Lily begins solving the equation 4(x – 1) – x = 3(x + 5) – 11. Her work is shown below. 4(x – 1) – x = 3(x + 5) – 11
4x – 4 – x = 3x + 15 – 11
3x – 4 = 3x + 4
How can her partial solution be interpreted?

The equation has one solution: x = 0.
The equation has one solution: x = 8.
The equation has no solution.
The equation has infinite solutions.

The 3rd option i.e. 'the equation has no solution' is the correct option.

Step-by-step explanation:

Given the given function

4(x – 1) – x = 3(x + 5) – 11

Lily's work is shown below

4(x – 1) – x = 3(x + 5) – 11

4x – 4 – x = 3x + 15 – 11

3x – 4 = 3x + 4

It is clear that the Left-hand side of the equation is not equal to the right-hand side of the equation as 3x – 4 can not be equal to 3x + 4.

i.e.

3x – 4 ≠ 3x + 4

3x - 3x -4 ≠ 4

            -4 ≠ 4

       L.H.S ≠ R.H.S

Therefore, the equation has no solution.

Hence, the 3rd option i.e. 'the equation has no solution' is the correct option.

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