Which of the values shown are potential roots of f(x)=3x^3-13x^2-3x+45? Select all that apply

Mathematics

1 answer:

GrogVix [38]2 years ago

5 0

<h3><u>Roots:</u></h3><h3>x=3</h3><h3>x=-5/3</h3>

You might be interested in

100 points

Pavlova-9 [17]

STEP
1
:

y
Simplify —
3
Equation at the end of step
1
:

y
(((18•(x5))•(y3))+((6•(x2))•(y4)))+((((24•(x6))•—)•x)•y)
3
STEP
2
:

Equation at the end of step
2
:

y
(((18•(x5))•(y3))+((6•(x2))•(y4)))+((((23•3x6)•—)•x)•y)
3
STEP
3
:

Canceling Out:

3.1 Canceling out 3 as it appears on both sides of the fraction line

Equation at the end of step
3
:

(((18•(x5))•(y3))+((6•(x2))•(y4)))+((8x6y•x)•y)
STEP
4
:

Equation at the end of step
4
:

(((18•(x5))•(y3))+((2•3x2)•y4))+8x7y2
STEP
5
:

Equation at the end of step
5
:

(((2•32x5) • y3) + (2•3x2y4)) + 8x7y2
STEP
6
:

STEP
7
:
Pulling out like terms

7.1 Pull out like factors :

8x7y2 + 18x5y3 + 6x2y4 = 2x2y2 • (4x5 + 9x3y + 3y2)

Trying to factor a multi variable polynomial :

7.2 Factoring 4x5 + 9x3y + 3y2

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Final result :
2x2y2 • (4x5 + 9x3y + 3y2)

3 0

2 years ago

● For the polygon you are assigned, assume the radius is 1 unit . Round all answers to the nearest hundredth , if necessary.

lorasvet [3.4K]

9514 1404 393

Answer:

1) 135°

2) 0.77 units

3) 0.92 units

4) 6.12 units

5) 2.83 square units

Step-by-step explanation:

1) The exterior angle at any vertex is 360°/n, where n is the number of sides. For the octagon, the exterior angle is 360°/8 = 45°. The interior angle will be the supplement of this: 180° -45° = 135°.

The measure of each interior angle is 135°.

2) Each sector of the octagon is an isosceles triangle with a central angle of 45° (also 360°/8). Since the radius is 1 unit, the length of one side is twice the sine of half the central angle.

s = 2·sin(45°/2) ≈ 0.765367

The length of one side is about 0.77 units.

3) Similarly, the apothem is the cosine of half the central angle:

a = cos(45°/2) ≈ 0.923880

The apothem is about 0.92 units.

4) For an octagon, the perimeter is 8 times the length of one side.

P = 8s = 8(0.765367) ≈ 6.12293

The perimeter is about 6.12 units.

5) The area of one sector (isosceles triangle) is given by the formula ...

A = (1/2)bh

A = 1/2sa ≈ 1/2(0.765367)(0.923880) ≈ 0.353553

Then the area of the octagon is 8 times this: