Answer:
11.8cm²
Step-by-step explanation:
The area of the regular pentagon is expressed as;
A = pa/2
p is the perimeter of the pentagon
a is the apothem
Since p = 5s
s is the side length, hence;
A = 5sa/2
Get the side length s;
central angle = 360/5
central angle = 72degrees
angle in the right angle triangle =72/2 = 36degrees
Using SOH CAH TOA
sin 36 = x/2
x = 2sin36
x = 1.1755
s = 2x
s = 2.35cm
Get the area
A = 5(2.35)(2)/2
A = 5(2.35)
A = 11.8cm²
Hence the area of the regular pentagon is 11.8cm²
Answer: 17500 meters
Step-by-step explanation: 7 times 2.5 is 17.5 and one meter is 0.001 kilometers so
17.5 in meters is 17500.
Answer:
y = 3
x = 2 - z
Step-by-step explanation:
We have the system:
2*x+y+2*z=7
2*x-y+2*z=1
5*x+y+5*z=13
In the first and second equations we have the term (2*x + 2*z) = A
Then we can rewrite the first two equations as:
A + y = 7
A - y = 1
isolating A in the first equation, we get:
A = 1 + y
Now we replace this in the other equation:
(1 + y) + y = 7
1 + 2*y = 7
2*y = 6
y = 3.
then:
A + y = 7
A + 3 = 7
A = 7- 3 = 4
A = 2*x + 2*z = 4.
Now let's go to the third equation:
(5*x + 5*z) + y = 13
we can rewrite the thing inside the parentheses as:
(5/2)*(2*x + 2*y) + y = 13
And we know that:
2*x + 2*z = 4
y = 3
then this can be written as:
(5/2)*(4) + 3 = 5*2 + 3 = 13
Then we can conclude that:
y = 3
2*z + 2*x = 4
2*(z + x) = 4
(z + x) = 4/2 = 2
x = 2 - z
Notice that the solution is not only a point, we have infinite solutions for this problem.
2x+3y=4
x=2-3/2y
3x+4y=7
3(2-3/2y)+4y=7
6-9/2y+4y=7
-1/2y=1
y=-2
3x+4(-2)=7
3x=15
x=5
So the two numbers are 5 and -2