Atriangle has two sides of lengths 7 and 9. what value could the length of the third side be?

The length of the third side could be all real numbers greater than 2 units and less than 16 units

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.

so

Applying the triangle inequality theorem

Let

x > the length of the third side

we have

First case

1) 7+9 > x

16 > x

Rewrite

x< 16 units

Second case

2) 7+x > 9

x > 9-7

x > 2 units

therefore

The solution for the third side is the interval

(2,16)

All real numbers greater than 2 units and less than 16 units

(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

answer: 819.89 miles across america

step-by-step explanation: