Mathematical Concepts and Problem Solving

The video tutorial covers three SAT math problems. Problem 18 involves finding the average of x, y, and z in terms of k and z by using algebraic substitution. Problem 19 focuses on geometry, specifically calculating the area of a circle using the properties of an equilateral triangle and the Pythagorean theorem. Problem 20 deals with finding integer values of k for which 15 divided by k leaves a remainder of 3, using a brute force approach.

If the average of x and y is k, what is the expression for the average of x, y, and z in terms of k and z?

• 2k + z/3

• k + 2z/3

• 2k + 3z

• k + z/3

In an equilateral triangle with side length 2, what is the length of the side opposite the 60-degree angle in a 30-60-90 triangle?

• 2

• √3/2

• 1

• √3

What is the radius of a circle if the diameter is √3?

• √3

• √3/2

• 3/2

• 1/2

What is the area of a circle with radius √3/2?

• 3π/2

• π/4

• π/2

• 3π/4

When 15 is divided by a positive integer k, the remainder is 3. Which of the following is a possible value of k?

• 6

• 5

• 8

• 7

How many positive integer values of k satisfy the condition that 15 divided by k leaves a remainder of 3?

• 5

• 4

• 2

• 3