Calculate the determinant of the given 3 x 3 matrix.

24. Step 1: Calculate the determinant of the given 3 × 3 matrix. The determinant of a matrix a & b & c \\ d & e & f \\ g & h & i can be found by expanding along the first column: a(ei - fh) - d(bi - ch) + g(bf - ce). For the given matrix 0 & 3 & 2 \\ 1 & 7 & 8 \\ 0 & 5 & 4 , we expand along the first column: = 0 · 7 & 8 \\ 5 & 4 - 1 · 3 & 2 \\ 5 & 4 + 0 · 3 & 2 \\ 7 & 8 Step 2: Simplify the expression. = 0 - 1 · ((3 × 4) - (2 × 5)) + 0 = -1 · (12 - 10) = -1 · (2) = -2 The correct option is A. The final answer is A. -2. 25. Step 1: Find the exterior angle of the regular polygon. The interior angle of the regular polygon is given as 135^. The sum of an interior angle and its corresponding exterior angle is 180^. Exterior Angle = 180^ - Interior Angle Exterior Angle = 180^ - 135^ Exterior Angle = 45^ Step 2: Calculate the number of sides of the polygon. The sum of the exterior angles of any polygon is 360^. For a regular polygon with n sides, all exterior angles are equal. n × Exterior Angle = 360^ n × 45^ = 360^ n = (360^)/(45^) n = 8 The correct option is A. The final answer is A. 8. 26. Step 1: Use the property of parallel lines to find LNM. Given that KL NM and LN is a transversal, the alternate interior angles are equal. Therefore, KLN = LNM. Given KLN = 54^, so LNM = 54^. Step 2: Use the angle bisector property to find KNL. Given that LN bisects KNM, it means LN divides KNM into two equal angles. So, KNL = LNM. Since LNM = 54^, then KNL = 54^. Step 3: Calculate the total angle KNM. KNM = KNL + LNM KNM = 54^ + 54^ KNM = 108^ Step 4: Calculate KMN using the sum of angles in KMN. The sum of angles in a triangle is 180^. In KMN: KMN + MKN + KNM = 180^ Given MKN = 35^ and we found KNM = 108^. KMN + 35^ + 108^ = 180^ KMN + 143^ = 180^ KMN = 180^ - 143^ KMN = 37^ The final answer is 37^. Send me the next one 📸