Test logs and Pythagorean Theorem 4th block
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Hard
+1
Standards-aligned
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1.
FLASHCARD QUESTION
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.
Tags
CCSS.8.G.B.8
2.
FLASHCARD QUESTION
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.
Tags
CCSS.8.G.B.8
3.
FLASHCARD QUESTION
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).
4.
FLASHCARD QUESTION
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).
Tags
CCSS.8.G.B.8
5.
FLASHCARD QUESTION
Front
What is the hypotenuse in a right triangle?
Back
The hypotenuse is the longest side of a right triangle, opposite the right angle.
6.
FLASHCARD QUESTION
Front
Simplify: 3log_3(a) + 2log_3(b)
Back
log_3(a³b²) using the properties of logarithms.
7.
FLASHCARD QUESTION
Front
What is the result of log(x²y)?
Back
2log(x) + log(y) using the properties of logarithms.
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