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Calculate the determinant of the given 3 x 3 matrix.
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Step-by-step solution
8 steps24.
Calculate the determinant of the given matrix.
The determinant of a matrix can be found by expanding along the first column: .
For the given matrix , we expand along the first column:Simplify the expression.
The correct option is A.
The final answer is .
25.
Find the exterior angle of the regular polygon.
The interior angle of the regular polygon is given as .
The sum of an interior angle and its corresponding exterior angle is .Calculate the number of sides of the polygon.
The sum of the exterior angles of any polygon is . For a regular polygon with sides, all exterior angles are equal.
The correct option is A.
The final answer is .
26.
Use the property of parallel lines to find .
Given that and is a transversal, the alternate interior angles are equal.
Therefore, .
Given , so .Use the angle bisector property to find .
Given that bisects , it means divides into two equal angles.
So, .
Since , then .Calculate the total angle .
Calculate using the sum of angles in .
The sum of angles in a triangle is . In :
Given and we found .
The final answer is .
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