hectictar

It is so close to zero that this calculator just says it is equal to zero.

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After thinking about this some more...I think this is a much better and simpler way to put it...

Jenny's number  =  2 * n²             , where  n  is an integer.

...I guess I'll leave the old answer there... even though I REALLY don't like it anymore    haha

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The prime factorization of Jenny's favorite positive integer must contain an odd number of 2's and an even number of anything other than 2.

For example, it could be..

2 * 3 * 3  =  18   ,

2 * 2 * 2 * 5 * 5  =  200   ,

2 * 7 * 7 * 3 * 3  =  882   , or just

2  =  2  .

If it satisfies this condition, then the square root of that number can always be written like this..

\(\sqrt2*\sqrt{\text{any positive integer}^2} \\~\\ \sqrt2*\text{any positive integer}\)

And multiplying, or dividing, this by \(\sqrt2\)  will result in an integer.

As long as this is in a right triangle, and the opposite and adjacent sides are not the hypotenuse...

tan( angle )  =  opposite / adjacent

                                                               Plug in the values we know for opposite and adjacent.

tan( angle )  =  1290 / 48

                                                               Take the inverse tangent of both sides.

angle  =  arctan( 1290 / 48 )

                                                               Put this into a calculator to get...

angle  ≈  87.869º

Here's another way to do that one....

2x² + 7x + 5

Multiply the  2  and the  5  together to get  10  .

What two numbers multiply to  10  and add to  7  ? →   +2   and   +5

So, we can split the middle term like this:

2x² + 2x + 5x + 5              Notice here how if we combined like terms, we'd get  7x  again.

                                          Factor  2x  out of the first two terms.

2x(x + 1) + 5x + 5

                                          Factor  5  out of the last two terms.

2x(x + 1) + 5(x + 1)

                                          Factor  (x + 1)  out of both remaining terms.

(x + 1)(2x + 5)

9.1e18

=  9.1 * 10¹⁸

Multiplying any number by 10 moves the decimal point to the right one place.

For example.......     2 * 10  =  20

                                20 * 10  =  200

                                2.5 * 10  =  25

So, multiplying any number by 10, 18 times,  moves the decimal point to the right 18  places.

For this problem, we need to move the decimal point to the right 18 places.

=  9 100 000 000 000 000 000

Yeah, I was thinking a video might be helpful..

I also wouldn't have expected a clean answer either...it beats me!!

I didn't understand at first so I tried doing it, I'll share some pictures in case it helps 

Since I didn't have any paper that was big enough to make it 12 inches by 9 inches,

I made it 12 centimeters by 9 centimeters.

Then, fold from the top right corner to the bottom left right corner ( I did it backwards..oops! ).

At that point, you can find what  x  is.

This picture shows why the side length is  x  and the hypotenuse is  12 - x  .

Then unfold it and draw a the line parallel to the bottom edge like this...

Now you're left with a right triangle where the legs are  9  and  12 - 2x  cm long, and the hypotenuse is the crease.  And looky here...it is right about 11 and a quarter centimeters long! 

I dont think I ever would have figured that one out on my own!!

x + ( - .50 )  =  4

x  -  0.5  =  4                 Add  0.5  to both sides of the equation.

x  =  4.5

x  =  45/10                    Reduce the fraction by 5 .

x  =  9/2

(3x + 2)²

=  (3x + 2)(3x + 2)

Multiply each term in the first set of parenthesees by each term in the second set of parenthesees and add these products together.

=  (3x)(3x) + (3x)(2) + (2)(3x) + (2)(2)

=  9x² + 6x + 6x + 4

=  9x² + 12x + 4

If you have an equation in this form:

\(ax^2+bx+c=0\)

, and then solve that equation for  x , you will get

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

, which is the quadratic formula.