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3 years ago

What are the real zeroes of x^3+ 6x^2- 9x - 54?

Mathematics

2 answers:

Nimfa-mama [501]3 years ago

8 0

Answer:

<h2>hope it helps you see the attachment for further information ✌✌✌✌</h2>

azamat3 years ago

6 0

Answer:

(x + 3) • (x - 3) • (x + 6)

Step-by-step explanation:

Step 1 :

Equation at the end of step 1 :

(((x3) + (2•3x2)) - 9x) - 54

Step 2 :

Checking for a perfect cube :

2.1 x3+6x2-9x-54 is not a perfect cube

Trying to factor by pulling out :

2.2 Factoring: x3+6x2-9x-54

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: -9x-54

Group 2: 6x2+x3

Pull out from each group separately :

Group 1: (x+6) • (-9)

Group 2: (x+6) • (x2)

-------------------

Add up the two groups :

(x+6) • (x2-9)

Which is the desired factorization

Trying to factor as a Difference of Squares :

2.3 Factoring: x2-9

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 9 is the square of 3

Check : x2 is the square of x1

Factorization is : (x + 3) • (x - 3)

Final result :

(x + 3) • (x - 3) • (x + 6)

Processing ends successfully

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What is .246 repeating (46 is repeating) as a fraction?

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Read 2 more answers

A grinding wheel manufacturer designed a new grinding wheel. Repeated tests were conducted on wheels of approximately the same w

sergejj [24]

Answer:

a) $a=225 +0.674*16.5=236.121$

So the value of height that separates the bottom 75% of data from the top 25% is 236.121.

b) $P(X \geq 3) = 1-P(X$

c) $P(\bar X \geq 225)=1- P(\bar X$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

2) Part a

Let X the random variable that represent the cuts of a population, and for this case we know the distribution for X is given by:

$X \sim N(225,16.5)$

Where $\mu=225$ and $\sigma=16.5$

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.25$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=0.674=\frac{a-225}{16.5}$

And if we solve for a we got

$a=225 +0.674*16.5=236.121$

So the value of height that separates the bottom 75% of data from the top 25% is 236.121.

Part b

For this case we know that the individual probability of select one wheel with a cutting rate higher than the calculated value in part a is 0.25, and we select n =10 so then we can use the binomial distribution for this case:

$X\sim Bin(n=10, p=0.25)$

And we want this probability:

$P(X \geq 3) = 1-P(X$

We can find the individual probabilities like this:

$P(X=0)=(10C0)(0.25)^0 (1-0.25)^{10-0}=0.0563$

$P(X=1)=(10C1)(0.25)^1 (1-0.25)^{10-1}=0.1877$

$P(X=2)=(10C2)(0.25)^2 (1-0.25)^{10-2}=0.2816$

$P(X \geq 3) = 1-P(X$

Part c

For this case we know that the distribution for the sample mean is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And we want this probability:

$P(\bar X \geq 225)$

And for this case we can use the complement rule and the z score given by:

$z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we replace we got:

$P(\bar X \geq 225)=1- P(\bar X$

4 0

3 years ago

Jacob is mixing salt with

77julia77 [94]

The number of tablespoons of salt jacob mixes with 1 cup of water is 4 tablespoon of salt.

<h3>How to interpret the division? </h3>

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.

Thus, if 10 mangoes are there, and 2 people, then 10 ÷ 2 is the number of mangoes each person would get, which is 5.

Division, thus, can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.

Thus, $a \div b = a$ divided in b equal parts.

Also, we can write: $a \div b = a \times \dfrac{1}{b}$

(it is since $a = a times 1 so a/b = 1 \times (a/b) = (1/b) \times a$ )

The given table is:

Tablespoons of salt Cups of water

8 2

16 4

24 6

2 cups of water gets 8 tablespoon of salt.

Then 1 cup of water gets 8/2 = 4 tablespoons of salt. (divided the numbre of cups of water and number of tablespoons of salts in 2 equal parts).

This pattern remains same for other rows of the table, since we have:

1 cup of water gets 8/2 = 16/4 = 24/6 = 4 tablespoons of salt.

Thus, the number of tablespoons of salt jacob mixes with 1 cup of water is 4 tablespoon of salt.

Learn more about division here:

brainly.com/question/26411682

#SPJ1

4 0

2 years ago

In a population of grasshoppers, the ratio of grasshoppers with a white marking to those without a white marking is 2:3. An ento

LekaFEV [45]

Answer:

D. 116

Step-by-step explanation:

Let the grasshoppers with a white marking be 2x.

Let the grasshoppers without a white marking be 3x.

2x + 3x = 290

5x = 290

x = 290 / 5

x = 58

The grasshoppers with a white marking

= 2x

= 2 ( 58 )

= 116

3 0

3 years ago