The value of x is calculated with the help of a similar triangle is 24.
<h3>What is the triangle?</h3>
A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
In a triangle, if there is a parallel line with any side of the triangle, then the line divides the other sides in the same ratio.
Then we have
x / 12 = 32 / 16
x = 24
Then the value of x is 24.
More about the triangle link is given below.
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Answer:
See proof below
Step-by-step explanation
cot^2(x) - csc^2(x) = -1
In trigonometry identity
cot^2x = cos²x/sin²x
Csc²x = 1/sin²x
Substitute into the original expression
cos²x/sin²x - 1/sin²x
Find the LCM
(Cos²x-1)/sin²x .... *
Recall that sin²x+cos²x = 1
Sin²x = 1-cos²x
-sin²x = -1+cos²x
-sin²x = cos²x-1 .... **
Substitute ** into *
(Cos²x-1)/sin²x
-sin²x/sin²x
= -1 (RHS)
Therefore cot^2(x) - csc^2(x) = -1 (Proved!)
Solution: Let 
be the number of adult ticket's.
The number of child ticket 
We are given, that an adult ticket cost's $10 and child ticket costs $6. Also the church luncheon made $842.
Therefore,
Therefore, the number of adult ticket's sold = 35
And the number of child ticket's sold = 2 x 35 + 12 = 70 + 12 = 82
I hope you understand....
$68.82
$68.82 - $5.32
$63.50 - $3.00
$60.50 / 2
$30.25 each pair of shoes
