5 6
7
8
9
e) The table describes some of the solutions of the
inequality 3m > 21. Which graph best describes
the solutions of 3m > 21?
15
18
21
24
27
3m
Solution?
No
No
Yes
Yes Yes
1
+
10
0
1
2
3
4
5
6
7
8
9
1
-
5
+
10
0
1
2
3
4
6
7
8
9
+ +
0 1
+ + + +
2 3
5
6
7
8
9
10
+
+
e
7
0
1
2
4
5
6
8
9
10

what is the original number? you forgot to add it.

493 would be the correct answer

step-by-step explanation:

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.

step-by-step explanation:

d would equal 12