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ScanSolve AI Answer
Here are the solutions to the problems from the image, arranged as requested: 1) Solve for x in each of the following linear equations: a) 2x+5=15 Step 1: Subtract 5 from both sides. 2x = 15 - 5 2x = 10 Step 2: Divide by 2. x = (10)/(2) x = 5 b) 4x-7=9 Step 1: Add 7 to both sides. 4x = 9 + 7 4x = 16 Step 2: Divide by 4. x = (16)/(4) x = 4 c) 7x-3=25 Step 1: Add 3 to both sides. 7x = 25 + 3 7x = 28 Step 2: Divide by 7. x = (28)/(7) x = 4 --- 2) Calculate the Shaded Area of the region in the figures below: Top Right Figure (Rectangle with an inner unshaded rectangle): The outer rectangle has a length of 28 cm and a width of 20 cm. The inner unshaded rectangle has a length of 28 - 2 - 2 = 24 cm and a width of 20 - 8 - 2 = 10 cm. Step 1: Calculate the area of the outer rectangle. A_outer = length × width = 28 cm × 20 cm A_outer = 560 cm^2 Step 2: Calculate the area of the inner unshaded rectangle. A_inner = length × width = 24 cm × 10 cm A_inner = 240 cm^2 Step 3: Calculate the shaded area by subtracting the inner area from the outer area. A_shaded = A_outer - A_inner A_shaded = 560 cm^2 - 240 cm^2 A_shaded = 320 cm^2 a) Middle Right Figure (Annulus - two concentric circles): The outer circle has a radius R = 14 cm. The inner circle has a radius r = 7 cm. We will use = (22)/(7). Step 1: Calculate the area of the outer circle. A_outer = R^2 = (22)/(7) × (14 cm)^2 A_outer = (22)/(7) × 196 cm^2 A_outer = 22 × 28 cm^2 = 616 cm^2 Step 2: Calculate the area of the inner circle. A_inner = r^2 = (22)/(7) × (7 cm)^2 A_inner = (22)/(7) × 49 cm^2 A_inner = 22 × 7 cm^2 = 154 cm^2 Step 3: Calculate the shaded area by subtracting the inner area from the outer area. A_shaded = A_outer - A_inner A_shaded = 616 cm^2 - 154 cm^2 A_shaded = 462 cm^2 b) Middle Right Figure (Faint Quarter Circle): Based on the grid, the radius of the quarter circle is 4 cm. We assume the shaded area is the area of this quarter circle. We will use = (22)/(7). Step 1: Calculate the area of the quarter circle. A_quarter circle = (1)/(4) r^2 = (1)/(4) × (22)/(7) × (4 cm)^2 A_quarter circle = (1)/(4) × (22)/(7) × 16 cm^2 A_quarter circle = (22 × 4)/(7) cm^2 = (88)/(7) cm^2 A_shaded = 12.57 cm^2 (to 2 decimal places) --- Homework 1) Calculate the area of the unshaded region in the figure below: Bottom Left Figure (Large rectangle with an inner shaded rectangle): The large rectangle has a length of 36 cm and a width of 25 cm (by counting grid squares). The inner shaded rectangle has a length of 20 cm and a width of 18 cm. Step 1: Calculate the area of the large rectangle. A_large = length × width = 36 cm × 25 cm A_large = 900 cm^2 Step 2: Calculate the area of the inner shaded rectangle. A_shaded = length × width = 20 cm × 18 cm A_shaded = 360 cm^2 Step 3: Calculate the unshaded area by subtracting the shaded area from the large area. A_unshaded = A_large - A_shaded A_unshaded = 900 cm^2 - 360 cm^2 A_unshaded = 540 cm^2 Last free one today — make it count tomorrow, or type /upgrade for unlimited.