7. the height of a sunflower plant varies directly with its age. once it has sprouted from the ground, when a sunflower is 2 week old, it is 38 centimeters tall. when it is 6 weeks old, it is 114 centimeters tall. how tall is a sunflower plant that is 3 1/2 weeks old?

66.5 centimeters.

Step-by-step explanation:

We have been given that the height of a sunflower plant varies directly with its age.

Since a directly proportional equation is in form: , where k is constant of proportionality.

We are told that when a sunflower is 2 week old, it is 38 centimeters tall. Let us find constant of proportionality with given information.

We are also told that when sunflower is 6 weeks old, it is 114 centimeters tall.

We can see that constant of proportionality is 19. Let us substitute k=19 and x= 3.5 in our proportional equation to find the height of plant after 3.5 weeks.

Therefore, the sunflower plant will be 66.5 centimeters tall after 3.5 weeks.

(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