Tickets at a particular movie theater have different rates for adults and children. on monday, the theater sold 8 adult tickets and 2 child tickets for $122. the next day, the theater sold 5 adult tickets and 9 children tickets for $115. what is the price for the child ticket?

Price for the child ticket (y) is 5 dollars.

Step-by-step explanation:

Let the price of adult tickets be x and price of child tickets be y.

Since theater sold 8 adult ticket and 2 child tickets for $122, therefore

Price of 8 adult tickets = 8x

Price of 2 child tickets = 2y

According to question,

8x + 2y = 122 ............(1)

8x = 122 -2y

Similarly, Price of 5 adult tickets = 5x

Price of 9 child tickets = 9y

According to question,

5x + 9y = 115

By substituting the value of x

=

=

=

=

=

Therefore the price for the child ticket is 5 dollars.

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

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it has the same slope and a different y-intercept

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