Given:
A figure of a triangular prism.
Height of triangular base =
yd
Base of triangular base = 4 yd
Height of prism = 4 yd.
To find:
The volume of the triangular prism.
Solution:
Volume of a triangular prism is:
...(i)
Where, B is the area of triangular base and h is the height of the prism.
Area of triangular base is:




Putting
and h=4 in (i), we get




The volume of the triangular prism is 77.3 cubic yards. Therefore, the correct option is 2.
Move all the terms involving the sine to one side, and all the numbers to the other:

Answer: -1
Step-by-step explanation:
slope formula: y=mx+b
m=slope
y=(-1)x+8
Let
be the two numbers. We have two pieces of information:
(the difference between the two numbers is 2)
(their product is 224)
From the first equation, we can deduce 
If we plug this expression in the second equation, we have

If you solve this equation with the usual quadratic formula you get the solutions

So, you have the following couple of solutions, recalling that x is 2 more than y:

Answer:
solution is
[-3,-1]
Step-by-step explanation:
we are given

Firstly, we will find critical values
so, let's assume it is equal

now, we can break absolute sign
For
:

we can solve for x

Add both sides by 20


Divide both sides by -10
and we get

For
:

we can solve for x

Subtract both sides by 20


Divide both sides by 10
and we get

so, critical values are


now, we can draw a number line and locate these values
and then we can check inequality on each intervals
For
:
We can select any random value from this interval and plug that in inequality
and we get
we can plug x=-5



so, this is FALSE
For
:
We can select any random value from this interval and plug that in inequality
and we get
we can plug x=-2



so, this is TRUE
For
:
We can select any random value from this interval and plug that in inequality
and we get
we can plug x=0



so, this is FALSE
so, solution is
[-3,-1]