hectictar

There is no way to express a mixed number as a proper fraction.

A fraction must be less than 1 to be proper.

If you have two and a half pizzas, that is more than one pizza.

It can be expressed as an improper fraction, though.

Two and a half pizzas is the same as five halves.

\(2\frac12=\frac52\)

My teachers taught it like this: multiply the whole number by the denominator and add the numerator to it..then take that number and put it over the denominator.

If you can't remember that, do it like this:

\(2\frac12=\frac21+\frac12=\frac{2\times2}{1\times2}+\frac12=\frac42+\frac12=\frac52\)

\(\frac{13,700,000,000\text{ years}}{80\text{ years}}=\frac{\text{x seconds}}{1\text{ seconds}} \\~\\ 171,250,000 \text{ seconds}=x\)

You can multiply both sides by any number and it will not affect the solutions.

For example:

x^2 + 6x - 7 = 0

has the same solutions as:

5(x^2 + 6x - 7) = 5(0)

5x^2 + 30x - 35 = 0

It could be any number.

We can just call it "c"

cx^2 +6cx - 7c = 0

" e " means " × 10ⁿ " where " n " is the number that comes after the " e ".

For example:

3.2e5 = 3.2 × 10⁵ = 3.2 × 100,000 = 320,000

and

4.53e-2 = 4.53 × 10^-2 = 0.0453

It probably stands for "exponent" or something like that..I don't really know. There is also an e that is a special number like pi. It doesn't "do" anything though, it's just a number.

(1/8)^x+3 = 16^2x-1

1/8 = 2^-3      and      16 = 2⁴ 

Substitute.

(2^-3)^x+3 = (2⁴)^2x-1

2^-3x-9 = 2^8x-4

Now that the bases are the same,

we can just set the exponents equal to each other.

-3x - 9 = 8x - 4

-9 = 11x - 4

-5 = 11x

x = -5/11     :)

x² - 8x + 8 = 0

Subtract 8 from both sides.

x² - 8x = -8

Add (-8/2)² = 16 to both sides.

x² - 8x + 16 = -8 + 16

Factor left side and simplify right side.

(x - 4)² = 8

(x + b)² = c

You can see that

b = -4 and c = 8

So.. -4 + 8 = 4

 You are definitely not the first person to make a careless mistake PB, we all do it!!! 

But 200 kilometers by 100 kilometers is still pretty humongous...that is about 124 miles by 62 miles.

I can still answer the question anyway, though.

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perimeter = length + length + width + width

perimeter = 200 + 200 + 100 + 100

perimeter = 600 kilometers

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area = length × width

area = 200 × 100

area = 20,000 square kilometers

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You can just replace the word "kilometers" with whatever units you have. 

volume of a prism = area of base * height

Here is a top-down view of the base.

As you can see, it can be split into 5 triangles.

The area of each triangle = (1/2)(2)(4 tan 36º)(4) = 16 tan 36º

So...

the area of the base = 5 * 16 tan 36º = 80 tan 36º

And so..

the volume of the prism = 80 tan 36º * 16 = 1,280 tan 36º ≈ 929.974 cubic cm

Hey! I got one...just came up with it right now. 

Question: Which side of an ice cube is the coolest?

Answer: Trick question..there's only one side—the west side 

MaxWong... I found out some terrible news!

Betty Crocker has abducted your cousins and is holding them hostage in her evil laboratory, where she steals their DNA and clones them! She uses them for inhumane and illegal research, then she gives the information to the public for monetary gain!

It's sickening.... see for yourself: