Apiece of work can be completed by 45 men in 90 days if only 30 men are available, how many days will it take to complete the same work ?

  135 days

Step-by-step explanation:

Often, we measure work in man·days. This piece of work requires ...

  (45 man)·(90 days) = 4050 man·days

When there are only 30 men, the number of days required can be found by dividing this work by the number of men:

  4050 man·days/(30 man) = 135 days

Another approach is to realize the time is inversely proportional to the number of men. If the number of men is 30/45 = 2/3 the original, then the time will be 3/2 the original, or ...

  (3/2)·90 days = 135 days.

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

your answer is c. 97 (don't delete this again)

step-by-step explanation: