Which lists the side lengths in order from shortest to longest?

the figure shows a triangle whose sides are labeled as d, e, and f. the angle opposite to side d is labeled as 48 degree and the angle opposite to side f is labeled as 73 degree.

a.
d, e, f

b.
d, f, e

c.
f, d, e

d.
f, e, d

A. d, e, f

Step-by-step explanation:

Suppose there is a triangle DEF in which,

EF = d, DF = e, DE = f, ∠D = 48°, ∠F = 73°,

∵ Sum of all interior angles of a triangle is 180°,

⇒ ∠D + ∠F + ∠E = 180°,

⇒ 48° + 73° + ∠E = 180°,

⇒ 121° + ∠E = 180°,

⇒∠E = 59°,

Now, in a triangle the angle opposite to the largest side is largest, opposite to medium angle is medium and opposite to the smallest side is smallest,

∵ ∠F > ∠E > ∠D

By the above statement,

f > e > d

Hence, FIRST OPTION is correct.

(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

the answer is c)8

step-by-step explanaction: