Solve the following mathematics problems: 1. Convert 21 (Base 10) to Base 2. 2. Calculate a 15% discount on N5,000. 3. List 3 cylindrical and 3 rectangular prism objects. 4. Simplify 5x + 10 - 2x + 4.

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Asked on April 7, 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 · 2026-04-07T09:52:53.763Z

Here are the solutions to your assignment: MATHEMATICS 1. Number Bases: Convert 21 (Base 10) to Base 2. To convert 21 from base 10 to base 2, we perform successive divisions by 2 and record the remainders. 21 ÷ 2 = 10 remainder 1 10 ÷ 2 = 5 remainder 0 5 ÷ 2 = 2 remainder 1 2 ÷ 2 = 1 remainder 0 1 ÷ 2 = 0 remainder 1 Reading the remainders from bottom to top, we get: The number 21 in Base 10 is 10101_2 in Base 2. 2. Percentages: Calculate the discount. Original cost = N5,000 Discount percentage = 15% Discount amount = 15\% of N5,000 Discount amount = (15)/(100) × 5000 Discount amount = 15 × 50 Discount amount = N750 The discount is N750. 3. Geometry: List 3 cylindrical and 3 rectangular prism objects. Cylindrical objects*: Can of soda Battery Toilet paper roll Rectangular prism objects*: Brick Book Cereal box 4. Algebra: Simplify the expression: 5x + 10 - 2x + 4. Step 1: Group like terms. (5x - 2x) + (10 + 4) Step 2: Combine like terms. 3x + 14 The simplified expression is 3x + 14. 5. Fractions: Fraction of cake left. Fraction eaten on Friday = (2)/(5) Fraction eaten on Saturday = (1)/(4) Step 1: Find the total fraction of cake eaten. Total eaten = (2)/(5) + (1)/(4) Find a common denominator, which is 20. Total eaten = (2 × 4)/(5 × 4) + (1 × 5)/(4 × 5) Total eaten = (8)/(20) + (5)/(20) Total eaten = (8+5)/(20) = (13)/(20) Step 2: Find the fraction of cake left. Fraction left = 1 - Total eaten Fraction left = (20)/(20) - (13)/(20) Fraction left = (7)/(20) The fraction of the whole cake left is (7)/(20). 6. Decimals: Multiply 12.5 × 0.4 without using a calculator. Step 1: Multiply the numbers as if they were whole numbers. 125 × 4 = 500 Step 2: Count the total number of decimal places in the original numbers. 12.5 has 1 decimal place. 0.4 has 1 decimal place. Total decimal places = 1 + 1 = 2. Step 3: Place the decimal point in the product. Starting from the right of 500, move the decimal point 2 places to the left. 5.00 The product is 5. 7. LCM: Find the Lowest Common Multiple (LCM) of 12, 18, and 24. Step 1: Find the prime factorization of each number. 12 = 2^2 × 3^1 18 = 2^1 × 3^2 24 = 2^3 × 3^1 Step 2: For each prime factor, take the highest power that appears in any of the factorizations. Highest power of 2 is 2^3. Highest power of 3 is 3^2. Step 3: Multiply these highest powers together. LCM = 2^3 × 3^2 = 8 × 9 = 72 The LCM of 12, 18, and 24 is 72. 8. Angles: Use a protractor to draw an angle of 120^ and label it correctly as "Obtuse". To draw a 120^ angle: 1. Draw a straight line segment. This will be one arm of the angle. 2. Place the center of a protractor on one endpoint of the line segment (the vertex). Align the baseline of the protractor with the line segment. 3. Locate the 120^ mark on the protractor. 4. Make a small mark at 120^. 5. Draw a second line segment from the vertex to the mark. 6. Label the angle as 120^. An angle of 120^ is an obtuse angle* because it is greater than 90^ but less than 180^. 9. Word Problem: Cloth needed for 6 outfits. Cloth for one outfit = 2.5 meters Number of outfits = 6 Total cloth = 2.5 meters/outfit × 6 outfits Total cloth = 15.0 meters 15 meters of cloth are needed for 6 outfits. 10. Symmetry: Draw a square and a rectangle. Draw all the lines of symmetry for each shape. Square: A square has 4 lines of symmetry*. Two lines pass through the midpoints of opposite sides (one horizontal, one vertical). Two lines pass through opposite vertices (the diagonals). Rectangle: A rectangle has 2 lines of symmetry*. One line passes through the midpoints of the longer opposite sides (horizontal). One line passes through the midpoints of the shorter opposite sides (vertical). DIGITAL TECHNOLOGIES Task: Open Microsoft Word and type a "Happy Holiday" message to Mr. Victor. a. Shortcut Challenge: Highlight your name and press Ctrl + B. What happened to the text? When you highlight text and press Ctrl + B in Microsoft Word, the selected text becomes bold. b. Press Ctrl + E. Where did your text move to on the page? When you press Ctrl + E in Microsoft Word, the selected text or the current paragraph is centered on the page. c. Press Ctrl

Accepted Answer · 2026-04-07T09:52:53.763Z

Here are the solutions to your assignment: MATHEMATICS 1. Number Bases: Convert 21 (Base 10) to Base 2. To convert 21 from base 10 to base 2, we perform successive divisions by 2 and record the remainders. 21 ÷ 2 = 10 remainder 1 10 ÷ 2 = 5 remainder 0 5 ÷ 2 = 2 remainder 1 2 ÷ 2 = 1 remainder 0 1 ÷ 2 = 0 remainder 1 Reading the remainders from bottom to top, we get: The number 21 in Base 10 is 10101_2 in Base 2. 2. Percentages: Calculate the discount. Original cost = N5,000 Discount percentage = 15% Discount amount = 15\% of N5,000 Discount amount = (15)/(100) × 5000 Discount amount = 15 × 50 Discount amount = N750 The discount is N750. 3. Geometry: List 3 cylindrical and 3 rectangular prism objects. Cylindrical objects*: Can of soda Battery Toilet paper roll Rectangular prism objects*: Brick Book Cereal box 4. Algebra: Simplify the expression: 5x + 10 - 2x + 4. Step 1: Group like terms. (5x - 2x) + (10 + 4) Step 2: Combine like terms. 3x + 14 The simplified expression is 3x + 14. 5. Fractions: Fraction of cake left. Fraction eaten on Friday = (2)/(5) Fraction eaten on Saturday = (1)/(4) Step 1: Find the total fraction of cake eaten. Total eaten = (2)/(5) + (1)/(4) Find a common denominator, which is 20. Total eaten = (2 × 4)/(5 × 4) + (1 × 5)/(4 × 5) Total eaten = (8)/(20) + (5)/(20) Total eaten = (8+5)/(20) = (13)/(20) Step 2: Find the fraction of cake left. Fraction left = 1 - Total eaten Fraction left = (20)/(20) - (13)/(20) Fraction left = (7)/(20) The fraction of the whole cake left is (7)/(20). 6. Decimals: Multiply 12.5 × 0.4 without using a calculator. Step 1: Multiply the numbers as if they were whole numbers. 125 × 4 = 500 Step 2: Count the total number of decimal places in the original numbers. 12.5 has 1 decimal place. 0.4 has 1 decimal place. Total decimal places = 1 + 1 = 2. Step 3: Place the decimal point in the product. Starting from the right of 500, move the decimal point 2 places to the left. 5.00 The product is 5. 7. LCM: Find the Lowest Common Multiple (LCM) of 12, 18, and 24. Step 1: Find the prime factorization of each number. 12 = 2^2 × 3^1 18 = 2^1 × 3^2 24 = 2^3 × 3^1 Step 2: For each prime factor, take the highest power that appears in any of the factorizations. Highest power of 2 is 2^3. Highest power of 3 is 3^2. Step 3: Multiply these highest powers together. LCM = 2^3 × 3^2 = 8 × 9 = 72 The LCM of 12, 18, and 24 is 72. 8. Angles: Use a protractor to draw an angle of 120^ and label it correctly as "Obtuse". To draw a 120^ angle: 1. Draw a straight line segment. This will be one arm of the angle. 2. Place the center of a protractor on one endpoint of the line segment (the vertex). Align the baseline of the protractor with the line segment. 3. Locate the 120^ mark on the protractor. 4. Make a small mark at 120^. 5. Draw a second line segment from the vertex to the mark. 6. Label the angle as 120^. An angle of 120^ is an obtuse angle* because it is greater than 90^ but less than 180^. 9. Word Problem: Cloth needed for 6 outfits. Cloth for one outfit = 2.5 meters Number of outfits = 6 Total cloth = 2.5 meters/outfit × 6 outfits Total cloth = 15.0 meters 15 meters of cloth are needed for 6 outfits. 10. Symmetry: Draw a square and a rectangle. Draw all the lines of symmetry for each shape. Square: A square has 4 lines of symmetry*. Two lines pass through the midpoints of opposite sides (one horizontal, one vertical). Two lines pass through opposite vertices (the diagonals). Rectangle: A rectangle has 2 lines of symmetry*. One line passes through the midpoints of the longer opposite sides (horizontal). One line passes through the midpoints of the shorter opposite sides (vertical). DIGITAL TECHNOLOGIES Task: Open Microsoft Word and type a "Happy Holiday" message to Mr. Victor. a. Shortcut Challenge: Highlight your name and press Ctrl + B. What happened to the text? When you highlight text and press Ctrl + B in Microsoft Word, the selected text becomes bold. b. Press Ctrl + E. Where did your text move to on the page? When you press Ctrl + E in Microsoft Word, the selected text or the current paragraph is centered on the page. c. Press Ctrl

Solve the following mathematics problems: 1. Convert 21 (Base 10) to Base 2. 2. Calculate a 15% discount on N5,000. 3. List 3 cylindrical and 3 rectangular prism objects. 4. Simplify 5x + 10 - 2x + 4.

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Solve the following mathematics problems: 1. Convert 21 (Base 10) to Base 2. 2. Calculate a 15% discount on N5,000. 3. List 3 cylindrical and 3 rectangular prism objects. 4. Simplify 5x + 10 - 2x + 4.

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