Rectangles
a. Quadrilateral MARK is a rectangle. Find each of the following:

1. MR= 4x - 60, AK= 30 - x, find MR.

2. MP= x^2 + 2, AP= x + 14, find AK.

3. MR= 4x - 60, MP= x + 5, find PR

 (1) 12     (2) 36 or 22      (3) 40

Step-by-step explanation:

NOTES about diagonals of a rectangle:

(1) Given: MR = 4x - 60   and   AK = 30 - x

   Per rule 1   →   MR = AK

                    4x - 60 = 30 - x  

                    5x - 60 = 30

                    5x         = 90

                      x         = 18

MR = 4(18) - 60

     =    72  - 60

     =         12

 (2) Given: MP = x² + 2   and   AP = x + 14

      Per rule 1   →   MP = AP

                         x² + 2 = x + 14  

                   x² - x - 12 = 0

               (x - 4)(x + 3) = 0

               x - 4 = 0      or      x + 3 = 0

                    x = 4       or            x = -3

AP(4) = (4) + 14 = 18

AP(-3) = (-3) + 14 = 11

Per rule 2   →   AK = 2AP

                      AK(4) = 2(18) = 36

                      AK(-3) = 2(11) = 22

(3) Given: MR = 4x - 60   and   MP = x + 5

     Per rule 2   →   MR = 2MP

                       4x - 60 = 2(x + 5)

                       4x - 60 = 2x + 10

                       2x - 60 =         10

                       2x         =        70

                         x         =        35

MP = (35) + 5

     =      40

Per rule 1   →   PR = MP

                       PR = 40

yes the total will be same because in both of them the expression.is rearranged but their sign remains the same hence it hss just been shuffled

i believe the correct answer is option 4.principalities were small territories that were run by russian rulers.

which statement correctly defines principalities in northern asia in the 1200s? principalities were small territories that were run by russian rulers.

hope i could ! : )