1. Calculate $2 \left( \frac{3}{5} \right)^2$. First, square $\frac{3}{5}$: $$\left( \frac{3}{5} \right)^2 = \frac{3^2}{5^2} = \frac{9}{25}$$ Then multiply by 2: $$2 \times \frac{9}{25} = \frac{2 \times 9}{25} = \frac{18}{25}$$ 2. Calculate $\frac{3}{4} + \frac{1}{2} \times \frac{2}{3}$. Multiply $\frac{1}{2}$ and $\frac{2}{3}$: $$\frac{1}{2} \times \frac{2}{3} = \frac{1 \times 2}{2 \times 3} = \frac{2}{6} = \frac{1}{3}$$ Add $\frac{3}{4}$ and $\frac{1}{3}$: Find common denominator 12: $$\frac{3}{4} = \frac{9}{12}, \quad \frac{1}{3} = \frac{4}{12}$$ Sum: $$\frac{9}{12} + \frac{4}{12} = \frac{13}{12}$$ 3. Expand $2x(x - 5)$. Distribute $2x$: $$2x \times x - 2x \times 5 = 2x^2 - 10x$$ 4. Simplify $x^2 - x + 3 + 3x^2 + 5x - 1$. Group like terms: $$x^2 + 3x^2 = 4x^2$$ $$-x + 5x = 4x$$ $$3 - 1 = 2$$ So: $$4x^2 + 4x + 2$$ 5. Simplify $(4x - 9) - (2x + 5)$. Distribute minus: $$4x - 9 - 2x - 5$$ Combine like terms: $$4x - 2x = 2x$$ $$-9 - 5 = -14$$ Result: $$2x - 14$$ 6. Simplify $\frac{12x^2 - 8x}{4x}$. Divide numerator and denominator by $4x$: $$\frac{\cancel{4} \times 3 x^2 - \cancel{4} \times 2 x}{\cancel{4} x} = \frac{3x^2 - 2x}{x}$$ Divide each term: $$\frac{3x^2}{x} - \frac{2x}{x} = 3x - 2$$ 7. Find the slope of $y = 3x - 2$. The slope is the coefficient of $x$: $$m = 3$$ 8. Find the y-intercept of $y = 3x - 2$. The y-intercept is the constant term: $$b = -2$$ 9. Sketch the line $y = 3x - 2$. This is a straight line with slope 3 and y-intercept -2. - Start at point $(0, -2)$ on the y-axis. - From there, rise 3 units and run 1 unit to the right to plot another point. - Draw a straight line through these points. Final answers: 1. $\frac{18}{25}$ 2. $\frac{13}{12}$ 3. $2x^2 - 10x$ 4. $4x^2 + 4x + 2$ 5. $2x - 14$ 6. $3x - 2$ 7. $3$ 8. $-2$ 9. Line with slope 3 and y-intercept -2