20. Adults and children attend a play. Tickets cost $2 per child and $3 per adult. The total cost for tickets is $31. In total, 12 people attend the
play. How many children attend the play?

5 children

Adults: x

Children: y

Cost for adults: 3x

Cost for children: 2y

Total cost: 3x + 2y = 31

Total people: x + y = 12

x = 12 - y

Substitute:

3 (12 - y) + 2y = 31

36 - 3y + 2y = 31

36 - y = 31

y = 5

Total Children: 5

step-by-step explanation:

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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°

hope this