Melody

a^b=27

and, a*(b)^2 = 8

so, what is the value of  a and b ?

I graphed both these equations and the intersection is where they are both true.

The approximate solution from the graph is a=0.4555   and   b= -4.191

Let's see how close this is

0.4555^-4.191 = 26.9944941684914683    rounded of to 1 dp   =    27.0

0.4555*(-4.191)^2 = 8.0006210955            rounded of to 1 dp   =     8.0

That is pretty close :)

Here is the graph that I used.

6/((-i(sqrt(3))/2)

I have assumed that   \(i=\sqrt{-1}\)

\(6\div ((-\sqrt3 i)/2)\\ =6\div \frac{-\sqrt3 i}{2}\\ =-6\times \frac{2}{\sqrt3 i}\\ = \frac{-12}{\sqrt3\; i}\\ = \frac{-12}{\sqrt3\; i}\times\frac{\sqrt3\;i}{\sqrt3\;i}\\ = \frac{-12\sqrt3\;i}{3*-1}\\ = \frac{4\sqrt3\;i}{1}\\ =4\sqrt3\;i \)

Good answer guest :)

This one is a bit horid isn't it.

I think the question should have stated more clearly that each child only has one type of pet.  Anyway,

I am going to try to :)

1) Beth has hamster s at her house.the number of hamsters is equal to the sum of the number of birds at Kristin's house and the number of dogs at Wendi s  house.

2) John has the same number of cats as Wendi has dogs. If these four children have a total of 12 pets how many pets are at each house. PLEAS EXPLAIN!!!!!

This is made to sound more complicated than it realy is because each child only has one type of pet and thew are all different from one another so you can just talk about 

hamsters, birds, cats and dogs.  So lets simplify the question.

1)  The number of hamsters is equal to the number of birds + the number of dogs.

2)  Number of cats = number of dogs.  

Let the number of cats be x, then number of dogs is x too

Let the number of birds be y

then the number of hamsters is x+y

so altogether we have x+x+y+(x+y) pets and this equals 12 pets.

x+x+y+(x+y) =12

3x+2y=12

x and y have to both be more than 0 and whole numbers

If x is 1 y is 4.5 which is not a whole number

If x=2 then y would  be 3

If x=3 y =1.5 which is not a whole number

If x=4 then 0 and that is too little

So x=2 and y=3

So there are 2 cats and 2 dogs and 3 birds and 2+3=5 hamsters.

Just like our guest found.  :)

How many yards of material from a 24-yard length of cloth remain after 3 pieces, each 31/2 yards long, and 5 pieces, each 21/4 yards long, are removed?

You have not said if you are allowed to use a calculator.  So I am going to assume that you are allowed to. :)

3 pieces, each 31/2 yards long = 3*(3+1/2) = 10.5 yards

and 5 pieces, each 21/4 yards long = 5*(2+1/4) = 11.25 yards

left = 24 - 10.5 - 11.25

24-10.5-11.25 = 2.25

So there will be 2.25 yards left

 tan(4.2/6.5)

I expect you mean

\(tan\theta = (4.2/6.5)\\ or\\ \theta=tan^{-1} (4.2/6.5) or\\ \theta=atan(4.2/6.5)\)

enter is as 

2nd  atan   (4.2/6.5)

makesure the calc is set to degrees

-5[4-(-3)(2)]

this means

-5x(4-(-3)x(2)]

What is -3 x -2  ?    that is the first thing you have to do :))

Start by multiplying both sides by 3 :)

3.5(x-8/4)=2.8

simplify 8/4=2

3.5(x-2)=2.8

now divide both sides by 3.5

\(\frac{3.5(x-2)}{3.5}=\frac{2.8}{3.5}\\ x-2=\frac{2.8}{3.5}\\ \mbox{Now plus 2 to both sides}\\ x-2+2=\frac{2.8}{3.5}+2\\ x=\frac{2.8}{3.5}+2\\\)

Now finish it with a calculator.  Remember that a fraction line is divide.  :)

2.8/3.5+2 = 2.8

oh,

It was just lucky that I saw you last post.  It is very easy to miss things here.

If you use someone's name in the first line it will help them to notice your post. :))