3/4(8p+12)+3/8(16p-8)
=3/4[(8p+12)+1/2(16p-8)]
=3/4[8p+12+8p-4]
=3/4[16p+8]
=3/4*8*[2p+1]
=6[2p+1]
=12p+6
Answer:
4
7
w
=
16
Multiply both sides of the equation by
7
4
.
7
4
⋅
4
7
⋅
w
=
7
4
⋅
16
Simplify
7
4
⋅
4
7
⋅
w
.
Step-by-step explanation:
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. :)
The shaded region is a parallelogram.
The formula for the area of any parallelogram is

.
The base of the parallelogram is 2 meters long (given).
The height of the parallelogram is 9 meters (do not be fooled by the unnecessary information of 14 meters)
The height is 9 meters because the height has to be perpendicular to the base. Thus, the side length must be 9 meters.
Multiply them together.

The area of the parallelogram is 18 square meters.
Well, if he shoots 15 shots in 5 minutes then that means he shoots 3 per minute.
3 x 12 = 36
In 12 minutes, he will have shot 36 shots.