Test logs and Pythagorean Theorem 4th block

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: c² = a² + b².

Front

How can you determine if three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the square of the longest length equals the sum of the squares of the other two lengths.

Front

What are the properties of logarithms?

Back

The properties of logarithms include: 1) log_b(mn) = log_b(m) + log_b(n) (Product Property), 2) log_b(m/n) = log_b(m) - log_b(n) (Quotient Property), 3) log_b(m^k) = k*log_b(m) (Power Property).

Front

If a triangle has sides of lengths 9, 12, and 15, does it form a right triangle?

Back

Yes, it forms a right triangle because 15² = 9² + 12² (225 = 81 + 144).

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

Simplify: 3log_3(a) + 2log_3(b)

Back

log_3(a³b²) using the properties of logarithms.

Front

What is the result of log(x²y)?

Back

2log(x) + log(y) using the properties of logarithms.

Front

If a right triangle has sides of lengths 2, 3, and 3.61, which is the hypotenuse?

Back

3.61 is the hypotenuse because it is the longest side.

Front

Do the lengths 6, 8, and 10 form a right triangle?

Back

Yes, because 10² = 6² + 8² (100 = 36 + 64).

Front

What is the formula to find the area of a right triangle?

Back

Area = (1/2) * base * height.