A Cepheid star is a type of variable star, which means its brightness is not constant. The relationship between the brightness of a Cepheid star and its period, or length of its pulse, is given by M = –2.78(log P) – 1.35, where M is the absolute magnitude, or brightness, of the star, and P is the number of days required for the star to complete one cycle. What is the absolute magnitude of a star that has a period of 45 days? Use a calculator. Round your answer to the nearest hundredth. –5.95 –4.60 3.25 4.60

The absolute brightness of the Cepheid star after a period of 45 days is -5.95

Step-by-step explanation:

Since the absolute magnitude or brightness of a Cepheid star is related to its period or length of its pulse by

M = –2.78(log P) – 1.35 where M = absolute magnitude and P = period or length of pulse.

From our question, it is given that P = 45 days.

So, M = –2.78(log P) – 1.35

M = –2.78(log 45) – 1.35

M = –2.78(1.6532) – 1.35

M = -4.60 - 1.35

M = -5.95

So, the absolute magnitude or brightness M of a Cepheid star after a period P of 45 days is -5.95

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

the answer is c.

step-by-step explanation: