In the coordinate plane, you plot the point $(2t + 3, -3t + 3)$ for every real number $t.$ for example, when $t=5$, we have $2t + 3 = 13$ and $-3t + 3 = -12$, so the point $(13,-12)$ is on the graph. explain why the resulting graph is a line, and find an equation whose graph is this line.

show your work an thoroughly explain why your answer is your answer !

The locus of the coordinates given is a straight line having equation 3x + 2y = 15.

Step-by-step explanation:

Let at any particular value of t, the coordinates of the point are (h,k).

So, h = 2t + 3

⇒ 2t = h - 3

⇒

Again, k = - 3t + 3

⇒ 3t = 3 - k

⇒

Therefore, eliminating t we get a relation between h and k.

Hence,

⇒ 3h - 9 = 6 - 2k

⇒ 3h + 2k = 15

Therefore, converting in to current coordinates we get the locus of the point (h,k) as 3x + 2y = 15, which is a straight line.

For this reason, the resulting graph is a line and its equation is 3x + 2y = 15. (Answer)

(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

step-by-step explanation: