Divisibility, Equations, and Functions

The video tutorial covers a series of math problems, starting with analyzing a graph problem involving a line segment and finding a point on it. It then moves on to a divisibility problem, determining which numbers a given integer is divisible by. The tutorial continues with solving a quadratic equation by finding its roots through factorization. It also includes evaluating expressions using order of operations and solving equations for specific variable values. Each problem is explained step-by-step, highlighting key mathematical concepts and techniques.

What is the point on segment PQ that is twice as far from P as it is from Q?

• (1, 1)

• (2, 1)

• (3, 2)

• (0, -1)

If a number is divisible by both 5 and 7, which of the following must it also be divisible by?

• 12

• 35

• 10

• 70

Given that 4 is a solution to the equation x^2 + 3x + k = 10, what is the other solution?

• -3

• 3

• 7

• -7

What is the value of -3 times the square of -3?

• -27

• 27

• 9

• -9

What is the result of 29 squared plus 29 divided by 29?

• 30

• 58

• 29

• 1

For what value of t does x = 1 - 3t equal y = 2t - 1?

• 3

• 2/5

• 1/2

• 5/2