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12 days ago

6

The polynomial 24x3 − 54x2 + 44x − 99 is factored by grouping. 24x3 − 54x2 + 44x − 99 24x3 + 44x − 54x2 − 99 4x() − 9()

What is the common factor that is missing from both sets of parentheses?

1 answer:

Leona [4.1K]11 days ago

3 0

Answer: $6x^2+11$

Step-by-step explanation:

For the polynomial of degree 3:

$24x^3 - 54x^2 + 44x -99$

You can notice that it can be divided into two pairs of terms:

$(24x^3 + 44x) - (54x^2 + 99)$

The Greatest Common Factor (GCF) is defined as the largest number that can evenly divide two or more numbers.

It can be seen that the GCF for each group is extracted ( $4x$ and $9$ ), after which you can identify the shared factor lacking in both sets of parentheses using this method:

$(\frac{24x^3}{4x}+\frac{44x}{4x})-(\frac{54x^2}{9}+\frac{99}{9})=(6x^2+11)-(6x^2+11)$

The shared factor that both parentheses miss is:

$6x^2+11$

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Answer:

The parameter λ has a value of 0.03692

Step-by-step explanation:

Take into account the given function.

$f(x) = 0.5\lambda e^{-\lambda |x|}$ for −∞ < x < ∞.

The standard deviation is stated to be 38.3 km.

Our task is to determine the parameter λ.

The formula for the probability density function of the double exponential distribution can be expressed as: $f(x)=\frac{e^{-|\frac{x-\mu}{\beta}|}}{2\beta}$

Here, μ represents the location parameter and β is the scale parameter.

When comparing the provided equation with the formula mentioned above, we have:

$\lambda=\frac{1}{\beta}$ and μ = 0.

The standard deviation = √2β

$S.D=\sqrt{2} \beta\\\beta=\frac{38.3}{\sqrt{2}}\\\beta=27.08219$

Next, insert the β value in $\lambda=\frac{1}{\beta}$ .

$\lambda=\frac{1}{27.08219}=0.03692$

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1 day ago

Brett has 2 dogs. Meaghan has four times as many cats as Brett adopts two more dogs, how many cats must meaghan adopt to maintai

AnnZ [3900]

Meaghan must take in 8 cats to keep the dogs-to-cats ratio consistent.

Step-by-step explanation:

Currently, Brett has 2 dogs while Meaghan possesses four times more cats than him. Therefore, Meaghan has 4 times 2 cats, making the current dogs to cats ratio:

2 dogs: 8 cats

2:8

1:4

When Brett adopts an additional 2 dogs, the total canine count rises to 2 + 2 = 4.

New ratio

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4:8

To sustain the previous 1:4 ratio, Meaghan's required cat count should satisfy:

1 = 4

4 =? ----cross-multiplication

Results in 16

In order for the ratio to hold, the relationship should be:

4:16

Thus, the number of cats to be adopted is 16 - 8 = 8 more cats.

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Keywords: dogs, cats, ratio, adopt, maintain

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2 days ago

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Last year, sales at a book store increased from $5,000 to $10,000. This year, sales decreased to $5,000 from $10,000. What perce

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1. 200% =2
5000 multiplied by 2 equals 10000
2.50% = 0.5
10000 multiplied by 0.5 equals 5000

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8 days ago

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Two planes A and B can each fly through still air at 550 mph. The distance from Paris to Los Angeles is 5000 miles. Wind blows f

PIT_PIT [3949]

Answer:2688.63 miles

Step-by-step explanation:

Given

The distance from Paris to Los Angeles $d=5000 miles$

Wind traveling at 100 mph from Los Angeles to Paris

The velocity of the plane through still air is $v=550 mph$

Relative velocity of Plane A is $v_a=550-100 =450 mph$ since Plane A is heading against the wind

Relative velocity of Plane B is $v_b=550+100=650 mph$

Plane A departs at noon

Distance covered by Plane A in 1 hour $=450\times 1=450 miles$

The total separation distance between the planes is $5000-450=4550 miles$

Assuming they meet after t hours

Distance covered by Plane B in that time frame $=v_b\times t=650\times t$

Distance traveled by Plane A in t hours is $=v_a\times t=450 t$

The total distance equals 4550 miles

$4550=650t+450t$

$t=\frac{4550}{1100}$

$t=4.13 hr$

Distance traveled by B is $=650\times 4.136=2688.63 miles$

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11 days ago

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tester [3938]

I have included a screenshot of the entire question along with its accompanying diagram.

Answer:
∠1 = 163°

Explanation:
1- finding angle 2:
Given that ∠2 together with 17° creates a straight angle, their total is 180°.
Thus:
180 = 17 + ∠2
Solving for ∠2 gives us:
∠2 = 180 - 17
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2- finding angle 1:
Since lines a and b are parallel, ∠1 and ∠2 are alternate angles and therefore equal.
We determined that ∠2 = 163°, leading to:
∠1 = 163°

I hope this clarifies things!:)

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