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 — 33. Step 1: Calculate the total selling price of the cars. Sam sold 6 cars, and each car was sold for sh 890 000. Total selling price = 6 × 890000 sh Total selling price = 5340000 sh Step 2: Calculate the commission earned. The commission rate is 2% of the total selling price. Commission = 2\% × 5340000 sh Commission = (2)/(100) × 5340000 sh Commission = 2 × 53400 sh Commission = 106800 sh The commission Sam earned that month was sh 106 800. 34. A parallelogram has opposite angles equal and consecutive angles supplementary (add up to 180^). Step 1: Determine the size of angle a. Angle a and the angle 110^ are consecutive interior angles along the bottom side, or a is opposite the 110^ angle if we consider the top-left angle as 110^ and bottom-right as a. Looking at the diagram, the angle 110^ is at the top-left vertex, and angle a is at the bottom-right vertex. In a parallelogram, opposite angles are equal. Therefore, a = 110^. Reason: Opposite angles in a parallelogram are equal. Step 2: Determine the size of angle b. Angle b is at the top-right vertex. The angle 70^ is at the bottom-left vertex. In a parallelogram, opposite angles are equal. Therefore, b = 70^. Reason: Opposite angles in a parallelogram are equal. Alternatively, using consecutive angles: Angle a and the 70^ angle are consecutive angles. a + 70^ = 180^ a = 180^ - 70^ = 110^ Angle b and the 110^ angle are consecutive angles. b + 110^ = 180^ b = 180^ - 110^ = 70^ The sizes of the angles are: a = 110^ because opposite angles in a parallelogram are equal. b = 70^ because opposite angles in a parallelogram are equal. 35. (a) To construct triangle NPQ with PQ = 7 cm, NQ = 9 cm, and angle NPQ = 60^: Step 1: Draw a line segment PQ. Using a ruler, draw a straight line segment PQ of length 7 cm. Step 2: Construct angle NPQ = 60^ at point P. • Place the compass needle at point P and draw an arc that intersects PQ. Let this intersection point be X. • Without changing the compass width, place the needle at X and draw another arc that intersects the first arc. Let this intersection point be Y. • Draw a ray from P through Y. This ray forms an angle of 60^ with PQ. Step 3: Locate point N. • Place the compass needle at point Q. • Open the compass to a radius of 9 cm (the length of NQ). • Draw an arc that intersects the ray drawn in Step 2. The intersection point is N. Step 4: Complete the triangle. • Draw a straight line segment from N to Q. Triangle NPQ is now constructed. Got more? Send 'em!