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
Here are the solutions to the questions: 1. Find the diameter of a circle whose radius is 3.4m. Step 1: The formula for the diameter (d) of a circle in terms of its radius (r) is d = 2r. Step 2: Substitute the given radius r = 3.4m into the formula. d = 2 × 3.4\, m Step 3: Calculate the diameter. d = 6.8\, m The correct option is B. The final answer is B. 6.8m. 2. In the balance below, the mass of one shape is given in kilogram. Find if = 15. Step 1: From the balance, two circles balance three squares. Let M_ be the mass of one circle and M_ be the mass of one square. 2 M_ = 3 M_ Step 2: Substitute the given mass of one circle, M_ = 15 kg. 2 × 15\, kg = 3 M_ 30\, kg = 3 M_ Step 3: Solve for M_. M_ = 30\, kg3 M_ = 10\, kg The correct option is C. The final answer is C. 10kg. 3. In the figure below MK and RS are straight lines. Find the value of angle marked n. Step 1: The angles 127^ and the angle adjacent to it on the straight line MK (or RS) are supplementary, meaning they add up to 180^. Let the angle adjacent to 127^ be x. 127^ + x = 180^ Step 2: Solve for x. x = 180^ - 127^ x = 53^ Step 3: Angle n and angle x are vertically opposite angles. Vertically opposite angles are equal. n = x n = 53^ The correct option is B. The final answer is B. 53°. 4. A line that divides a circle into two segments is called... A chord is a line segment whose endpoints lie on the circle, dividing the circle into two segments. A diameter is a special type of chord that passes through the center. The correct option is B. The final answer is B. Chord. 5. Which of the following construction of angles represents 45°? A 45^ angle is half of a 90^ angle. To construct a 45^ angle, one typically constructs a 90^ angle first and then bisects it. Option A shows the construction of a 90^ angle being bisected, which results in a 45^ angle. The correct option is A. The final answer is A. 6. Simplify: 2^3 × 3^2 × 5. Step 1: Calculate the powers. 2^3 = 2 × 2 × 2 = 8 3^2 = 3 × 3 = 9 Step 2: Substitute the calculated values back into the expression. 8 × 9 × 5 Step 3: Perform the multiplication. 8 × 9 = 72 72 × 5 = 360 The correct option is B. The final answer is B. 360. 7. Solve for n: 2n + 5 = 3n - 7. Step 1: Subtract 2n from both sides of the equation to gather terms with n on one side. 5 = 3n - 2n - 7 5 = n - 7 Step 2: Add 7 to both sides of the equation to isolate n. 5 + 7 = n 12 = n The correct option is A. The final answer is A. 12.