Is the following shape a rectangle? how do you know?

The answer is (D). No, the adjacent sides are not perpendicular.

Step-by-step explanation: We are given a shape on the co-ordinate plane and we are to check the correct statement about the shape from the given options.

The shape has four vertices A(4, -1), B(2, 4), C(-2, 2) and D(0, -3). So, the shape is definitely a quadrilateral. We are to check whether it is a rectangle or not.

We will find the slope of all the sides AB(m), BC(n), CD(o) and DA(p) as follows:

Since,

so the opposite sides are parallel, but

so the adjacent sides are not perpendicular.

Thus, (D) 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

answer: y=4000x+14000

step-by-step explanation: