A classroom measures (x+2)m by (x-5)m. If the area of the classroom is 60 extm2. Find its dimensions.

Here are the solutions to questions 8, 9, and 10.

8. A classroom measures $(x+2)$m by $(x-5)$m. If the area of the classroom is $60\text{m}^2$. Find its dimensions.

Step 1: Set up the equation for the area of the classroom.

$$(x+2)(x-5) = 60$$

Step 2: Expand the left side of the equation.

$$x^2 - 5x + 2x - 10 = 60$$ $$x^2 - 3x - 10 = 60$$

Step 3: Rearrange the equation into a standard quadratic form $ax^2 + bx + c = 0$.

$$x^2 - 3x - 10 - 60 = 0$$ $$x^2 - 3x - 70 = 0$$

Step 4: Factor the quadratic equation. We need two numbers that multiply to -70 and add to -3. These numbers are -10 and 7.

$$(x-10)(x+7) = 0$$

Step 5: Solve for $x$.

$$x-10 = 0 \quad \text{or} \quad x+7 = 0$$ $$x = 10 \quad \text{or} \quad x = -7$$

Step 6: Choose the valid value for $x$. Since dimensions cannot be negative, $x=10$ is the valid solution.

Step 7: Calculate the dimensions using $x=10$.
Length: $x+2 = 10+2 = 12\text{ m}$
Width: $x-5 = 10-5 = 5\text{ m}$
The dimensions of the classroom are $\boxed{12\text{ m by } 5\text{ m}}$.

9. A bag contains 3 red balls and 4 blue balls. A ball is picked at random:

Total number of balls = $3 \text{ (red)} + 4 \text{ (blue)} = 7$ balls.