1. Represent 7/5 and 4/5 on the number line. - The fractions 7/5 and 4/5 are represented as points on the number line between 1 and 2. - 4/5 is less than 1, approximately 0.8, so mark a point before 1. - 7/5 is greater than 1, exactly 1.4, so mark a point after 1. 2. Express 3x = 7 in ax + by + c = 0 form and find a, b, c. - Given equation: $$3x = 7$$ - Bring all terms to LHS: $$3x - 7 = 0$$ - Comparing with $$ax + by + c = 0$$, we get $$a=3$$, $$b=0$$, $$c=-7$$. 3. Find 3 rational numbers between 3 and 4 using mean method. - Mean of 3 and 4 is $$\frac{3+4}{2} = \frac{7}{2} = 3.5$$. - Now find means between 3 and 3.5: - Mean of 3 and 3.5: $$\frac{3 + 3.5}{2} = 3.25$$. - Means between 3.5 and 4: - Mean of 3.5 and 4: $$\frac{3.5 + 4}{2} = 3.75$$. - So three rational numbers between 3 and 4 are $$3.25$$, $$3.5$$, and $$3.75$$. 4. Nikhitha says median of 2x, 5x, 3x, x² is 15 and x=6. - Arrange numbers in increasing order for median. - For x=6: values are 2*6=12, 5*6=30, 3*6=18, and $$6^2=36$$. - Sort: 12, 18, 30, 36. - Median of 4 numbers is average of 2nd and 3rd terms: $$\frac{18 + 30}{2} = 24$$, not 15. - So Nikhitha is incorrect because with x=6 median is 24, not 15. 5. Ratio of complementary angles is 2:3, find angles. - Complementary angles sum to 90°. - Let angles be $$2k$$ and $$3k$$. - Equation: $$2k + 3k = 90$$. - $$5k = 90 \Rightarrow k=18$$. - Angles are $$2k=36^\circ$$ and $$3k=54^\circ$$. 6. Show (6, -4) and (3, -2) satisfy $$2x + 3y = 0$$. - For (6, -4): $$2(6) + 3(-4) = 12 - 12 = 0$$, satisfies equation. - For (3, -2): $$2(3) + 3(-2) = 6 - 6 = 0$$, satisfies equation. Final answers included in steps.