The length of a rectangle is 2 more than 3 times its width. if the perimeter is 68, find the length and width.

The length is 26 and the width 8.

Step-by-step explanation:

First you have to consider that the perimeter of a rectangle = 2·length + 2width. If length = 3width + 2, you can call "x" to the width. Then

x = width ⇒ length = 3x + 2.

Perimeter = 2·(3x + 2) + 2·x ⇒ Perimeter = 6x + 4 + 2x ⇒

Perimeter =  8x + 4 ⇒ 68 = 8x + 4 ⇒ 68 - 4 = 8x ⇒ 64 = 8x ⇒ 64/8 = x

⇒ x = 8.

Finally, width = 8 and length = 3x + 2 ⇒ length = 26

(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

a. turk and mcalister

b. howard, mission, and market

c. yes. since streets end some do not cross yet are not parallel to others. example: mcalister and 5th

step-by-step explanation:

parallel lines are lines which do not intersect ever and look a lot like railroad tracks. turk, mcalister and golden gate are examples of these.

intersect are streets which cross each other and a car on one can reach the other. howard, mission, and market intersect with 6th.

skew lines are lines which neither intersect nor are parallel. these lines exist here because some streets end and never intersect another like mcalister and 5th.