Like all problems that involve images within the question, we should definitely try to draw this out. In the picture above, I have done this.
Now, we can see that this is just a simple proportion problem. For every 2.5 cm of height of the flower, we are 2 cm from the opening, or aperture. For every 20 cm of height, how far are we? We can set up the problem like this:
20 ............2.5
-------- = ---------
...x ............. 2
where x is the unknown distance to the aperture from the flower. Now, we just need to get x by itself. A typical way of solving something like this is by doing "butterfly multiplication" which is really just a shortcut haha. Anyway, I can rewrite that equation ^ as:
20×2 = 2.5 × x
Then, to solve for x, we would divide both sides by 2.5. (If you don't know why that is, please let me know and I'll elaborate).
We would then have:
20×2
------- = x
2.5
Which then simplifies to:
x = 16
Try using the same logic for your second question, and if you get stuck, I'd be happy to help! please let me know if any of this doesn't make sense. :)
Answer: C: 12-7x
Step-by-step explanation:
This expression is a good example of the difference of two squares, as 144 is the square of 12, while 49x² is the square of 7x.
Any difference of two squares
can be factored into the sum of their square roots times the difference of their square roots
.
Let's factor our expression.

Out of all the options given, only
is a factor. Hence, option C is correct.
This appears to be just an expression we are simplifying, not an equation we are solving. I THINK you are saying that the expression looks like this:

If you rationalize the denominator, you would get this expression:

which, after simplifying, looks like this:

and that's as simple as I can see that one getting. You can't factor anything out of the denominator to cancel with the numerator, so I think you're as simple as you can get there!
Answer:
18 units^2
Step-by-step explanation:
In dialation, you are essentially multiplying the dimensions by the given scale, in this case 0.5.
0.5 * 6 = 3 units
0.5 * 12 = 6 units
Then, find the area as normal.
3 * 6 = 18 units^2