1}{B_1}\]

Answer 38

i dont know.I just understand it when you try to explain it to me

Answer 39

yes it is attached

Answer 40

That is what I am trying to say..

This is called the coefficient of x..

So, this is called slope also in case of Lines..

It is another vast concept..

But here you can remember that the term attached to x is called slope if the given line is of the form: y = mx + c

Here m is the slope..

So,

\[Slope = \frac{-A_1}{B_1}\]

Okay??

Answer 41

yes

Answer 42

therefore?

Answer 43

Similarly find the Slope of second given equation:

\[A_2x + B_2y = C_2\]

I am writing directly:

\[y = \frac{-A_2}{B_2}x + \frac{C_2}{B_1}\]

So, slope of the second line is :

\[Slope_2 = \frac{-A_2}{B_2}\]

Got till here??

Answer 44

@waterineyes this is parallel to A1+B1=C1

Answer 45

A1x+B1y=C1

Answer 46

I am coming to all your doubts..

Firstly answer me do you get these steps also??

Till now we have calculated the slope of first and second line..

Answer 47

yes, You explain it good to me steb by steb

Answer 48

So, now I am writing it in CAPITAL:

IF THE TWO LINES ARE PARALLEL, THEN THERE SLOPES ARE EQUAL..

Can you remember this for lifetime??

Answer 49

yes and if it is perpendicular lines consist of two slopes are negative reciprocal

Answer 50

I remembered my teacher teach us this

Answer 51

So, according to this property:

\[\color{green}{\frac{-A_1}{B_1} = \frac{-A_2}{B_2}}\]

Finally we have found the relation in case of PARALLEL LINES:

\[\large \color {blue}{\frac{A_1}{B_1} = \frac{A_2}{B_2}}\]

Answer 52

Thanks a lot

Answer 53

Hawwwwwwww..
You have been taught this thing.....

Now this becomes easy then..


Now, in Case of Perpendicular, one slope is negative reciprocal of the other.

So, in case of PERPENDICULAR LINES:

\[\large \color{green}{\frac{-A_1}{B_1} = -(\frac{B_2}{-A_2})}\]

Or,

\[\large \color{blue}{\frac{A_1}{B_1} = \frac{-B_2}{A_2}}\]

Answer 54

so this is the perpendicular?

Answer 55

yeah he is explain it a little in our class though

Answer 56

@waterineyes are u a teacher? U teach us good

Answer 57

No, I am still a student..

I Love Mathematics..

In School Times, my Math Teacher Mr. S Arjunan was an excellent teacher..

Today, What I know about Mathematics is just because of him..

Answer 58

Instead I am in College now..

Answer 59

@waterineyes where u from? He did well in teaching you. You are definitely Great!

Answer 60

I am from \(\large \color{green}{INDIA}..\)

Answer 61

my Indian Classmates are smart in Math too.

Answer 62

Oh that is the really nice thing..

Answer 63

@waterineyes we are done right? my teacher will be herein a minute.

Answer 64

They are excellent in terms of Math here.

Answer 65

Yes we have done..