The necessary and sufficient condition for a non - empty subset W of a vector space V(F) to be a subspace of V is a,b in F and alpha , beta in W implies a alpha + b beta in W I need to prove the postulates of vector space with this condition

The transverse axis of a hyperbola is double the conjugate axes. Whats the eccentricity of the hyperbola $$\begin{gathered} A)\frac{\sqrt{5}}{4} \\ B)\frac{\sqrt{7}}{4} \\ C)\frac{7}{4} \\ D)\frac{5}{3} \end{gathered}$$

Which of the following is an example of a pair of parallel lines?
Sides of a triangle
Surface of a ball
Corner of a room
Railway track

State whether the statements are True or False. All rectangles are parallelograms.

Point T(3, −8) is reflected across the x-axis. Which statements about T' are true?

If two parallel lines are cut by a transversal, then:
each pair of alternate angles are equal
each pair of alternate angles add up to 180 degrees
each pair of corresponding angles add up to 180 degees.
each pair of corresponding angles is equal.

The opposite faces of a dice always have a total of ___ on them.

What is the term for a part of a line with two endpoints?
A. Line Segment
B. Line
C. Ray
D. Point

ABCD is a parallelogram. Which of the following is not true about ABCD?
AB=CD
AD=CB
AD||CD
AB||CD

If the points $(a,0)$, $(0,b)$ and $(1,1)$ are collinear then which of the following is true?
$\frac{1}{a}+\frac{1}{b}=1$
$\frac{1}{a}-\frac{1}{b}=2$
$\frac{1}{a}-\frac{1}{b}=-1$
$\frac{1}{a}+\frac{1}{b}=2$

The angles of a triangle are in the ratio 1 : 1 : 2. What is the largest angle in the triangle?
$$\begin{gathered} A){90}^{\circ <!--\; \circ \; -->} \\ B){135}^{\circ <!--\; \circ \; -->} \\ C){45}^{\circ <!--\; \circ \; -->} \\ D){150}^{\circ <!--\; \circ \; -->} \end{gathered}$$

What is the greatest number of acute angles that a triangle can contain?

How many right angles are required to create a complete angle?
1) Two
2) Three
3) Four
4) Five

Find the sum of interior angles of a polygon with 12 sides in degrees.$$\begin{gathered} {1800}^{\circ } \\ {1200}^{\circ } \\ {1500}^{\circ } \\ {1400}^{\circ } \end{gathered}$$

In Euclid's Division Lemma when $a=bq+r$ where $a,b$ are positive integers then what values $r$ can take?

When two lines cross each other at a point we call them ___ lines.