Dorothy is thinking of two numbers. The sum of the two numbers is 40 and the difference is 6. Write a system of equations and use the elimination method to find the two numbers.

x = 23

y = 17

Step-by-step explanation:

x = 1st number

y = 2nd number

System of Equations:

x + y = 40

x - y = 6;    this can be used as x = 6+y

6+y + y = 40

6 + 2y = 40

2y = 34

y = 17

x + 17 = 40

x = 23

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