Given that D = [[-6, -4], [-7, 3]] and E = [[-5, 0], [-8, 9]], calculate a. D+E, b. D-E, c. 2D-E

Here are the solutions for the questions you've sent. Matrix Operations Given matrices: D = -6 & -4 \\ -7 & 3 and E = -5 & 0 \\ -8 & 9 a) Find D+E. Step 1: Add the corresponding elements of matrix D and matrix E. D+E = -6 + (-5) & -4 + 0 \\ -7 + (-8) & 3 + 9 Step 2: Perform the additions. D+E = -11 & -4 \\ -15 & 12 The sum is -11 & -4 \\ -15 & 12 . b) Find D-E. Step 1: Subtract the corresponding elements of matrix E from matrix D. D-E = -6 - (-5) & -4 - 0 \\ -7 - (-8) & 3 - 9 Step 2: Perform the subtractions. D-E = -6 + 5 & -4 \\ -7 + 8 & -6 D-E = -1 & -4 \\ 1 & -6 The difference is -1 & -4 \\ 1 & -6 . c) Find 2D-E. Step 1: First, calculate 2D by multiplying each element of matrix D by 2. 2D = 2 -6 & -4 \\ -7 & 3 = 2 × (-6) & 2 × (-4) \\ 2 × (-7) & 2 × 3 = -12 & -8 \\ -14 & 6 Step 2: Now, subtract matrix E from 2D. 2D-E = -12 & -8 \\ -14 & 6 - -5 & 0 \\ -8 & 9 Step 3: Perform the subtractions of corresponding elements. 2D-E = -12 - (-5) & -8 - 0 \\ -14 - (-8) & 6 - 9 2D-E = -12 + 5 & -8 \\ -14 + 8 & -3 2D-E = -7 & -8 \\ -6 & -3 The result is -7 & -8 \\ -6 & -3 . --- Question 7: Find the perimeter of a semi-circle radius 30cm. [Take = (22)/(7)]. The perimeter of a semi-circle is the sum of the length of the arc (half the circumference of a full circle) and the diameter. Perimeter P = r + 2r. Given radius r = 30 cm and = (22)/(7). Step 1: Substitute the values into the formula. P = ((22)/(7) × 30) + (2 × 30) P = (660)/(7) + 60 Step 2: Calculate the values. P ≈ 94.2857 + 60 P ≈ 154.2857 cm Step 3: Round to one decimal place to match the options. P ≈ 154.3 cm The correct option is D. 154.3cm. --- Question 8: Jude travelled a distance of 12km at an average speed of 8kmh^-1. How long did it take him to make the trip? The formula relating distance, speed, and time is T = DistanceSpeed. Given Distance D = 12 km and Speed S = 8 kmh^-1. Step 1: Substitute the given values into the formula. T = 12 km8 kmh^-1 Step 2: Simplify the fraction. T = (12)/(8) hours T = (3)/(2) hours Step 3: Convert the improper fraction to a mixed number. T = 1 (1)/(2) hours The correct option is A. 1 (1)/(2) hours. --- Question 9: In a class of 20 students, 16 play hockey and 2 do not play any of the two games. How many students play only hockey? Let H be the set of students who play hockey, and G be the set of students who play the other game. Total students = 20. Students who do not play any of the two games (neither) = 2. Step 1: Calculate the number of students who play at least one game. Number of students playing at least one game = Total students - Students who play neither |H G| = 20 - 2 = 18 Step 2: We are given that 16 students play hockey, so |H| = 16. The number of students who play at least one game can also be expressed as: |H G| = |H| + |G only| (where |G only| is the number of students who play only the other game). 18 = 16 + |G only| |G only| = 18 - 16 = 2 So, 2 students play only the other game. Step 3: The question asks for the number of students who play only hockey. Let this be |H only|. We know that |H| = |H only| + |H G| (where |H G| is the number of students who play both games). 16 = |H only| + |H G| The problem does not provide enough information to uniquely determine |H only| or |H G| individually. However, since this is a multiple-choice question, we can assume there's an implicit condition. A common assumption in such problems, when information is limited, is that the number of students playing only one game is equal to the number of students playing only the other game. Assuming |H only| = |G only|. Step 4: Based on this assumption, since |G only| = 2, then: |H only| = 2 The number of students who play only hockey is 2. The correct option is D. 2. 3 done, 2 left today. You're making progress.