What is 0.31111... as a fraction

Which of the values shown are potential roots of f(x) = 3x3 – 13x2 – 3x + 45? Select all that apply.

galina1969 [7]

Answer:

All potential roots are 3,3 and $-\frac{5}{3}$ .

Step-by-step explanation:

Potential roots of the polynomial is all possible roots of f(x).

$f(x)=3x^3-13x^2-3x+45$

Using rational root theorem test. We will find all the possible or potential roots of the polynomial.

p=All the positive/negative factors of 45

q=All the positive/negative factors of 3

$p=\pm 1,\pm 3,\pm 5\pm \pm 9,\pm 15\pm 45$

$q=\pm 1,\pm 3$

All possible roots

$\frac{p}{q}=\pm 1,\pm 3,\pm 5\pm \pm 9,\pm 15\pm 45,\pm \frac{1}{3},\pm \frac{5}{3}$

Now we check each rational root and see which are possible roots for given function.

$f(1)= 3\times 1^3-13\times 1^2-3\times 1+45\Rightarrow 32\neq 0$

$f(-1)= 3\times (-1)^3-13\times (-1)^2-3\times (-1)+45\Rightarrow \neq 32$

$f(-3)= 3\times (-3)^3-13\times (-3)^2-3\times (-3)+45\Rightarrow \neq -144$

$f(3)= 3\times (3)^3-13\times (3)^2-3\times (3)+45\Rightarrow =0\\\\ \therefore x=3\text{ Potential roots of function}$

Similarly, we will check for all value of p/q and we get

$f(-5/3)=0$

Thus, All potential roots are 3,3 and $-\frac{5}{3}$ .

5 0

2 years ago

Read 2 more answers

Apr 23, 8:46:54 AM What is the missing term?

kipiarov [429]

Answer: -10x
Explanation: Multiply -2 by 5x

7 0

2 years ago

A farmer’s rectangular pen has an area of 2,700 square feet, and the width is 15 feet shorter than the length. Find the dimensio

svetoff [14.1K]

The length of the rectangle is 60 feet and the width of the rectangle is 45 feet.

<h3>What is the area of the rectangle?</h3>

Let L be the length and W be the width of the rectangle.

Then the area of the rectangle will be

Area of the rectangle = L×W square units

A farmer’s rectangular pen has an area of 2,700 square feet, and the width is 15 feet shorter than the length.

L = W + 15

Then we have

2700 = W(W + 15)

W² + 15W - 2700 = 0

W² + 60W - 45W - 2700 = 0

(W + 60)(W - 45) = 0

W = 45, -60

Then the dimension of the rectangle will be

W = 45 feet

L = W + 15

L = 45 + 15

L = 60 feet

More about the area of the rectangle link is given below.

brainly.com/question/20693059

#SPJ1

4 0

2 years ago

Find the measure of an interior angle and exterior angle of a regular 24gon

Julli [10]

Answer:

Interior Angle: 165°

Exterior Angle: 15°

Step-by-step explanation:

So first you have to find the sum of all interior angles of a polygon with 24 sides. This can be found using the formula:

sum = ( n - 2 ) * 180° where 'n' is the number of sides.

When 'n = 24' then the sum is:

sum = ( 24 - 2 ) * 180°

Simplify and solve.

sum = 22 * 180°

sum = 3960°

Since there are 24 sides to the polygon, there are 24 interior angles. Assuming that this polygon is equilateral, you can surmise that:

Interior Angle = sum° / n where n is the number of sides,

3960° / 24 = 165° = Interior Angle

Using that information, and combine it with the [Supplementary Angles Theorem] the exterior angle can be found by:

165° + x = 180°

Solve for x.

8 0

2 years ago

one leg of a right triangle is 5 millimeters shorter than the longer leg and the hypotneuse is 5 millimeters longer than the lon

Makovka662 [10]

The answer, in short, is that the short leg equals 15 mm, the long leg equals 20 mm, and the hypotenuse equals 25mm. but if you'd like to see how I solved it, here are the steps.
-----------------------------
The Pythagorean theorem (also known as Pythagoras's Theorem) can be used to solve this. This theorem states that one leg or a right triangle squared plus the other side of that same triangle squared equals the hypotenuse of that triangle squared. To put it in equation form, L² + L² = H².

Let's call the longer leg B, the shorter leg A, and the hypotenuse H.
From the question, we know that A = B - 5, and H = B + 5.

So if we put those values into an equation, we have (B - 5)² + B² = (B + 5)²

Now, to solve. Let's square the two terms in parentheses first:
(B² - 5B - 5B + 25) + B² = B² + 5B + 5B + 25

Now combine like terms:
2B² -10B + 25 = B² + 10B + 25

And now we simplify. Subtract 25 from each side:
2B² - 10B = B² + 10B

Subtract B² from each side:
B² - 10B = 10B

Add 10B to each side:
B² = 20B

And finally, divide each side by B:
B = 20

So that's the length of B. Now to find out A and H.
A = B - 5, so A = 15.
H = B + 5, so H = 25.

And your final answer is A = 15mm, B = 20mm, and H = 25mm

7 0

3 years ago