If a = 1 \ 4 and b = -3 \ 4 , find 2a + b.

Here are the solutions to the questions from the image: Question 6: If a = 1 \\ 4 and b = -3 \\ 4 , find 2a + b. Step 1: Calculate 2a. 2a = 2 1 \\ 4 = 2 × 1 \\ 2 × 4 = 2 \\ 8 Step 2: Add 2a and b. 2a + b = 2 \\ 8 + -3 \\ 4 = 2 + (-3) \\ 8 + 4 = -1 \\ 12 The vector 2a + b is -1 \\ 12 . Question 7: If the scale is 1:10 000, what length will 45 cm on the map represent in km? Step 1: Calculate the real distance in centimeters. A scale of 1:10 000 means 1 cm on the map represents 10 000 cm in real life. For 45 cm on the map, the real distance is: 45 cm × 10 000 = 450 000 cm Step 2: Convert the real distance from centimeters to meters. Since 1 m = 100 cm: 450 000 cm = (450 000)/(100) m = 4500 m Step 3: Convert the real distance from meters to kilometers. Since 1 km = 1000 m: 4500 m = (4500)/(1000) km = 4.5 km The length represented is 4.5 km. Question 8: Find vector x in terms of a and b. Step 1: Apply the triangle law of vector addition. The diagram shows vector 'a' and vector 'b' connected head-to-tail. Vector 'x' is the resultant vector that connects the tail of 'a' to the head of 'b'. Step 2: Write the vector equation. According to the triangle law of vector addition, the resultant vector 'x' is the sum of vectors 'a' and 'b'. x = a + b Vector x in terms of a and b is a + b. Question 9: Contour lines that are close together show that the land has a ____ quantities. Contour lines on a map connect points of equal elevation. When these lines are drawn close to each other, it indicates a rapid change in elevation over a short horizontal distance. Contour lines that are close together show that the land has a steep gradient. Last free one today — make it count tomorrow, or type /upgrade for unlimited.