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

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!