All Triangles are equilateral ( each side = 4)
Area of a Triangle is (B x H)/2. B being the base ( 4) & H the altitude.
WE know that altitude in an equilateral triangle, H = ( side x√3)/2
So H= (4√3)/2 = 2√3
The area of one triangle = (4 x 2√3)/2 = 4√3
And for the 3 triangles the lateral area = (4√3) x 3 = 12√3
Answer:
The answer is that x = 6 and y = -6
Step-by-step explanation:
In order to find these values, we can use elimination. To do so, we multiply the first equation by 2 and then add the equations together.
4x + 8y = -24
-4x - 2y = -12
------------------
6y = -36
y = -6
Now that we have this value, we can plug the value into one of the originals and find x.
2x + 4y = -12
2x + 4(-6) = -12
2x - 24 = -12
2x = 12
x = 6
Answer:

Step-by-step explanation:
The given system is:


Since I prefer to use smaller numbers I'm going to divide both sides of the first equation by 3 and both sides of the equation equation by 6.
This gives me the system:


We could solve the first equation for
and replace the second
with that.
Let's do that.

Subtract
on both sides:

So we are replacing the second
in the second equation with
which gives us:





Now recall the first equation we arranged so that
was the subject. I'm referring to
.
We can now find
given that
using the equation
.
Let's do that.
with
:



So the solution is (8,-1).
We can check this point by plugging it into both equations.
If both equations render true for that point, then we have verify the solution.
Let's try it.
with
:


is a true equation so the "solution" looks promising still.
with
:


is also true so the solution has been verified since both equations render true for that point.
The temperature must rise 5 degrees to reach the original temperature
Answer:




Solving for
we got
and replacing this we got:



And then the best option for this case would be:
b.csc x
Step-by-step explanation:
For this case we have the following expression given:

We know from math properties that the definition for cot is 
If we use this definition we got:


Now we can use the following identity:

Solving for
we got
and replacing this we got:



And then the best option for this case would be:
b.csc x