Melody

10

I think there is a problems with this question.

3 points is enough to define a parabola

I am assuming this is supposed to be a standard concave up parabola.

Now (-5,5) and (4,5) both have the same y value so the x half way between them should be the axis of symmetry.

\(x=\frac{-5+4}{2}=\frac{-1}{2}=-0.5\)

The axis of symmetry is x= -0.5

Since one root is at x=-1, the other root should be at x= 0

So the parabola is  

\(y=a(x-0)(x--1)\\ y=a(x)(x+1)\\ \text{Another point is (4,5) so sub that in to find }a\\ 5=a(4)(4+1)\\ 5=a(4)(5)\\ 5=20a\\ a=0.25 so\\ y=0.25(x^2+x)\\ \)

Here is the graph - you can see that this parabola cannot include the point (2,2)

Vertex.  

\(x=-0.5\\ y=0.25*(0.25-0.5)\\ y=0.25*-0.25\\ y=\frac{-1}{16}\\ \text{Vertex is } (\frac{-1}{2},\frac{-1}{16})\)

\(\)

Please put different questions on different posts.

I have no idea what the 'opposite' of a number is...

3. Simplify: y^-7x^3zx^-1y^7z^-4

\(y^{-7}x^{3}zx^{-1}y^7z^{-4}\\ =y^{-7}y^7x^{3}x^{-1}z^{-4}z^1\\ =y^{-7+7}x^{3+-1}z^{-4+1}\\ =y^{0}x^{2}z^{-3}\\ =1x^{2}z^{-3}\\ =x^{2}z^{-3}\\ =\dfrac{x^2}{z^3}\)

LOL

Oh ok whatever you say Chris   

Yep, guest is right, I cant add up properly LOL

9+4+6=19  !!

Thanks guest ;)

2)

\(f(x)=3x-1 \qquad g(x)=x-1\qquad find (f \circ g)(x)\\~\\ (f \circ g)(x)=f(g(x))=f(x-1)\\ \text{So replace the x in the f function with (x-1) }\\ f(x-1)=3(x-1)-1=3x-3-1=3x-4\\ (f \circ g)(x)=3x-4 \)

I have set up the 2 ratios here.  You must keep the same ratios but make the number of guinea pigs the same.

The lowest common multiple of 2 and 3 is 6

So this is the ratio of the animals

The number of animals in total is a multiple or 18.  The smallest number is 18    :)

There is a reason :)

Think about this

\(4^2\div 4^2 = 4^{2-2}=4^0 \qquad \text {I have used the index laws}\)

but

\(4^2 \div 4^2 = 16\div 16 = 1\)

therefore

\(4^0=1\)

On the calculator you can also use the  x^y   button :)

 Please watch and learn MathNerd(version2.0) :)

What can be divided into 25 billion to get 7 billion EXACTLY?

25/7 = 3.5714285714285714

So the answer is

\(3.\dot57142\dot8 \quad billion\:\: times\)

This is a recurring decimal - it can be expressed exactly as a fraction.

So it is NOT an irrational number. It can and is an exact value.