Answer:
A. {e, h}
Step-by-step explanation:
In a Venn diagram, the set of elements in any intersection can simply be visualised. The elements contained in the region where the circles representing different sets overlap, are the set of elements of intersection.
In the Venn diagram given, the set of elements contained in the region where the circles representing A and B overlap are {e, h}.
{e, h} is common to both set A and set B.
Answer:
$7.25
Step-by-step explanation:
Total amount spent on the ticket = $40.75
Number of ticket purchased = 5
Processing fee per ticket = $0.90
Unknown:
Cost of each ticket = ?
Solution:
To solve this problem, we need to find the processing fee for the 5 tickets purchase;
Processing fee = number ticket x processing fee per ticket
Processing fee = 5 x 0.9 = $4.5
Now, the real cost a ticket = $40.75 - $4.5 = $36.25
So, cost per ticket is;
Cost =
= $7.25
Answer:
AAS Congruence Theorem
Step-by-step explanation:
Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just don’t want to waste my time in case you don’t want me to :)
Answer:
x = - 
Step-by-step explanation:
To find f(g(x)) substitute x = g(x) into f(x), that is
f(g(x))
= f(x + 1)
= 2(x + 1)² ← expand using FOIL
= 2(x² + 2x + 1) ← distribute
= 2x² + 4x + 2
To find g(f(x)) substitute x = f(x) into g(x), that is
g(f(x))
= g(2x²)
= 2x² + 1
----------------------------------------------------------
Equating gives
2x² + 4x + 2 = 2x² + 1 ( subtract 2x² + 1 from both sides )
4x + 1 = 0 ( subtract 1 from both sides )
4x = - 1 ( divide both sides by 4 )
x = - 
tan2x*cotx - 3 = 0
We know that: tan2x = sin2x/cos2x and cotx = cosx/sinx
==> sin2x/cos2x *cosx/sinx = 3
Now we know that sin2x = 2sinx*cosx
==> 2sinxcosx/cos2x * cosx/sinx = 3
Reduce sinx:
==> 2cos^2 x/ cos2x = 3
Now we know that cos2x = 2cos^2 x-1
==> 2cos^2 x/(2cos^2 x -1) = 3
==> 2cos^2 x = 3(2cos^2 x -1)
==> 2cos^2 x = 6cos^2 x - 3
==> -4cos^2 x= -3
==> 4cos^2 x = 3
==> cos^2 x = 3/4
==> cosx = +-sqrt3/ 2
<span>==> x = pi/6, 5pi/6, 7pi/6, and 11pi/6</span>