Quadrilateral ABCD has vertices A(- 3, 1), B(4, 2) B(4, 2), C(9, - 3) , and D(2, - 4) . aProve that quadrilateral ABCD is a rhombus b )Prove that ABCD is not a square .

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Explanation:

The vectors representing the diagonals are ...

  AC = C - A = (9, -3) -(-3, 1) = (12, -4)

  BD = D - B = (2, -4) -(4, 2) = (-2, -6)

The dot-product of these vectors is the sum of the products of corresponding coordinates:

  (12)(-2) +(-4)(-6) = -24 +24 = 0

When the dot-product is zero, the vectors are perpendicular. These vectors are different lengths (BD = 1/2·AC), so they are not the diagonals of a square.

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The midpoints of the diagonals will be in the same place if the quadrilateral is a rhombus.

  (A +C)/2 = (B +D)/2

We can simplify our effort a bit by multiplying by 2.

  A+C = B+D

  (9, -3) +(-3, 1) = (2, -4) +(4, 2)

  (6, -2) = (6, -2) . . . . . . . . . . . . . . . . yes, the midpoints are the same point

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We have shown the diagonals of the quadrilateral are different lengths and perpendicular bisectors of each other, so the quadrilateral IS A RHOMBUS, NOT A SQUARE.

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.

answer: -1

step-by-step explanation: