![What are the answers to the following questions: 12. m9 / m2=?, 13. Find the gradient of the line passing through points (0,2) and (1,5). 14. If Q = [50, 30, 60]^T and P = [60, 20, 70]^T, what is Q+P?](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1777143387678-855140dca6e5c558.png&w=3840&q=75)
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — 12. Step 1: Apply the rule of exponents for division, a^x ÷ a^y = a^x-y. m^9 ÷ m^2 = m^9-2 Step 2: Simplify the exponent. m^9-2 = m^7 The simplified expression is B. m^7. 13. Step 1: Identify the coordinates of the two points. Point B: (x_1, y_1) = (0, 2) Point D: (x_2, y_2) = (1, 5) Step 2: Use the formula for the gradient (slope) of a line: m = (y_2 - y_1)/(x_2 - x_1). m = (5 - 2)/(1 - 0) Step 3: Calculate the gradient. m = (3)/(1) m = 3 The gradient of the line is D. 3. 14. Step 1: Identify the given matrices P and Q. Q = 50 \\ 30 \\ 60 , P = 60 \\ 20 \\ 70 Step 2: To determine Q+P, add the corresponding elements of the matrices. Q+P = 50+60 \\ 30+20 \\ 60+70 Step 3: Perform the addition. Q+P = 110 \\ 50 \\ 130 The result of Q+P is B. 110 \\ 50 \\ 130 . 29. Step 1: State the given map distance and actual distance. Map distance = 16 cm Actual distance = 640 km Step 2: Express the scale as a ratio of map distance to actual distance. Scale = 16 cm : 640 km Step 3: Simplify the ratio so that the map distance is 1 cm. Divide both sides by 16. 1 cm : (640)/(16) km 1 cm : 40 km The scale of the map in statement form is 1 cm represents 40 km. 30. Step 1: State the given map distance and actual distance. Map distance = 4 cm Actual distance = 1.2 km Step 2: Convert the actual distance to centimeters to have consistent units for the ratio. 1 km = 1000 m 1 m = 100 cm So, 1 km = 1000 × 100 cm = 100,000 cm. Actual distance = 1.2 km × 100,000 cm/km = 120,000 cm. Step 3: Express the scale as a ratio of map distance to actual distance. Scale = 4 cm : 120,000 cm Step 4: Simplify the ratio so that the map distance is 1 cm. Divide both sides by 4. 1 cm : (120,000)/(4) cm 1 cm : 30,000 cm The scale of the map is 1:30,000. 31. Step 1: State the given map scale and map distance. Scale = 1:50000 (This means 1 cm on the map represents 50,000 cm in actual distance). Map distance = 4 cm Step 2: Calculate the actual distance in centimeters. Actual distance = Map distance × Scale factor Actual distance = 4 cm × 50,000 Actual distance = 200,000 cm Step 3: Convert the actual distance from centimeters to kilometers. 1 km = 100,000 cm Actual distance in km = 200,000 cm100,000 cm/km Actual distance = 2 km The actual length of the road is 2 km. Got more? Send 'em!