1. **Convert 678 cm² to m²** Since 1 m = 100 cm, area conversion is: $$1 \text{ m}^2 = 100^2 = 10,000 \text{ cm}^2$$ Therefore, $$678 \text{ cm}^2 = \frac{678}{10,000} = 0.0678 \text{ m}^2$$ 2. **Convert 0.58 m² to cm²** Using the same factor: $$0.58 \text{ m}^2 = 0.58 \times 10,000 = 5800 \text{ cm}^2$$ 3. **Solve equation: $$5(7q - 3) = 28(q - 1)$$** Step 1: Expand both sides: $$35q - 15 = 28q - 28$$ Step 2: Bring variables to one side and constants to the other: $$35q - 28q = -28 + 15$$ $$7q = -13$$ Step 3: Solve for $$q$$: $$q = \frac{-13}{7}$$ 4. **Sum of four consecutive even numbers is 76. Find the smallest number.** Let the smallest even number be $$x$$. The numbers are: $$x, x+2, x+4, x+6$$ Their sum is: $$x + (x+2) + (x+4) + (x+6) = 76$$ Simplify: $$4x + 12 = 76$$ $$4x = 76 - 12 = 64$$ $$x = \frac{64}{4} = 16$$ So smallest even number is $$16$$. 5. **Area of the given shape (rectangle with four quarter circles removed).** Step 1: Calculate area of rectangle: $$6 \text{ m} \times 2 \text{ m} = 12 \text{ m}^2$$ Step 2: Each quadrant is a quarter circle with radius $$1$$ m. Area of one circle: $$\pi r^2 = \pi \times 1^2 = \pi$$ Area of one quadrant: $$\frac{\pi}{4}$$ Four quadrants make one full circle: $$4 \times \frac{\pi}{4} = \pi$$ Step 3: Area of the shape after removing four quadrants: $$12 - \pi \approx 12 - 3.1416 = 8.8584 \text{ m}^2$$ 6. **Find value of:** $$\frac{-8 - \{18 + (-4)^2\} + 2^3}{2}$$ Step 1: Calculate inside the braces: $$(-4)^2 = 16$$ So, $$18 + 16 = 34$$ Step 2: Calculate $$2^3 = 8$$ Step 3: Substitute back: $$\frac{-8 - 34 + 8}{2} = \frac{-34}{2} = -17$$ 7. **Solve equation:** $$\frac{6(x-2)}{7} = \frac{2(x-7)}{3}$$ Step 1: Cross multiply: $$3 \times 6(x-2) = 7 \times 2(x-7)$$ $$18(x-2) = 14(x-7)$$ Step 2: Expand: $$18x - 36 = 14x - 98$$ Step 3: Bring terms together: $$18x - 14x = -98 + 36$$ $$4x = -62$$ Step 4: Solve for $$x$$: $$x = \frac{-62}{4} = -15.5$$