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3 years ago

Select the correct answer from each drop-down menu. Factor the expression 8x3y − 8x2y − 30xy. 8x3y − 8x2y − 30xy = ( )( )

Mathematics

1 answer:

pychu [463]3 years ago

8 0

Answer:

$8x^3y-8x^2y-30xy=2xy(2x+3)(2x-5)$

Step-by-step explanation:

we are given an expression as

$8x^3y-8x^2y-30xy$

Firstly, we will find factors

$(2xy)\times 4x^2-(2xy)\times 4x-(2xy)\times 15$

We can see that 2xy is common in all terms

so, we can factor out 2xy from all terms

and we get

$8x^3y-8x^2y-30xy=2xy(4x^2-4x-15)$

now, we can factor again

$4x^2-4x-15=(2x+3)(2x-5)$

we get

$8x^3y-8x^2y-30xy=2xy(2x+3)(2x-5)$

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How many ways can eight letters be arranged into groups of five where order matters and the first two letters are already chosen

fenix001 [56]

Answer:

120

Step-by-step explanation:

Since we're dealing with a problem where the order matters and the first two letters are already chosen we need to subtract the number of letters and the number of available slots per group.

We use the permutation formula to find the answer, but before that let's check values.

n = 8

k = 5

Now since there are two letters already chosen we have to deduct two from both the value of n and k.

n = 6

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Now we can use the permutation formula:

$_{n}P_{k}=\dfrac{n!}{(n-k)!}$

$_{6}P_{3}=\dfrac{6!}{6-3)!}$

$_{6}P_{3}=\dfrac{6!}{3!}$

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The 3*2*1 cancels out and leaves us with:

$_{6}P_{3}=6*5*4$

$_{6}P_{3}=120$

So there are 120 possible ways to arrange eight letters into groups of five where order matters and the first two letters are already chosen.

6 0

3 years ago

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Can you please help me

Slav-nsk [51]

Answer:

Step-by-step explanation:

Hi there!

To answer this, we must set it up as

$3x(2x^4-12x^2+7)$

Now we just use the distributive property to solve.

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I hope this helps!

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3 years ago

A student dropped a textbook from the top floor of his dorm and it fell according to the formula s(t) = −16t 2 + 8√t , where t i

Sidana [21]

Answer:

Step-by-step explanation:

Given the distance of fall of the student in term of the time t expressed by the equation s(t) = −16t² + 8√t, to get the average speed of fall of the pencil after 2.8 secs, we will need to differentiate the given function first since Velocity is the change in distance of a body with respect to time i.e

V = d(s(t))/dt

s(t) = −16t² + 8t^1/2

V = -32t+1/2(8)t^(1/2 - 1)

V = -32t+4t^-1/2

The average speed of the fall Using the fact that the pencil hit the ground in exactly 2.8 seconds, will be gotten by substituting t = 2.8 into the resulting equation.

V = -32t+4(2.8)^-1/2

V = -32t+4/√2.8

V = -32+4/1.6733

V = -32+2.391

v = -29.61m/s

<em>Hence the average speed of the fall is -29.61m/s</em>

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3 years ago