Answer:
you need 100ml of 5X TAE and 400ml of water.
Step-by-step explanation:
You need to use a rule of three:

where:

and

Therefore:


Then just rest the TAE volume to the final Volume and you get the amount of water that you need to reduce the concentration.
The table you drew under the question is exactly the right way to start.
-- Make a second column, next to the 6 and 7. This column will be
the actual number of each thing.
-- You know that there are 42 marbles, so write '42' in the box
next to the 6, on the 'Marbles' line.
Now you need to figure out what to write in the 'Stones' line, next to the 7.
-- Look at the 'Marbles' line. There's a 6 and then a 42.
Ask yourself: " Self ! What does the 6 have to be multiplied with to get 42 ?"
-- Whatever the answer is, drop down to the 'Stones' line,
and multiply the 7 by the same number.
The product is the total number of stones, and it goes in the box.
.
.
.
(The mystery number is 7. There are 49 stones.)
I cannot see the images, but...
y = | x | + 5
consider the absolute value function. You know that for every value of x, y will be greater than or equal to 5. this means that the y-intercept will also be the bottom of the curve.
Plug a few values in for an idea of what the graph will look like:
f(-1) = 6 (-1,6)
f(1) = 6 (1, 6)
f(-2) = 7 (-2, 7)
f(2) = 7 (2, 7)
The graph will have a minimum value at (0,5), where two lines will converge. The graph will look like a pointy cone with its point at (0,5), with two lines pointing outward and upward from this point. Confirm that the graph passes through the coordinates provided above!
It is true. YOU'RE WELCOME :D