Given that x = 3/4 : 1/2 = 1/9 : 8, find the value of x.

Here are the solutions to the problems:

Question 37: Given that $x = \frac{3}{4} \div \frac{1}{2} \times \frac{9}{8}$, find the value of $x$.

Step 1: Perform the division first, as division and multiplication have equal precedence and are performed from left to right.

$$x = \left(\frac{3}{4} \div \frac{1}{2}\right) \times \frac{9}{8}$$ $$x = \left(\frac{3}{4} \times \frac{2}{1}\right) \times \frac{9}{8}$$

Step 2: Multiply the fractions.

$$x = \frac{6}{4} \times \frac{9}{8}$$

Step 3: Simplify the first fraction and then multiply.

$$x = \frac{3}{2} \times \frac{9}{8}$$ $$x = \frac{3 \times 9}{2 \times 8} = \frac{27}{16}$$

The calculated value is $\frac{27}{16}$. This value is not among the given options.

Question 38: The roots of a quadratic equation are $-\frac{2}{3}$ and $-\frac{1}{4}$. Find the equation.

Step 1: Let the roots be $\alpha = -\frac{2}{3}$ and $\beta = -\frac{1}{4}$. Calculate the sum of the roots.

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