Podcast
Questions and Answers
What is the least common multiple of 9 and 12?
What is the least common multiple of 9 and 12?
36
What is the greatest common divisor of 30 and 75?
What is the greatest common divisor of 30 and 75?
15
19 / 7 (solve for the quotient and remainder)
19 / 7 (solve for the quotient and remainder)
quotient 2, remainder 5
-32 / 3 (solve for the quotient and remainder)
-32 / 3 (solve for the quotient and remainder)
What is the prime factorization of 12?
What is the prime factorization of 12?
(10/7)*( -1/3) =
(10/7)*( -1/3) =
(3/10) / (7/13) =
(3/10) / (7/13) =
Simplify the √24
Simplify the √24
(√5)/(√15) =
(√5)/(√15) =
(3²)(3⁴) =
(3²)(3⁴) =
(y³)(y⁻¹) =
(y³)(y⁻¹) =
T³ / t⁸ =
T³ / t⁸ =
(2³)(3³) =
(2³)(3³) =
(3/4)² =
(3/4)² =
(2⁵)² =
(2⁵)² =
F(x) = 2x / (x-6) Find the domain of f (all permissible inputs of x)
F(x) = 2x / (x-6) Find the domain of f (all permissible inputs of x)
On a circle, points A and C have the angle 50°. The radius length is 5. What is the length of points A to C?
On a circle, points A and C have the angle 50°. The radius length is 5. What is the length of points A to C?
On a circle, a piece is cut that has an angle of 50°, where the radius length is 5. What is the area of the pie slice?
On a circle, a piece is cut that has an angle of 50°, where the radius length is 5. What is the area of the pie slice?
What is the probability of rolling a 3 twice on a six-sided die?
What is the probability of rolling a 3 twice on a six-sided die?
From a box of 10 lightbulbs you remove 4. How many different sets of 4 lightbulbs could you remove?
From a box of 10 lightbulbs you remove 4. How many different sets of 4 lightbulbs could you remove?
Flashcards are hidden until you start studying
Study Notes
Least Common Multiple and Greatest Common Divisor
- Least common multiple (LCM) of 9 and 12 is 36.
- Greatest common divisor (GCD) of 30 and 75 is 15.
Division with Quotients and Remainders
- For the division of 19 by 7, the quotient is 2, and the remainder is 5.
- For the division of -32 by 3, the quotient is -11, and the remainder is 1.
Prime Factorization and Simplification
- Prime factorization of 12 is expressed as (2)(3)(3) or (2²)(3).
- The result of (10/7) * (-1/3) simplifies to -10/21.
- The division (3/10) / (7/13) gives the result of 39/70.
- Simplifying √24 leads to 2√6, since √4 is 2 and √6 remains.
- (√5)/(√15) simplifies to √(1/3).
Exponentiation
- (3²)(3⁴) equals 3⁶, which is 729.
- The multiplication (2³)(3³) results in 6³, equivalent to 216.
- (3/4)² simplifies to 9/16, represented as 3²/4².
- Squaring (2⁵) gives 2¹⁰, which equals 1,024.
Functions and Domains
- The function f(x) = 2x / (x-6) has a domain of all real numbers except 6, as division by zero is undefined.
Circle Geometry
- For points A and C on a circle with a radius of 5 and an angle of 50°, the length between points A and C is approximately 4.4.
- The area of a pie slice with the same radius and angle measurement of 50° is approximately 10.9.
Probability and Combinations
- The probability of rolling a 3 twice on a six-sided die is 1/36, calculated as (1/6) * (1/6).
- The number of different sets of 4 lightbulbs removed from a box of 10 is 210, determined using combinations: (10)(9)(8)(7) / (4)(3)(2)(1).
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
