Distance, Algebra, and Triangle Properties

The video tutorial covers five mathematical problems, each focusing on different concepts. Problem 63 involves determining the shorter route Carlotta can take to her office. Problem 64 examines whether x is greater than y using two statements. Problem 65 explores whether m is an odd integer. Problem 66 calculates the area of a triangle using given dimensions. Finally, Problem 67 finds the value of b plus c through algebraic manipulation.

What is the total distance Carlotta drives if she takes the shorter route to the office and the longer route back?

• 23 kilometers

• 46 kilometers

• 42 kilometers

• 19 kilometers

If Carlotta drives both ways using the longer route, what is the total distance she covers?

• 42 kilometers

• 46 kilometers

• 23 kilometers

• 19 kilometers

Given x = y + 2, which statement is true?

• x is sometimes greater than y

• x is always less than y

• x is always equal to y

• x is always greater than y

If x/2 = y - 1, which of the following can be concluded?

• x is always equal to y

• x can be either greater or less than y

• x is always less than y

• x is always greater than y

If m divided by 2 is not an even integer, what can be inferred about m?

• m is definitely odd

• m is definitely even

• m is a prime number

• m could be either odd or even

If m - 3 is an even integer, what can be concluded about m?

• m is odd

• m is even

• m is a prime number

• m is a composite number

What is the area of a triangle if the product of its base and height is 20?

• 20

• 40

• 10

• 5

If a triangle has angles of 45, 45, and 90 degrees, what can be said about its size?

• It is an equilateral triangle

• It is a small triangle

• It is a large triangle

• Its size cannot be determined

If ab + cd + ac + bd = 6 and a + d = 4, what is the value of b + c?

• 2

• 1.5

• 3

• 1

What algebraic property is used to simplify ab + cd + ac + bd into (a + d)(b + c)?

• Commutative Property

• Associative Property

• Distributive Property

• Identity Property