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GalinKa [24]
2 years ago
9

The table shows the running speeds of 10 randomly selected grizzly bears.

Mathematics
1 answer:
True [87]2 years ago
8 0
The answer is Most likely D
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Factor the cubic polynomial 6x3 – 11x2 – 12x 5. use the rational root theorem and synthetic division
pochemuha

The factorization of given cubic polynomial 6x³ - 11x² - 12x + 5 is:  

6x³ - 11x² - 12x + 5 = (x + 1)(x - \frac{5}{2})(x - \frac{1}{3})

For given question,

We have been given the cubic polynomial 6x³ - 11x² - 12x + 5

We need to factorize given cubic polynomial.

By the rational roots theorem, any rational zero of f(x) is expressible in the form ± \frac{p}{q} for integers p, q with p a divisor of the constant term 5 and q a divisor of the coefficient 6 of the leading term.

Factors of p = 5: 1, 5

Factors of q = 6: 1, 2, 3, 6

That means that the only possible rational zeros are:

±{ \frac{1}{1} ,\frac{1}{2} ,\frac{1}{3} ,\frac{1}{6} ,\frac{5}{1} ,\frac{5}{2} ,\frac{5}{3} ,\frac{5}{6} }

= ±{ 1 ,\frac{1}{2} ,\frac{1}{3} ,\frac{1}{6} ,5 ,\frac{5}{2} ,\frac{5}{3} ,\frac{5}{6} }

We need to find the exact zeros of given cubic polynomial.

For x = 1,

6(1)³ - 11(1)² - 12(1) + 5 = -12

This means, x = 1 is not a zero of given cubic polynomial.

For x = -1,

6(-1)³ - 11(-1)² - 12(-1) + 5 = 0

This means, x = -1 is a zero of given cubic polynomial and (x + 1) is a factor.

To factorize given cubic polynomial we use synthetic division.

The synthetic division (6x³ - 11x² - 12x + 5) ÷ (x + 1) is as shown in following image.

⇒ 6x³ - 11x² - 12x + 5 = (x + 1)(6x² - 17x + 5)

The factors of above quadratic polynomial 6x² - 17x + 5 are:

⇒ 6x² - 17x + 5 = (x - \frac{5}{2})(x - \frac{1}{3})

So, the factors of given cubic polynomial are:

⇒ 6x³ - 11x² - 12x + 5 = (x + 1)(x - \frac{5}{2})(x - \frac{1}{3})

Therefore, the factorization of given cubic polynomial 6x³ - 11x² - 12x + 5 is:  6x³ - 11x² - 12x + 5 = (x + 1)(x - \frac{5}{2})(x - \frac{1}{3})

Learn more about the polynomial here:

brainly.com/question/16594008

#SPJ4

4 0
2 years ago
What is the length of the hypotenuse
Liula [17]

Answer:

20

Step-by-step explanation:

To find Hypotenuse: Pythagorean Theroem

a^2+ b^2= c^2

The legs are A and B

The side that is directly across from the Right angle is C

12^2 + 16^2 =C^2

144+256=400

400 = c^2

Square root on both sides to get rid of c^2

The square root of 400 is 20

c=20

8 0
3 years ago
Read 2 more answers
the sum of the internal angles of a regular polygon is equivalent to 56 right angles. Find the measure of the central angle of t
kykrilka [37]
If x is the number of sides of the regular polygon, then the sum of the interior angles is (x - 2) * 180 = 56 * 90. Solving for x gives 30 for the number of sides of the regular polygon.

To get the central angles measure, divide 360 by 30 to get 12 degrees for the measure of one of the 30 central angles.

Answer: 12 degrees
7 0
3 years ago
Female giraffes reach a height of 4.3 meters, and males reach a height of 5.5 meters. Kendra created a bar diagram and wrote an
Flura [38]
It should be 5.5 - d not 5.5 first
5 0
3 years ago
Read 2 more answers
What are the possible values of x if (4x – 5)2 = 49?
STatiana [176]
2(4x - 5) = 49
8x - 10 = 49
8x - 10 + 10 = 49 + 10
8x = 59
8x/8 = 59/8
x = 7.375
3 0
3 years ago
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