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4 years ago

Factor the GCF: −6x3y + 9x2y2 − 12xy3

Mathematics

2 answers:

sweet-ann [11.9K]4 years ago

6 0

-6x^3y + 9x^2y^2 - 12xy^3
-3xy(2x^2) - 3xy(-3xy) - 3xy(4y^2)
-3xy(2x^2 - 3xy + 4y^2)

The answer is C.

Orlov [11]4 years ago

6 0

Answer:

Option C is the answer.

Step-by-step explanation:

We have to factor the GCF of the given expression:

-6x³y + 9x²y² - 12xy³

To get the GCF of the given expression we will find the factors of each term first.

Factors of 6x³y = 2 × 3 × (x) × (x) (x) (y)

Factors of 9x²y² = 3 × 3 × (x) (x) (y) (y)

Factors of 12xy³ = 2 × 2 × 3 × (x) (y) (y) (y)

So the common factor is 3 × (x) (y)

Now we will take out the GCF as a factor of the given expression = 3xy (-2x² + 3xy - 4y² )

= -3xy ( 2x² - 3xy + 4y² )

Option C is the answer.

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Write a rule for the nth term of the geometric sequence if r = 1/4 and a3 = 2.

GarryVolchara [31]

Answer:

$a_{n} = 32(\frac{1}{4})^{n-1}$

Step-by-step explanation:

The nth term of a geometric sequence is given by the following equation.

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In which r is the common ratio.

This can be expanded for the nth term in the following way:

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In which $a_{1}$ is the first term.

This means that for example:

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$2 = a_{1}(\frac{1}{4})^{2}$

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4 years ago

Select the quadratic that has roots x=8 and x=-5 a x^2 + 3x -40

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3 years ago

When Mrs. Stewart makes pie dough, she uses 2/3 cup of shortening for every 2 1/2 cups of flour which proportion could be used t

zloy xaker [14]

Answer:

The amount of flour Mrs.Stewart needs for 5 cups of shortening $=\frac{75}{4} =18\tfrac{3}{4}$ cups.

Step-by-step explanation:

Mrs.Stewart pie dough needs $\frac{2}{3}$ cups of shortening for $2\tfrac{1}{2}=\frac{5}{2}$ cups of flour.

Now we assume that the shortening needed for $x$ cups of flour is $y$ cups.

Accordingly we can arrange the ratios.

So for one cup of shortening how many cups of flour is needed we have to use the unitary method:

$\frac{cups\ of flour\ (x)}{cups\ of\ shortening\ (y)} =\frac{x}{y} =\frac{5/2}{2/3}$

Plugging the value of $y=5$ as it is number of cups of shortening Mrs.Stewart have used.

And multiplying both sides with $5$ .

Number of cups of flour needed when $5$ cups of shortenings are used $(x) =\frac{x}{y} =\frac{5/2}{2/3}$ .

So, $(x)=\frac{5\times 3\times 5}{2\times 2} =\frac{75}{4} = 18\tfrac{3}{4}$

The amount of floor Mrs.Stewart needed for $5$ cups of shortening $= 18\tfrac{3}{4}\$ cups of floor.

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3 years ago

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3 years ago

On Texas Avenue between University Drive and George Bush Drive, accidents occur according to a Poisson process at a rate of thre

Zarrin [17]

Answer:

(a) The probability is 0.6514

(b) The probability is 0.7769

Step-by-step explanation:

If the number of accidents occur according to a poisson process, the probability that x accidents occurs on a given day is:

$P(x)=\frac{e^{-at}*(at)^{x} }{x!}$

Where a is the mean number of accidents per day and t is the number of days.

So, for part (a), a is equal to 3/7 and t is equal to 1 day, because there is a rate of 3 accidents every 7 days.

Then, the probability that a given day has no accidents is calculated as:

$P(x)=\frac{e^{-3/7}*(3/7)^{x}}{x!}$

$P(0)=\frac{e^{-3/7}*(3/7)^{0}}{0!}=0.6514$

On the other hand the probability that February has at least one accident with a personal injury is calculated as:

P(x≥1)=1 - P(0)

Where P(0) is calculated as:

$P(x)=\frac{e^{-at}*(at)^{x} }{x!}$

Where a is equivalent to (3/7)(1/8) because that is the mean number of accidents with personal injury per day, and t is equal to 28 because 4 weeks has 28 days, so:

$P(x)=\frac{e^{-(3/7)(1/8)(28)}*((3/7)(1/8)(28))^{x}}{x!}$

$P(0)=\frac{e^{-(3/7)(1/8)(28)}*((3/7)(1/8)(28))^{0}}{0!}=0.2231$

Finally, P(x≥1) is:

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