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3 years ago

How to use synthetic division to show how to methodically obtain the factors from the polynomial 2x^5+6x^4-42x^3-86x^2+192x+360

Mathematics

1 answer:

MA_775_DIABLO [31]3 years ago

6 0

Okay so first you need to find your prrs which in this case would be all factors of 360 and all of the factors of 360 divided by two since the factors of two are two and one. (Which I pulled from the first x’s coefficient)

Then you do Descartes law to find out how many positives or negatives in this equation. There looks to be 2 positives and 3 or 0 negatives. Since there are guaranteed positives I’d recommend doing those first. Start from the lowest number since that’s easier and more mathematically correct and do synthetic division. (x+1) The resulting polynomial should be factorable and of not then try to synthetically divide again.

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Snezhnost [94]

Answer:

Step-by-step explanation:

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3 years ago

3y=12x+6 in slope-intercept form

tresset_1 [31]

Answer:

$\displaystyle y = 4x + 2$

Step-by-step explanation:

$\displaystyle \frac{3y}{3} = \frac{4x + 12}{3} \\ \\ y = 4x + 2$

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3 years ago

A sequence of Bernoulli trials consists of choosing components at random from a batch of components. A selected component is eit

Drupady [299]

Answer:

a) 0.0287 = 2.87% probability that three non-defective components in a batch of seven components.

b) 0.0336 = 3.36% probability that 8 non-defective components are drawn before the first defective component is chosen.

Step-by-step explanation:

A sequence of Bernoulli trials composes the binomial distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The probability that a selected component is non-defective is 0.8

This means that $p = 0.8$

a) Three non-defective components in a batch of seven components.

This is P(X = 3) when n = 7. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{7,3}.(0.8)^{3}.(0.2)^{4} = 0.0287$

0.0287 = 2.87% probability that three non-defective components in a batch of seven components.

b) 8 non-defective components are drawn before the first defective component is chosen.

Now the order is important, so the we just multiply the probabilities.

8 non-defective, each with probability 0.8, and then a defective, with probability 0.2. So

$p = (0.8)^8*0.2 = 0.0336$

0.0336 = 3.36% probability that 8 non-defective components are drawn before the first defective component is chosen.

4 0

3 years ago

If a 30-foot silo casts a 20-foot shadow, what is the approximate measure from the tip of the shadow to the top of the silo?

KATRIN_1 [288]

9514 1404 393

Answer:

(d) 36 feet

Step-by-step explanation:

Use your sense of geometry.

The hypotenuse of a right triangle will never be less than the longest side, and will never be greater than 1.5 times the longest side*.

That means the only reasonable answer choices will be between 30 and 45 feet. There is only one such choice.

The measure is about 36 feet.

If you like, you can find a more exact value using the Pythagorean theorem. The distance d of interest is ...

d^2 = 20^2 +30^2 = 1300

d = √1300 = 10√13 ≈ 36.0555 ≈ 36 . . . feet

_____

* The longest hypotenuse will be √2 ≈ 1.4142 times the longest right triangle leg when the two legs are equal length.

3 0

3 years ago

Taiga wants to make a circular loop that she can twirl around her body for exercise. He will use a tube that is 2.5 meters long.

Travka [436]

Answer: 0.796 meters

Step-by-step explanation:

Circumference of circle = $2\pi r$ , where r=radius

Here, Circumference of loop = 2.5 meters

i.e. $2\pi r=2.5$

$\Rightarrow\ r=\dfrac{2.5}{2\pi}$

$\Rightarrow\ r=\dfrac{2.5}{2\times\dfrac{22}{7}}\\\\\Rightarrow\ r=\dfrac{2.5\times7}{2\times22}\\\\\Righttarrow\ r=0.398\ m$

Diameter = 2r = 2(0.398) = 0.796 meters

Hence, The diameter of Taiga's exercise hoop = 0.796 meters

7 0

3 years ago