A rectangle inscribed in a square is also a square. Proof Let rectangle MNPQ be inscribed in square ABCD as shown in Fig 2.6. Drop perpendiculars from P to AB and from Q to BC at R and S, respectively. Clearly PR  QS. Furthermore, PM  QN. SO PMR  QNS, and hence PMR  QNS. Consider quadrilateral MBNO where O is the point of intersection of QN and PM. Its exterior angle at the vertex N is congruent to the interior angle at the vertex M, so that the two interior angles at the vertices N and M are supplementary. Thus, the interior angles at the vertices B and O must also be supplementary. But ABC is a right angle, and hence, NOM must also be a right angle. Therefore the diagonals of rectangle MNPQ are perpendicular. Hence, MNPQ is a square.

the expected value of the random variable : 0, 1 and 2

step-by-step explanation:

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.

answer: plz mark me brainliest

7 hours, 0 minutes, 0 seconds

or:  

0.04

total weeks

or:  

0.29

total days

or:  

7.00

total hours

or:  

420.00

total minutes

or:  

25,200.00

total seconds

step-by-step explanation: