Find the value of X AND Y: Show your work.

We are given:                                                                                                        

AB = 7x + 10

BD = 9x - 2

∠DBC = 9y - 9

∠ABC = 90°

AB = BD

Solving for x:                                                                                                          

We are given that AB = BD

7x + 10 = 9x - 2               [since AB = 7x+10 and BD = 9x-2]

10 = 2x - 2                       [subtracting 7x from both sides]

2x = 12                            [adding 2 on both sides]

x = 6                               [dividing both sides by 2]

Hence, x = 6

Solving for y:  

We know that AD is a straight line,

So, ∠ABC and ∠DBC must form a linear pair

∠ABC + ∠DBC = 180°

90 + 9y-9 = 180

9y - 9 = 90             [subtracting 90 from both sides]

9y = 99                  [adding 9 on both sides]

y = 11                      [dividing both sides by 9]

Hence, y = 11

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

there are no multiple choices