CPhill

Did you leave something out???....    " X " could take on many values......

An angle > 90  and < 180  is known as an obtuse angle

This  is just a multiple  of the basic Pythagorean "triple,"  3 - 4 - 5

So.......multiplying through by 3, we get

9 - 12 - 15

And.....the  legs are   9 and 12

2x^2 + 3x + 1   =

(2x + 1) ( x + 1)

Using   a^n / a^m   =   a^(n-m)   we have

5^4 / 5^2   =   5^(4 - 2)   =  5^2   =   25

Since the log bases are the same, we can forget the log part and solve this :

x^2 - 4x   = 3x - 10       subtract 3x from both sides....add 10 to both sides

x^2 - 4x - 3x + 10  = 0     

x^2 - 7x + 10  = 0     factor

(x - 5) (x - 2)  = 0

Set both factors to = 0   and x = 5   or x  = 2

However.....we must reject 2 because it makes both logs undefined.....so.....

x = 5  is the solution

Actually....you probably divided the figure into a trapezoid and a triangle or as a rectangle and two triangles??....I just thought  it might be kinda' neat to show you another way.....plus.....it gives me a chance to "show off"....LOL!!!!

3. The corresponding angles in triangle ABC are congruent to the corresponding angles in triangle FGH. The measures of two corresponding sides of the triangles are given. 

AB=6, AC=8, FG=x+10, and FH=4x. What is the length of FH?

We have, by similar triangles, that

AB/AC  = FG/FH

6 / 8  =  [ x + 10] / [4x]        cross-multiply

6 * 4x  =  8 [x + 10 ]     simplify

24x   =   8x + 80     subtract 8x from both sides

16x  = 80      divide  both sides by 16

x  = 5

So.....FH  = 4(5)   = 20

Kenya.....(1) can be solved with something called "Pick's" Theorem...it can be used when the vertices of a figure lie on integer values for x and y....just like yours do.....!!!

The "points" described below  are the occasions where the grid lines intersect

The area is given by

Boundary points/ 2  +  interior points  - 1

The number of boundary points  =  14

The number of interior points  = 20

So

The area  is

14/2 + 20 - 1  =

7 + 20 - 1  =

26 sq units

Here's a pic of the boundary points and the interior points:

It will do this....

Hit the log key

Then ... type in 2.17, 5.1   and hit "="

It will return.....