CPhill

4a^5          2b^2

____   *   _____             swap denominators

7b^4          2a^4

4a^5         2b^2

____   *   ______

2 a^4        7b^4

2a  *    2

         ______

          7 b^2

4a

___

7b^4

Second answer, NSS!!!

x^2  - 16                x^2 + 5x + 4

__________    ÷    ___________

x^2 + 5x + 6          x^2 - 2x  - 8

(x + 4) (x - 4)             (x + 1) ( x + 4)

____________    ÷    ___________

(x + 3) ( x + 2)            (x - 4) ( x + 2)        invert the second faction and multiply

(x + 4) ( x - 4) (x - 4) ( x + 2)

______________________

(x + 3) ( x + 2) (x + 1) (x + 4)

(x - 4)^2 

____________       x cannot be    -3,  -2, 4, -1, -4

(x + 3) ( x + 1)

Third answer

YAH!!!!!!!

We can use the Secant-Tangent Theorem first to find BC

Specifically

The length of the tangent squared  =  the product of length of the tangent * its exterior segment

8^2  =  (4 + BC) * 4  simplify

64  =  16 + 4BC         subtract  16 from both sides

48  =  4BC    divide both sides by 4

12  =  BC

So......AD  = 8  and  AC =   4 + BC  =  16

And these will form two legs of a right triangle with CD as a hypotenuse

So

CD   =  √  ( 8^2 + 16^2)  = √ [ 8^2 ( 1 + 2^2) ]  =   8√5   units

3xy - 4x^2 - 36y + 48x = 0   (1)

x^2 - 2y^2 = 16   (2)

Look at the graph here :

https://www.desmos.com/calculator/kfu7s3izs1

Note that, oddly, the first graph is a straight line ......this is known as a "degenerate conic" which never intersects the second function (a hyperbola)....so....no solutions

I  =  6.5%  =  .065

Yearly

A  =  1234 ( 1 + .065)^4   ≈ $1587.50

Monthly

A  =  1234 ( 1 + .065/12)^(4*12)  ≈ $1599.29

Continuously   ....this uses   Pe^(r * t)

So  we have

1234 *e^(.065 * 4)   ≈ $1600.41

Note that continous compounding isn't much more than monthly  !!!

The common ratio between terms is  1.1

If we are just trying to find the  nth term, we can use

a_n  =  (2.2)(1.1)^(n - 1)

If you are summing these terms we have...

        inf

2.2 * ∑  (1.1)^(n - 1)  

       n=1

I can't see any of the images....I've noted the problem to the Admin

Glad to help, OBT....!!!

How are you seeing this, alan??

What browser do you use  ??