A theater wants to take in at least $2000 for a certain matinee. Children's tickets cost $5 each and adult tickets cost $10 each. The theater has a maximum of 350 seats.

The correct answer is x + 2y 400 and also y and x .

Step-by-step explanation:

Amount a theater wants for a certain matinee = $2000

Cost of Children's ticket is $5 and for adult is $10.

Let there are x children and y adults in the theater. Total capacity of the theater is maximum 350. Thus x + y 350.

Thus the above situation can be demonstrated as:

5x + 10y 2000

⇒ x + 2y 400 and also y and x .

Thus the set of solutions can be given by the above three inequalities. One such possibility could be 300 students and 50 adults for the matinee.

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for