D. 14
LL = 1/2 * Hsqrt3
7sqrt3 = 1/2 * ysqrt3
24.25 = ysqrt3
24.25/sqrt3 = y
y = 14
440...marked down by 30% means u pay 70%
70% of 440 = 0.70(440) = 308
308 ..marked down by 10% means u pay 90%
90% of 308 = 0.90(308) = 277.20 <== price after markdowns
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. :)
to write 98 as a product of its prime factors we have to first find the prime factors of 98
prime factors are prime numbers by which the given number can be divided by.
98 we have to keep dividing it by prime numbers
98 is an even number so we can first divide by 2
98 / 2 = 49
49 is a multiple of 7 which too is a prime number so we can divide 49 by 7
49/7 = 7
7 can be divided again by 1
7/7 = 1
98 is divisible by 2 and 7
so 98 written as a product of prime factors is
98 = 2 x 7 x 7