Answer:
Step-by-step explanation:
a) period is the length of one cycle ( one full squiggle ) If you are lucky and the graph is on exact numbers.. at a high point and to the next high point.. then just take that horizontal distance, that's one period also if it's not you could find the period, T, by using T = 2pi / k where k is a number that represents how fast , or how many times the wave cycles in one second or some other amount of time.
b) Amplitude is a number that goes right before the sinusoid, which is multiplied by it because, sin , cos, are at max 1 or at min -1
c) vertical shift is what is added , for upwards shift... before or after the sinusoid ie sin , cos, ect ect.
does this help?
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.
A is correct because 445.50 Divided By 150 is Equal to $2.97.
Answer:
Step-by-step explanation:
a|c means that c=a*k k is some positive integer. We know that b|c so b| ak and (a,b)=1, so it must be b|k, i.e k=b*r, r is some positive integer number. Now we have that c=abr, so ab| c.
B) if x and x’ are both solution then we have that
mi | x-x’ for every i.
By a) we have that m1m2...mk| x-x’, so x and x’ are equal by mod od m1m2...mk.
