The factors of x² + 7x + 6 are?

The expression is $x^2 + 7x + 6$.

The numbers are 1 and 6, because $1 \times 6 = 6$ and $1 + 6 = 7$.

The factors are $(x+1)$ and $(x+6)$.

The correct option is A.

6. The value of $\sqrt{6} \times \sqrt{27}$ is:

So, the expression becomes $\sqrt{162}$.

The value is $9\sqrt{2}$.

The correct option is B.

7. Observe the triangles, the correct statement among the following is:

In $\triangle ABC$:
Side $AB = 6$ cm
Side $BC = 4$ cm
Angle $\angle B = 90^\circ$ (indicated by the square symbol)

In $\triangle QPR$:
Side $QP = 6$ cm
Side $PR = 4$ cm
Angle $\angle P = 90^\circ$ (indicated by the square symbol)

We have:
$AB = QP = 6$ cm
$\angle B = \angle P = 90^\circ$
$BC = PR = 4$ cm

Since two sides and the included angle of $\triangle ABC$ are equal to two sides and the included angle of $\triangle QPR$, the triangles are congruent.
The correspondence of vertices is $A \leftrightarrow Q$, $B \leftrightarrow P$, $C \leftrightarrow R$.

The correct option is A.

8. If one side of an isosceles triangle is 5 cm & its equal sides measure 3 cm each, then half of its perimeter is:

The equal sides are 3 cm each. The third side is 5 cm.
So, the side lengths are 3 cm, 3 cm, and 5 cm.

Perimeter $P = \text{sum of all sides}$

The correct option is B.

9. Two angles measure $(55^\circ + 3a)$ and $(115^\circ - 2a)$ if each angle is a supplement of the other, then calculate the value of "a".

If two angles are supplementary, their sum is $180^\circ$.

The value of $a$ is $10^\circ$.

10. Write any two of Euclid's axioms.

Here are two of Euclid's axioms:

• Things which are equal to the same thing are equal to one another.
• The whole is greater than the part.