Answer:

Step-by-step explanation:
Given

i.e. first to fifth
Required
Determine number of selection
1st position = Any of the 30 students
2nd position = Any of the 29 students
3rd position = Any of the 28 students
4th position = Any of the 27 students
5th position = Any of the 26 students
Number of selection is then calculated as:


The function in vertex form is

(refer to your other post I solved it there).
The general form of quadratic equations in vertex form is

, where (h, k) is the vertex of the parabola.
Here, a = 1, h = -6 and k = -54
Therefore, the vertex is (-6, -54) and it is a maximum because a = 1 is postive.
Answer:400 miles per hour
Step-by-step explanation:
Let w = speed at which the plane travelled west
Let s = speed at which the plane travelled south
Distance moved in 5 hrs heading west = 5*w = 5w
Distance moved in 4 hrs heading south = 4*s = 4s
Total distance, 3444= 5w + 4s
w = s + 39( 39 miles/hr faster)
5(s+39) + 4s = 3444
5s + 195 + 4s = 3444
9s = 3249
s = 361 miles per hour
w = s + 39 = 361 +39
= 400 miles per hour
Answer:Triangle A: 38 degrees
Triangle B: Unknown (not enough information)
Triangle C: Unknown (not enough information)
Triangle D: 70 degrees
Triangle E: 40 degrees
Step-by-step explanation:
Answer:
Carrie and Joan have 80 nickels and 40 dimes, respectively, and each one has an amount of money of 4 US dollars.
Step-by-step explanation:
Let be
and
the amounts of nickels and dimes that Carrie and Joan have, as
the total amount of money that both Carrie and Joan have. A nickel is a five cent coin and a dime is a ten cent coin.
The following equations are constructed after a careful reading on statement:
Carrie's amount of money:
(Eq. 1)
Joan's amount of money:
(Eq. 2)
Relation between amounts of coins:
(Eq. 3)
First we eliminate
by equalizing (Eq. 1) and (Eq. 2):

Then, we reduce the resulting formula by (Eq. 3):



And rest of variable are now determined:




Carrie and Joan have 80 nickels and 40 dimes, respectively, and each one has an amount of money of 4 US dollars.