Kaia is designing a square mosaic tile for an art project. She draws a square on a coordinate grid with corners at (10, 12), (19, 12), (19, 21), and (10, 21). Inside the square, she paints a circular pattern with a radius of 3 units. What is the area of the square that is NOT covered by the circle? Use π = 3.14.Answer: ______________
Sophia is designing a square mosaic for an art project. She draws a large square on a grid, where each side is 7 units long. Inside the square, she places a smaller square at the center. The side length of the smaller square is 2 units. What is the area of the large square that is NOT covered by the smaller square? (Hint: Write an expression using exponents to find both areas, then subtract.)Answer: ______________
Liam is planning a school fundraiser and needs to buy supplies. He has a budget of $1,500. He spends 35% of his budget on decorations and then uses 2/5 of the remaining money on food. How much money does Liam have left after these purchases?Answer: ______________
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Answer Key & Explanations
Expressions with Exponents · Grade 6 · Worksheet 2
(-3)² × (5 + 15 ÷ 3) - 18 = ?Answer: 72 Solution: Evaluate inside the parentheses: 5 + 15 ÷ 3 Division first: 15 ÷ 3 = 5 Then addition: 5 + 5 = 10 Now we have (-3)² × 10 - 18 Evaluate the exponent: (-3)² = 9 Now we have 9 × 10 - 18 Multiplication next: 9 × 10 = 90 Finally subtraction: 90 - 18 = 72 The answer is 72.Full step-by-step solution
Step 1: Evaluate inside the parentheses: 5 + 15 ÷ 3
Step 2: Division first: 15 ÷ 3 = 5
Step 3: Then addition: 5 + 5 = 10
Step 4: Now we have (-3)² × 10 - 18
Step 5: Evaluate the exponent: (-3)² = 9
Step 6: Now we have 9 × 10 - 18
Step 7: Multiplication next: 9 × 10 = 90
Step 8: Finally subtraction: 90 - 18 = 72
The answer is 72.
Kaia is designing a square mosaic tile for an art project. She draws a square on a coordinate grid with corners at (10, 12), (19, 12), (19, 21), and (10, 21). Inside the square, she paints a circular pattern with a radius of 3 units. What is the area of the square that is NOT covered by the circle? Use π = 3.14.Answer: 52.74 Solution: Find the side length of the square. The corners are at (10, 12), (19, 12), (19, 21), and (10, 21). The horizontal distance from x = 10 to x = 19 is 19 - 10 = 9 units.Full step-by-step solution
Step 1: Find the side length of the square. The corners are at (10, 12), (19, 12), (19, 21), and (10, 21). The horizontal distance from x = 10 to x = 19 is 19 - 10 = 9 units. So side length = 9 units.
Step 2: Find the area of the square. Area = side × side = 9 × 9 = 81 square units.
Step 3: Find the area of the circle. Radius r = 3 units. Area of circle = π × r^2 = 3.14 × (3)^2 = 3.14 × 9 = 28.26 square units.
Step 4: Find the area not covered by the circle. Uncovered area = Area of square - Area of circle = 81 - 28.26 = 52.74 square units.
The answer is 52.74.
Sophia is designing a square mosaic for an art project. She draws a large square on a grid, where each side is 7 units long. Inside the square, she places a smaller square at the center. The side length of the smaller square is 2 units. What is the area of the large square that is NOT covered by the smaller square? (Hint: Write an expression using exponents to find both areas, then subtract.)Answer: 45 Solution: Find the area of the large square. The side length is 7 units. Area of a square = side × side = 7 × 7 = 7² = 49 square units.Full step-by-step solution
Step 1: Find the area of the large square. The side length is 7 units. Area of a square = side × side = 7 × 7 = 7² = 49 square units.
Step 2: Find the area of the small square. The side length is 2 units. Area = 2 × 2 = 2² = 4 square units.
Step 3: Subtract the area of the small square from the area of the large square: 49 − 4 = 45 square units.
Final answer: 45 square units.
(-3)² + 4 × (15 - 20) ÷ 2 = ?Answer: -1 Solution: Start with the expression: (-3)² + 4 × (15 - 20) ÷ 2 Calculate inside the parentheses: 15 - 20 = -5 The expression becomes: (-3)² + 4 × (-5) ÷ 2 Calculate the exponent: (-3)² = 9 The expression becomes: 9 + 4 × (-5) ÷ 2 Perform multiplication and division from left to right: 4 × (-5) = -20 The…Full step-by-step solution
Step 1: Start with the expression: (-3)² + 4 × (15 - 20) ÷ 2
Step 2: Calculate inside the parentheses: 15 - 20 = -5
Step 3: The expression becomes: (-3)² + 4 × (-5) ÷ 2
Step 4: Calculate the exponent: (-3)² = 9
Step 5: The expression becomes: 9 + 4 × (-5) ÷ 2
Step 6: Perform multiplication and division from left to right: 4 × (-5) = -20
Step 7: The expression becomes: 9 + (-20) ÷ 2
Step 8: Continue with division: (-20) ÷ 2 = -10
Step 9: The expression becomes: 9 + (-10)
Step 10: Perform the addition: 9 + (-10) = -1
The answer is -1.
Liam is planning a school fundraiser and needs to buy supplies. He has a budget of $1,500. He spends 35% of his budget on decorations and then uses 2/5 of the remaining money on food. How much money does Liam have left after these purchases?Answer: 585 Solution: Find the amount spent on decorations. Liam's total budget = $1500 He spends 35% on decorations. Amount on decorations = 35% of 1500 = (35/100) × 1500 = 0.35 × 1500 = 525 Find the money remaining after decorations.Full step-by-step solution
Let's go step-by-step.
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**Step 1: Find the amount spent on decorations.**
Liam's total budget = $1500
He spends 35% on decorations.
Amount on decorations = 35% of 1500
= (35/100) × 1500
= 0.35 × 1500
= 525
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**Step 2: Find the money remaining after decorations.**
Remaining money = 1500 − 525
= 975
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**Step 3: Find the amount spent on food.**
Food = 2/5 of the remaining money after decorations.
Amount on food = (2/5) × 975
= 2 × 195
= 390
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**Step 4: Find the final money left.**
Money left = Remaining after decorations − Food cost
= 975 − 390
= 585
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**Final answer:** 585
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