Convert 21 from base 10 to base 2. Calculate 15% discount on N5,000. List 3 cylindrical and 3 rectangular prism household objects. Simplify 5x + 10 - 2x + 4.

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Asked on March 31, 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 · 2026-03-31T10:01:04.363Z

Here are the solutions to your assignment questions: MATHEMATICS 1. Number Bases: Convert 21 from Base 10 to Base 2 Step 1: Divide 21 by 2. 21 ÷ 2 = 10 remainder 1 Step 2: Divide 10 by 2. 10 ÷ 2 = 5 remainder 0 Step 3: Divide 5 by 2. 5 ÷ 2 = 2 remainder 1 Step 4: Divide 2 by 2. 2 ÷ 2 = 1 remainder 0 Step 5: Divide 1 by 2. 1 ÷ 2 = 0 remainder 1 Step 6: Read the remainders from bottom to top. The base 2 representation of 21 is: 10101_2 2. Percentages: Calculate the discount on an Easter hamper Step 1: Calculate 15% of N5,000. Discount = 15\% × N5,000 Discount = (15)/(100) × 5000 Step 2: Perform the multiplication. Discount = 15 × 50 Discount = 750 The discount is: N750 3. Geometry: List 3 cylindrical and 3 rectangular prism household objects Cylindrical Objects: Tin can (e.g., for food) Toilet paper roll Drinking glass Rectangular Prism Objects: Book Shoebox Brick 4. Algebra: Simplify the expression 5x + 10 - 2x + 4 Step 1: Group like terms. (5x - 2x) + (10 + 4) Step 2: Combine the x terms. (5 - 2)x = 3x Step 3: Combine the constant terms. 10 + 4 = 14 The simplified expression is: 3x + 14 5. Fractions: Calculate the fraction of cake left Step 1: Find the total fraction of cake eaten. Total eaten = (2)/(5) + (1)/(4) Step 2: 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 3: Subtract the eaten fraction from the whole cake (1). Fraction left = 1 - (13)/(20) Fraction left = (20)/(20) - (13)/(20) Fraction left = (20 - 13)/(20) = (7)/(20) The fraction of the whole cake left is: (7)/(20) 6. Decimals: Solve 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 (500) two places from the right. 5.00 The product is: 5 7. LCM: Find the Lowest Common Multiple (LCM) of 12, 18, and 24 Step 1: List 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. For 2: The highest power is 2^3 (from 24). For 3: The highest power is 3^2 (from 18). Step 3: Multiply these highest powers together. LCM = 2^3 × 3^2 LCM = 8 × 9 LCM = 72 The Lowest Common Multiple is: 72 8. Angles: Draw an angle of 120^ and label it correctly as "Obtuse" An angle of 120^ is an obtuse angle because it is greater than 90^ but less than 180^. To draw it: • Draw a straight line segment. This will be one arm of the angle. • Place the protractor's center on one endpoint of the line segment (the vertex). Align the baseline of the protractor with the line segment. • Find the 120^ mark on the protractor and make a small dot. • Draw a second line segment from the vertex to the dot. • Label the angle as 120^ and indicate that it is an obtuse angle. 9. Word Problem: Calculate cloth needed for 6 outfits Step 1: Multiply the cloth needed for one outfit by the number of outfits. Total cloth = 2.5 meters/outfit × 6 outfits Step 2: Perform the multiplication. Total cloth = 15 meters The total meters of cloth needed is: 15 meters 10. Symmetry: Draw a square and a rectangle and their lines of symmetry Square: A square has 4 lines of symmetry. Two lines pass through the midpoints of opposite sides (horizontal and vertical). Two lines pass through opposite vertices (diagonals). Rectangle: A rectangle has 2 lines of symmetry. Two lines pass through the midpoints of opposite sides (one horizontal, one vertical). (A rectangle does not have diagonal lines of symmetry unless it is also a square). DIGITAL TECHNOLOGIES Shortcut Challenge: a)* Highlight your name and press Ctrl + B. What happened to the text? The text became bold*. b)* Press Ctrl + E. Where did your text move to on the page? The text moved to the center* of the page. c)* Press Ctrl + J three times. Did the text get smaller or larger? Ctrl + J is the shortcut for Justify alignment in Microsoft Word. It aligns text to both the left and right margins. It does not* make the text smaller or larger. d)* Observation: In the "Insert" tab, click "Shapes". Draw a star. Which menu tab appears at the very top (usually in a different color) once the star is selected? The Format* tab (specifically "Shape Format" or "Drawing Tools Format") appears.

Accepted Answer · 2026-03-31T10:01:04.363Z

Here are the solutions to your assignment questions: MATHEMATICS 1. Number Bases: Convert 21 from Base 10 to Base 2 Step 1: Divide 21 by 2. 21 ÷ 2 = 10 remainder 1 Step 2: Divide 10 by 2. 10 ÷ 2 = 5 remainder 0 Step 3: Divide 5 by 2. 5 ÷ 2 = 2 remainder 1 Step 4: Divide 2 by 2. 2 ÷ 2 = 1 remainder 0 Step 5: Divide 1 by 2. 1 ÷ 2 = 0 remainder 1 Step 6: Read the remainders from bottom to top. The base 2 representation of 21 is: 10101_2 2. Percentages: Calculate the discount on an Easter hamper Step 1: Calculate 15% of N5,000. Discount = 15\% × N5,000 Discount = (15)/(100) × 5000 Step 2: Perform the multiplication. Discount = 15 × 50 Discount = 750 The discount is: N750 3. Geometry: List 3 cylindrical and 3 rectangular prism household objects Cylindrical Objects: Tin can (e.g., for food) Toilet paper roll Drinking glass Rectangular Prism Objects: Book Shoebox Brick 4. Algebra: Simplify the expression 5x + 10 - 2x + 4 Step 1: Group like terms. (5x - 2x) + (10 + 4) Step 2: Combine the x terms. (5 - 2)x = 3x Step 3: Combine the constant terms. 10 + 4 = 14 The simplified expression is: 3x + 14 5. Fractions: Calculate the fraction of cake left Step 1: Find the total fraction of cake eaten. Total eaten = (2)/(5) + (1)/(4) Step 2: 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 3: Subtract the eaten fraction from the whole cake (1). Fraction left = 1 - (13)/(20) Fraction left = (20)/(20) - (13)/(20) Fraction left = (20 - 13)/(20) = (7)/(20) The fraction of the whole cake left is: (7)/(20) 6. Decimals: Solve 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 (500) two places from the right. 5.00 The product is: 5 7. LCM: Find the Lowest Common Multiple (LCM) of 12, 18, and 24 Step 1: List 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. For 2: The highest power is 2^3 (from 24). For 3: The highest power is 3^2 (from 18). Step 3: Multiply these highest powers together. LCM = 2^3 × 3^2 LCM = 8 × 9 LCM = 72 The Lowest Common Multiple is: 72 8. Angles: Draw an angle of 120^ and label it correctly as "Obtuse" An angle of 120^ is an obtuse angle because it is greater than 90^ but less than 180^. To draw it: • Draw a straight line segment. This will be one arm of the angle. • Place the protractor's center on one endpoint of the line segment (the vertex). Align the baseline of the protractor with the line segment. • Find the 120^ mark on the protractor and make a small dot. • Draw a second line segment from the vertex to the dot. • Label the angle as 120^ and indicate that it is an obtuse angle. 9. Word Problem: Calculate cloth needed for 6 outfits Step 1: Multiply the cloth needed for one outfit by the number of outfits. Total cloth = 2.5 meters/outfit × 6 outfits Step 2: Perform the multiplication. Total cloth = 15 meters The total meters of cloth needed is: 15 meters 10. Symmetry: Draw a square and a rectangle and their lines of symmetry Square: A square has 4 lines of symmetry. Two lines pass through the midpoints of opposite sides (horizontal and vertical). Two lines pass through opposite vertices (diagonals). Rectangle: A rectangle has 2 lines of symmetry. Two lines pass through the midpoints of opposite sides (one horizontal, one vertical). (A rectangle does not have diagonal lines of symmetry unless it is also a square). DIGITAL TECHNOLOGIES Shortcut Challenge: a)* Highlight your name and press Ctrl + B. What happened to the text? The text became bold*. b)* Press Ctrl + E. Where did your text move to on the page? The text moved to the center* of the page. c)* Press Ctrl + J three times. Did the text get smaller or larger? Ctrl + J is the shortcut for Justify alignment in Microsoft Word. It aligns text to both the left and right margins. It does not* make the text smaller or larger. d)* Observation: In the "Insert" tab, click "Shapes". Draw a star. Which menu tab appears at the very top (usually in a different color) once the star is selected? The Format* tab (specifically "Shape Format" or "Drawing Tools Format") appears.

Convert 21 from base 10 to base 2. Calculate 15% discount on N5,000. List 3 cylindrical and 3 rectangular prism household objects. Simplify 5x + 10 - 2x + 4.

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Convert 21 from base 10 to base 2. Calculate 15% discount on N5,000. List 3 cylindrical and 3 rectangular prism household objects. Simplify 5x + 10 - 2x + 4.

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