Answer:
Step-by-step explanation:
(Let the point where the altitude from 
intersects 
be called as point 
.) First, let's find the area of parallelogram 
. The area of a parallelogram is simply 
, where 
is the parallelogram's base and 
is the parallelogram's height. If we let and 
be the base and height respectively, since we are already given their lengths, we know that the area of parallelogram will be 
.
Now, how does this information matter, you might ask? Well, we can take either <em>or </em>
to be the base and either or 
to be the height. In this case, let's take the latter two options, as we are looking to find the length of .
Therefore, we know that the area of parallelogram can also be found by calculating 
. Since we know the values of the area and , we can write the following equation to solve for :
(Substitute 
and 
into the equation)
(Divide both sides of the equation by 
to get rid of 's coefficient)
(Simplify)
(Symmetric Property of Equality)
Hope this helps!
Answer:
k = -2.
Step-by-step explanation:
5(3 - 2k) = 2k + 39 Distribute the 5 over the parentheses:
15 - 10k = 2k + 39
15 - 39 = 2k + 10k
12k = -24
k = -2.
Answer:
48 square m
Step-by-step explanation:
The area of a parallelogram is simply b * h, where b is base and h is height. In this case, b = 8 and h = 6. So:
A = bh = 8 * 6 = 48 square m
Answer: b) they loaded 112356 lbs of cargo
Step-by-step explanation:
When a boat or an object floats in water, the volume of water that it displaces is equivalent to its weight.
When moving into the port, the cargo boat displaced 2200 ft³ of water. Since the density of water is 62.42 lb/ft³ and mass = density × volume, then the mass of the cargo boat on entering the port is
2200 × 62.42 = 137324 lbs
On leaving the port, it displaces 4000 ft³ of water. The mass of the cargo boat on leaving the port is
4000 × 62.42 = 249680 lbs
The difference in both masses is
249680 - 137324 = 112356 lbs
Therefore, they loaded 112356 lbs of cargo
