CPhill

If we join the centers of the top three circles....we will have an equilateral triangle with a side of 8

The height of this triangle  4√ 3  units

And if we join the bottom three circles...we have another equilateral triangle with the same height

So....by symmetry......the total height  =  2r + 2 (4√ 3) =    2(4) + 8√ 3  =

8 + 8√ 3 =

8 ( 1 + √ 3) units

First one

Consider    2^x

When x =  0      y = 2^0  = 1

So...the point (0, 1)  is on the graph of g(x)

The only graph on which this happens for (x) is the first one

So the solutions are x = 0   and x = 2

For the second one we have only one intersection point  ... x = 1

2x + 6y= 18

-3x - 9y= -27

To make this easier  divide the first equation through by 2    and the second through by 3 and we have that

x + 3y   =  9

-x - 3y  = - 9          add these

0 = 0

When we have this situation.....there are infinite solutions  for (x, y)

For instance   (0, 3)  solves the equations

or

(9, 0)  also   works

This is actually the same line....mutiply the second equation by -1  and we get

x + 3y = 9       the same as the first equation  !!!

Second graph : https://www.desmos.com/calculator/hn25azutsv

Domain : All real numbers

Range : (-inf, 4.848 ]

Rel max at (-1,0)      Global max at  (1.366, 4.848)

Rel min at (-.366, -.48)

End behavior : DOWN on both sides

Inc intervals :  (-inf, -1)   and (-.366, 1.366)

Dec Intervals :  (-1, -.366) and (1.366, inf )

Here is the first graph :  https://www.desmos.com/calculator/tujglplzxg

Domain : All real numbers

Range : All real numbers

Rel max : (-4, 7)

Rel Min : (-4/3, -2.481)

End behavior   :    as f(x) approaches Inf  ....UP

                             as x approaches - inf ....DOWN

Inc intervals   (-inf, -4)   and (-4/3, if)

Dec intervals :  ( -4, -4/3)

Let the first number = x

And the second number  = x + 3

And we know that

2(x + 3) + 4  = 3x     simplify

2x + 6 + 4  =  3x

2x + 10 =  3x

10 =  x   =  the smaller number

I think the problem that you are having is determining which graph is the correct one

Consider the funtion     (7/3)x - 3

This is straight line

Note that when x = 0   then y = -3

So   the line contains the point (0, - 3)

Note that the second graph has to be correct because the straight line contains the point (0, -3)

Notice that the graphs intersect at  x = 0    and x = 3  .....the are the solutions

Does that make sense ???

I like this problem.....!!!

Were you assigned this or did you make it up   ????

Let's find the slope to   7x + 6y = 17

The slope in the form Ax + By = C  is    -A / B

So....the slope is  -7 / 6

And a perpendicular line to this will have negative reciprocal slope =    6/7  = m

And  if this perpendicular line has a y intercept of 12....the point (0, 12) is on the line = (x1, y1)

So...the equation is

y = m ( x - x1) + y1         fill in what we know

y = (6/7) ( x - 0 ) + 12

y = (6/7)x + 12

Here's a graph : https://www.desmos.com/calculator/oyd29rauvm

Great job !!!!