Explanation:
Level 2
Part 1: √250 would be simplified to 5√10, because you need to find two factors that equal 250. 25 multiplied by 10 are two factors that you can utilize. Because 25 is a perfect square, it could be reduced to 5. Because 10 isn't a perfect square, you leave it as a radical.
Part 2: √250 is an irrational number because it's a non-terminating decimal and you cannot convert it into a fraction, so it wouldn't be rational.
Level 3
Part 1: √150x^5 would be simplified to 5x^2√6x. Again, find two factors that equal the product, 150. 25 multiplied by 6 are two factors that are useable. Just like the first question, 25 is a perfect square, so it can be reduced to 5. 6 is not a perfect square, so you would leave as a radical. Now, moving onto x^5. You can factor out x^4, because it's a perfect square. x^4 can become x^2. Move x^2 next to 5 and x would be left in the radical with 6.
Part 2: It's rational because 2√4 is simply just 2 x 2 because √4 is a perfect square. 4+7=11. 11 can be converted into a fraction, so it wouldn't be irrational.
Level 4
Part 1: 13√750x*5 y*8 would be simplified to 65x^2y^4√30x. Find two factors that equal 750, which are 25 and 30. You know the drill, 25 is reduced to 5 and 30 stays as a radical. Multiply 13 and 5 to get 65. Factor out x^4 out of x^5 to get x^2. x^8 is a perfect square that can be reduced to x^4.
Part 2: Two unique expressions are 4√16+3 and 5√8 x 34. √16 is a perfect square, so it can become 4. 4 x 4 is 16 and 16 + 3 = 19. 19 is a rational number. 5√8 is irrational, so right off the bat, you'll know it's an irrational expression.
Answer: C. The set is not a subspace of set of prime numbers P 9. The set does not contain the zero vector of set of prime numbers P 9.
Step-by-step explanation:
Answer:
m∠B = 43°
b = 26.1
c = 38.3
Step-by-step explanation:
By applying triangle sum in the given triangle,
47° + 90° + m∠B = 180°
137° + m∠B = 180°
m∠B = 43°
By applying sine ratio to the angle measuring 47°.
sin(47°) = 
= 
c = 
c = 38.28
c ≈ 38.3
By applying cosine rule,
cos(47°) = 
= 
= 
b = 38.3[cos(47°)]
b = 26.1
Answer:
16/25
Step-by-step explanation:
We have 4 red marbles and a total of 4 + 1 = 5 marbles.
Probability is simply (# times a specific event can occur) / (# times any event can occur).
Here, the probability of drawing a red marble is: 4/5 (because there are 4 red marbles to choose from and a total of 5 marbles to choose from).
We replace the marble afterward, so the probability that the second pick is also red would still be 4/5.
Then, multiply the two fractions together: (4/5) * (4/5) = 16/25.
Hope this helps!
