A rally car travelled for 2 hours 40 minutes at an average speed of 120 km/h. The car consumes an average of 1 litre of fuel for every 4 kilometers. A litre costs Ksh. 189. Calculate the amount of mon

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Asked on April 26, 2026Mathematics

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.

Accepted Answer · 2026-04-26T15:05:15.285Z

Morning I — let's get this done. Here are the solutions to your math questions: 1. A rally car travelled for 2 hours 40 minutes at an average speed of 120 km/h. The car consumes an average of 1 litre of fuel for every 4 kilometers. A litre costs Ksh. 189. Calculate the amount of money spent on fuel. Step 1: Convert the total time to hours. 2 hours 40 minutes = 2 + (40)/(60) hours = 2 + (2)/(3) hours = (8)/(3) hours Step 2: Calculate the total distance traveled. Distance = Speed × Time Distance = 120 km/h × (8)/(3) hours = 40 × 8 km = 320 km Step 3: Calculate the total fuel consumed. The car consumes 1 litre for every 4 km. Fuel consumed = Total distanceKilometers per litre = 320 km4 km/litre = 80 litres Step 4: Calculate the total cost of fuel. Total cost = Fuel consumed × Cost per litre Total cost = 80 litres × Ksh. 189/litre = Ksh. 15120 The amount of money spent on fuel is Ksh. 15120. 2. One interior angle of a polygon is equal to 80^ and each of the other interior angles are 128^. Find the number of sides of the polygon. Step 1: Let n be the number of sides of the polygon. The sum of the interior angles of an n-sided polygon is given by the formula: S = (n-2) × 180^ Step 2: Express the sum of the interior angles using the given angle values. One angle is 80^. The remaining (n-1) angles are each 128^. S = 80^ + (n-1) × 128^ Step 3: Equate the two expressions for the sum of interior angles and solve for n. (n-2) × 180 = 80 + (n-1) × 128 180n - 360 = 80 + 128n - 128 180n - 360 = 128n - 48 180n - 128n = 360 - 48 52n = 312 n = (312)/(52) n = 6 The number of sides of the polygon is 6. 3. (a) Using a pair of compasses and a ruler only, construct a triangle ABC such that AB = 4 cm, BC = 6 cm and angle ABC = 135^. a) Construction steps: 1. Draw a line segment AB of length 4 cm. 2. At point B, construct an angle of 135^. To do this, construct a 90^ angle, then bisect the adjacent 90^ angle to get 45^, and add it to 90^ (90^ + 45^ = 135^). Alternatively, construct a straight line through B, then construct a 45^ angle from the extension of AB, which will give 135^ on the other side. 3. Along the 135^ line from B, measure and mark a point C such that BC = 6 cm. 4. Join points A and C to complete triangle ABC. (b) Construct the height of triangle ABC in (a) above taking AB as the base, hence calculate the area of triangle ABC.* b) Construction steps for height: 1. Extend the line segment AB beyond B. 2. From point C, drop a perpendicular to the extended line AB. To do this, place the compass at C, draw an arc that intersects the extended line AB at two points. 3. From these two intersection points, draw two more arcs that intersect below (or above) the line. 4. Draw a straight line from C through the intersection of these two arcs. This line is the height of the triangle from C to the base AB (extended). Let the intersection point on the extended line AB be D. CD is the height. Calculation of the area: Given AB = 4 cm, BC = 6 cm, and ABC = 135^. The area of a triangle can be calculated using the formula: Area = (1)/(2)ab C Here, a = BC = 6 cm, b = AB = 4 cm, and the included angle is ABC = 135^. Area = (1)/(2) × 4 cm × 6 cm × (135^) We know that (135^) = (180^ - 45^) = (45^) = sqrt(2)2. Area = (1)/(2) × 24 × sqrt(2)2 Area = 12 × sqrt(2)2 Area = 6sqrt(2) cm^2 Using sqrt(2) ≈ 1.414: Area ≈ 6 × 1.414 = 8.484 cm^2 The area of triangle ABC is 6sqrt(2) cm^2 or approximately 8.484 cm^2. 4. Solve the following inequalities and present your solution on a number line: 2x - 2 3x + 1 < x + 11 Step 1: Split the compound inequality into two separate inequalities. Inequality 1: 2x - 2 3x + 1 Inequality 2: 3x + 1 < x + 11 Step 2: Solve Inequality 1. 2x - 2 3x + 1 -2 - 1 3x - 2x -3 x x -3 Step 3: Solve Inequality 2. 3x + 1 < x + 11 3x - x < 11 - 1 2x < 10 x < 5 Step 4: Combine the solutions. We need values of x that satisfy both x -3 and x < 5. The combined solution is -3 x < 5. Step 5: Present the solution on a number line. Draw a number line. Place a closed circle at -3 (because x can be equal to -3) and an open circle at 5 (because x cannot be equal to 5). Draw a line connecting these two circles. ` <-----|-----|-----|-----|-----|-----|-----|-----|-----|-----> -4 -3 -2 -1 0 1 2 3 4 5 [------------------------------------------------) ` The solution is -3 x < 5. 5. Without using mathematical tables or a calculator, evaluate leaving your answer as a simplified fraction: The expression to evaluate is missing from the image. Please provide the expression for question 5. 6. Two similar solids have surface areas 48 cm^2 and 108 cm^2 respectively. Find the volume of the smaller solid if the bigger one has a volume of 162 milliliters. Step 1: Find the ratio of the surface areas. Let A_1 = 48 cm^2 (smaller solid) and A_2 = 108 cm^2 (bigger solid). The ratio of surface areas is (A_1)/(A_2) = (48)/(108). Simplify the ratio: (48)/(108) = (24)/(54) = (12)/(27) = (4)/(9) Step 2: Find the ratio of corresponding linear dimensions. For similar solids, the ratio of surface areas is the square of the ratio of corresponding linear dimensions (L_1/L_2). (A_1)/(A_2) = ((L_1)/(L_2))^2 (4)/(9) = ((L_1)/(L_2))^2 (L_1)/(L_2) = sqrt((4)/(9)) = (2)/(3) Step 3: Find the ratio of the volumes. The ratio of volumes is the cube of the ratio of corresponding linear dimensions. (V_1)/(V_2) = ((L_1)/(L_2))^3 (V_1)/(V_2) = ((2)/(3))^3 = (2^3)/(3^3) = (8)/(27) Step 4: Calculate the volume of the smaller solid. Given V_2 = 162 milliliters. Since 1 ml = 1 cm^3, V_2 = 162 cm^3. (V_1)/(162 cm)^3 = (8)/(27) V_1 = (8)/(27) × 162 cm^3 V_1 = 8 × (162)/(27) cm^3 V_1 = 8 × 6 cm^3 V_1 = 48 cm^3 The volume of the smaller solid is 48 cm^3. 7. A triangular flower garden has an area of 28 cm^2. Two of its edges are 14 m and 8 m. find the angle between the two edges. Step 1: Use the formula for the area of a triangle given two sides and the included angle. Area = (1)/(2)ab Given Area = 28 m^2, a = 14 m, b = 8 m. Let be the angle between the two edges. 28 = (1)/(2) × 14 × 8 × Step 2: Solve for . 28 = 7 × 8 × 28 = 56 = (28)/(56) = (1)/(2) Step 3: Find the angle . The angle whose sine is (1)/(2) is 30^. = ^-1((1)/(2)) = 30^ The angle between the two edges is 30^. 8. Simplify the expression: (9t^2 - 25a^2)/(6t^2 + 19at + 15a^2) Step 1

Accepted Answer · 2026-04-26T15:05:15.285Z

Morning I — let's get this done. Here are the solutions to your math questions: 1. A rally car travelled for 2 hours 40 minutes at an average speed of 120 km/h. The car consumes an average of 1 litre of fuel for every 4 kilometers. A litre costs Ksh. 189. Calculate the amount of money spent on fuel. Step 1: Convert the total time to hours. 2 hours 40 minutes = 2 + (40)/(60) hours = 2 + (2)/(3) hours = (8)/(3) hours Step 2: Calculate the total distance traveled. Distance = Speed × Time Distance = 120 km/h × (8)/(3) hours = 40 × 8 km = 320 km Step 3: Calculate the total fuel consumed. The car consumes 1 litre for every 4 km. Fuel consumed = Total distanceKilometers per litre = 320 km4 km/litre = 80 litres Step 4: Calculate the total cost of fuel. Total cost = Fuel consumed × Cost per litre Total cost = 80 litres × Ksh. 189/litre = Ksh. 15120 The amount of money spent on fuel is Ksh. 15120. 2. One interior angle of a polygon is equal to 80^ and each of the other interior angles are 128^. Find the number of sides of the polygon. Step 1: Let n be the number of sides of the polygon. The sum of the interior angles of an n-sided polygon is given by the formula: S = (n-2) × 180^ Step 2: Express the sum of the interior angles using the given angle values. One angle is 80^. The remaining (n-1) angles are each 128^. S = 80^ + (n-1) × 128^ Step 3: Equate the two expressions for the sum of interior angles and solve for n. (n-2) × 180 = 80 + (n-1) × 128 180n - 360 = 80 + 128n - 128 180n - 360 = 128n - 48 180n - 128n = 360 - 48 52n = 312 n = (312)/(52) n = 6 The number of sides of the polygon is 6. 3. (a) Using a pair of compasses and a ruler only, construct a triangle ABC such that AB = 4 cm, BC = 6 cm and angle ABC = 135^. a) Construction steps: 1. Draw a line segment AB of length 4 cm. 2. At point B, construct an angle of 135^. To do this, construct a 90^ angle, then bisect the adjacent 90^ angle to get 45^, and add it to 90^ (90^ + 45^ = 135^). Alternatively, construct a straight line through B, then construct a 45^ angle from the extension of AB, which will give 135^ on the other side. 3. Along the 135^ line from B, measure and mark a point C such that BC = 6 cm. 4. Join points A and C to complete triangle ABC. (b) Construct the height of triangle ABC in (a) above taking AB as the base, hence calculate the area of triangle ABC.* b) Construction steps for height: 1. Extend the line segment AB beyond B. 2. From point C, drop a perpendicular to the extended line AB. To do this, place the compass at C, draw an arc that intersects the extended line AB at two points. 3. From these two intersection points, draw two more arcs that intersect below (or above) the line. 4. Draw a straight line from C through the intersection of these two arcs. This line is the height of the triangle from C to the base AB (extended). Let the intersection point on the extended line AB be D. CD is the height. Calculation of the area: Given AB = 4 cm, BC = 6 cm, and ABC = 135^. The area of a triangle can be calculated using the formula: Area = (1)/(2)ab C Here, a = BC = 6 cm, b = AB = 4 cm, and the included angle is ABC = 135^. Area = (1)/(2) × 4 cm × 6 cm × (135^) We know that (135^) = (180^ - 45^) = (45^) = sqrt(2)2. Area = (1)/(2) × 24 × sqrt(2)2 Area = 12 × sqrt(2)2 Area = 6sqrt(2) cm^2 Using sqrt(2) ≈ 1.414: Area ≈ 6 × 1.414 = 8.484 cm^2 The area of triangle ABC is 6sqrt(2) cm^2 or approximately 8.484 cm^2. 4. Solve the following inequalities and present your solution on a number line: 2x - 2 3x + 1 < x + 11 Step 1: Split the compound inequality into two separate inequalities. Inequality 1: 2x - 2 3x + 1 Inequality 2: 3x + 1 < x + 11 Step 2: Solve Inequality 1. 2x - 2 3x + 1 -2 - 1 3x - 2x -3 x x -3 Step 3: Solve Inequality 2. 3x + 1 < x + 11 3x - x < 11 - 1 2x < 10 x < 5 Step 4: Combine the solutions. We need values of x that satisfy both x -3 and x < 5. The combined solution is -3 x < 5. Step 5: Present the solution on a number line. Draw a number line. Place a closed circle at -3 (because x can be equal to -3) and an open circle at 5 (because x cannot be equal to 5). Draw a line connecting these two circles. ` <-----|-----|-----|-----|-----|-----|-----|-----|-----|-----> -4 -3 -2 -1 0 1 2 3 4 5 [------------------------------------------------) ` The solution is -3 x < 5. 5. Without using mathematical tables or a calculator, evaluate leaving your answer as a simplified fraction: The expression to evaluate is missing from the image. Please provide the expression for question 5. 6. Two similar solids have surface areas 48 cm^2 and 108 cm^2 respectively. Find the volume of the smaller solid if the bigger one has a volume of 162 milliliters. Step 1: Find the ratio of the surface areas. Let A_1 = 48 cm^2 (smaller solid) and A_2 = 108 cm^2 (bigger solid). The ratio of surface areas is (A_1)/(A_2) = (48)/(108). Simplify the ratio: (48)/(108) = (24)/(54) = (12)/(27) = (4)/(9) Step 2: Find the ratio of corresponding linear dimensions. For similar solids, the ratio of surface areas is the square of the ratio of corresponding linear dimensions (L_1/L_2). (A_1)/(A_2) = ((L_1)/(L_2))^2 (4)/(9) = ((L_1)/(L_2))^2 (L_1)/(L_2) = sqrt((4)/(9)) = (2)/(3) Step 3: Find the ratio of the volumes. The ratio of volumes is the cube of the ratio of corresponding linear dimensions. (V_1)/(V_2) = ((L_1)/(L_2))^3 (V_1)/(V_2) = ((2)/(3))^3 = (2^3)/(3^3) = (8)/(27) Step 4: Calculate the volume of the smaller solid. Given V_2 = 162 milliliters. Since 1 ml = 1 cm^3, V_2 = 162 cm^3. (V_1)/(162 cm)^3 = (8)/(27) V_1 = (8)/(27) × 162 cm^3 V_1 = 8 × (162)/(27) cm^3 V_1 = 8 × 6 cm^3 V_1 = 48 cm^3 The volume of the smaller solid is 48 cm^3. 7. A triangular flower garden has an area of 28 cm^2. Two of its edges are 14 m and 8 m. find the angle between the two edges. Step 1: Use the formula for the area of a triangle given two sides and the included angle. Area = (1)/(2)ab Given Area = 28 m^2, a = 14 m, b = 8 m. Let be the angle between the two edges. 28 = (1)/(2) × 14 × 8 × Step 2: Solve for . 28 = 7 × 8 × 28 = 56 = (28)/(56) = (1)/(2) Step 3: Find the angle . The angle whose sine is (1)/(2) is 30^. = ^-1((1)/(2)) = 30^ The angle between the two edges is 30^. 8. Simplify the expression: (9t^2 - 25a^2)/(6t^2 + 19at + 15a^2) Step 1

A rally car travelled for 2 hours 40 minutes at an average speed of 120 km/h. The car consumes an average of 1 litre of fuel for every 4 kilometers. A litre costs Ksh. 189. Calculate the amount of mon

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A rally car travelled for 2 hours 40 minutes at an average speed of 120 km/h. The car consumes an average of 1 litre of fuel for every 4 kilometers. A litre costs Ksh. 189. Calculate the amount of mon

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