Solve the following equations: Q.5: 3x + 4 = 19 − 2x; Q.6: Find the zeroes of 2x2 - 7x + 3; Q.7: Find the hypotenuse of a right-angled triangle with legs 6cm and 8cm.

The given equation is $3x + 4 = 19 - 2x$.
Add $2x$ to both sides:

Subtract 4 from both sides:

Divide both sides by 5:

The final answer is $\boxed{x=3}$.

Q.6

The polynomial is $2x^2 - 7x + 3$.

We look for two numbers that multiply to $2 \times 3 = 6$ and add up to $-7$. These numbers are $-1$ and $-6$.
Rewrite the middle term:

Factor by grouping:

The zeroes of the polynomial are $\frac{1}{2}$ and 3.
The final answer is $\boxed{x=\frac{1}{2}, x=3}$.

Q.7

In $\triangle ABC$, it is right-angled at B.
The lengths of the two legs are $AB = 6$ cm and $BC = 8$ cm.
We need to find the length of the hypotenuse $AC$.

For a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (legs).

Take the square root of both sides:

The final answer is $\boxed{AC=10 \text{ cm}}$.

Q.8

The tangent of an angle in a right-angled triangle is the ratio of the length of the opposite side to the length of the adjacent side. For $45^\circ$, the opposite and adjacent sides are equal.

The final answer is $\boxed{\tan 45^\circ = 1}$.