Triangle Area and Inequalities

The video tutorial covers solving algebraic equations to determine relationships between variables, such as whether x is less than y, and if v equals 0. It also explores solving for n in an exponential equation and determining if the area of a triangle is greater than a given value using coordinate geometry.

Given the equation x/2 = 3/y, which statement is sufficient to determine if x is less than y?

• y is greater than or equal to 3

• y is less than or equal to 4

• Neither statement is sufficient

• Both statements are needed

If y is greater than or equal to 3, what is the maximum possible value of x?

• 1.5

• 2

• 1

• 3

In the equation vw = v^2, what can be concluded if v and w are different integers?

• v must be 0

• w must be 0

• v and w must be equal

• v and w must be negative

What does statement 2, 'w is equal to 2', imply about v in the equation vw = v^2?

• v must be 0

• v must be 2

• v can be any integer

• v must be greater than 2

What are the possible values of n given the equation n^2 - 5n + 6 = 0?

• n = 4 or n = 5

• n = 3 or n = 4

• n = 2 or n = 3

• n = 1 or n = 2

Which statement is needed in addition to n^2 - 5n + 6 = 0 to determine the value of n?

• n minus 2 does not equal 0

• n is greater than 3

• n is less than 2

• n is a prime number

What is the height of the triangle OPQ if point P is at (6, 8)?

• 10

• 8

• 6

• 12

What is the base of the triangle OPQ if point Q is at (13, 0)?

• 13

• 6

• 8

• 10

What is the area of triangle OPQ if OP is less than PQ and P is at (6, 8)?

• 52

• 48

• 36

• 24

Which statement alone is sufficient to determine if the area of triangle OPQ is greater than 48?

• Coordinates of point P

• Neither statement is sufficient

• Coordinates of point Q

• Both statements are needed