Sorry BluePhoenix but what does P and NP stand for? 

Please username, can you post your working as well otherwise the question asker cannot learn.

if you edit you post to do this, and it is correct, then i will give you 3 points.  

CPhill gave you lots of great ideas.

If you want to plot   $$y=x^2+5x+4$$   without plotting a whole lot of points this is the best way.

First the y intercept is where x=0 so substitute in x=0 and you will get y=4 (the number tacked on the end- this is called the constant) 

This in not an overly important point to find but it is very easy to find (0,4)

Now lets look for some important points.  If they exist we want to find the x intercepts these can also be called the roots or less often the zeros of the equation.  You can factorise and find them that way or you can find them using the quadratic equation.

I'm going to factorise.  I need 2 numbers that multiply to 4 and add to 5. That is easy, 4 and 1

$$y=(x+4)(x+1)$$    I want the answers when y=0  (That is the equation of the x axis)

$$0=(x+4)(x+1)$$     If 2 things multiply to give zero then one of them must be zero.

x+4=0   or   x+1=0

x=-4 or x=-1

Thes are the roots so plot them.

 now parabolas are symetrical so the axis of symmetry must be

 $$x=\frac{-4+-1}{2}\\

x=\:-2.5$$

Find the vertex by sub'ing in x=-2.5 to find the y value

Then you have the vertex and 2 roots and that is enough to fully define your parabola.

Did you post the question and the answer Username?

How novel!  Did you get it right?  

Is this what you mean?

$$\frac{x+7}{x}\div \frac{x}{9}$$

I didn't know that you spelt caret like that!  I learn some thing every day!

This is an exerpt from Wolfram|alpha,

It seems the shape is a caret, but the symbol is a hat.

Just a technicality, I know - I am sure either is fine.

Hat

what is 2(a-10)=6a

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I think there's a slight error, here.

We have

2a -20 = 6a    subtract 2a from both sides

-20 = 4a         divide by 4 on both sides

-5 = a      or      a = -5

That's only found on "apple" computers......

Seriously, I think you meant "caret" symbol (for use as an exponent??)

It should be under the "6" on your keyboard

If you're talking about the calculator, just hit the x^y key

7x/2+7y/3=28/3 x/4+y/3=5/6 How would I solve for elimination?

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So we have

7x/2+7y/3=28/3

x/4+y/3=5/6

Let's multiply the first equation through on both sides by the common denominator of 2 and 3, (6), and let's multiply the second equation on both sides by the common denominator between 4, 3 and 6, (12). This gives

21x + 14y = 56  (Equation A)

3x   + 4y =   10  (Equation B)

Notice how this gets rid of those nasty fractions !! Now, I know there is a unique solution to this - don't ask me how I know, I just do - so let's proceed thusly:

Let's "eliminate" x........We can do this by multiplying the second equation by -7  on both sides. This gives...

21x + 14y =  56

-21x - 28y = -70      ......Now. just add the two equations together....this gives

-14y = -14     ........so it appears that y =1

Now, to find x , just substitute "1" for y in any of the equations - hint, I might pick Equation B - and see what x is.  You should check these values in all the equations to make sure they "work."

Re: How do you draw a quadratic function without plugging in numbers and plotting points?

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If you're taking Algebra, you will probably learn how to do some of this. If you take Pre-Calculus or Calculus, you will learn many other techniques that will enable you to "see" what a particular quadratic might look like. Barring that, unless it's a "basic" graph, you might have to be stuck with plotting (some) points. This could become tedious.

Here's a site where you can look at the graph of any quadratic (or any other polynomial in one variable) you specify:

The answer is 1316.072 .

Where

tan-1(x)=7/11

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We're just looking for an angle whose tangent = 7/11. Go to the on-site calculator, hit the 2^nd button, and then the "atan" button......key in your "7/11" and hit enter.

Note that this angle could also lie in the 3^rd quadrant, depending on the situation.

$${\frac{{\mathtt{1.85}}}{{\mathtt{3.25}}}} = {\mathtt{0.569\: \!230\: \!769\: \!230\: \!769\: \!2}}$$Ms^2 and you were the 1000th question. Good Job Sir!

2a-20=6a

4a=20

the answer is a=5

Questions?

Um, post any questions

the answer is 11/12

what is the formula to find the area of a trapazoid and please give an example

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I always relate this to the same "formula" as the area of a triangle.......(1/2)hb.

But, instead of one "base," we have to add the two parallel bases. Thus we have (1/2)h(b₁ + b₂).

Have a look at the following illustration.........

Let the height (CE) = 3

Let (AB) = base one = b₁  = 6

Let (CD) = base two = b₂ = 4

So the area = (1/2)h(b₁ + b₂) = (1/2)(3)(6 + 4) = (1/2)(3)(10) = (1/2)(30) = 15 sq. units

To see how this "formula" could be developed, look at this

Notice that we have a rectangle (CDFE) which has an area of (EF)*(CE)

And notice that we have two additional triangles with bases (AE) and (BF) and height (CE).

And the area of these two triangles = (1/2)(AE)(CE) + (1/2)(BF)(CE) = (1/2)(CE)(AE + BF)

So the total area is given by (EF)*(CE) + (1/2)(CE)(AE + BF) = (1/2)(CE)(2EF + AE + BF)

Now, note that 2EF = (EF + CD), since EF = CD     .... So we really have

(1/2)(CE)(2EF + AE + BF) = (1/2)(CE)(CD + EF + AE + BF)

But AE + EF + BF = AB   ...  So we have

(1/2)(CE)(CD + EF + AE + BF) = (1/2)(CE)(CD + AB) = (1/2)(CE)(AB + CD ) = (1/2)h(b₁ + b₂)  !!!

I hope this helps you to see how the "formula" "works".....

BTW.....we're glad to have you on the forum, bioschip !!

If x is an obtuse angle whose sine = !/2, then x must lie in the second quadrant. This angle would be the same as a 30° reference angle in the first quadrant, i.e., 150 degrees. And cos(x) would have the same value as a 30 degree angle in the first quadrant, (√3)/2. except that it would be negative in the second quad.

top and base * hight

Hi bioschip,

I think a trapezoid is another name for a trapezium and the area of a trapezium is

A = the average of the two parralel sides x perpendicular height

Does that make sense to you? 

To get the average of 2 numbers, you add them together and divide by 2.