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3 years ago

What is the factored form of 125x6 – 8?

Mathematics

2 answers:

bonufazy [111]3 years ago

5 0

Hello,

Answer C

(5x²)^3-(2)^3=(5x²-2)((5x²)²+5x²*2+2²)

ryzh [129]3 years ago

5 0

Answer:

$(5x^2-2)(25x^4 +10x^2+4)$

Step-by-step explanation:

125x^6 – 8

We write the numbers in exponential form

125= 5*5*5 = 5^3

8 = 2*2*2= 2^3

Now 125x^6 - 8 becomes 5^3x^6 - 3^3

5^3x^2*3- 3^3

$(5x^2)^3 - 2^3$

We got the expression in cube form a^3- b^3= (a-b)(a^2+ab+b^2)

$(5x^2)^3 - 2^3$

a= 5x^2 and b= 2

$(5x^2)^3 - 2^3=(5x^2-2)((5x^2)^2- 5x^2 * 2+ 2^2)$

= $(5x^2-2)(25x^4 +10x^2+4)$

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A 20m ladder and a 15m ladder were leaned against a building. The bottom of the longer ladder was 7m farther from the building t

vovangra [49]

Answer:

The correct answer is: d=9m

Step-by-step explanation:

Ok, the ladders leaned against a building make two right triangles with same the same height, which we will call h. For the 20m ladder, its leg is (7+d) and for the 15m ladder, its leg is d, and the two hypotenuses are 20 and 15 respectively.

Then, using the Pythagorean Theorem we have:

20m ladder:

20^2 = h^2 + (d+7)^2 (Eq. 1)

400 = h^2 + d^2 + 2*7*d + 7^2 (expanding the theorem)

400 = (h^2 + d^2) + 14*d + 49 (Eq. 2)

15m ladder:

15^2 = h^2 + (d)^2 (Eq. 3)

Since h^2 + (d)^2 is equal to 15^2, we can substitute (2) into (3):

400 = (15^2) + 14*d + 49

400 = 225 + 14*d + 49

14*d = 400 - 225 - 49 (clearing the variable d)

14*d = 126

d = 9 m

And since we now know that d is equal to 9m. For the longer ladder is (d+7)=(9+7)=16m.

And, then the shorter ladder is 9m from the building and the longer ladder is 16m from the building

5 0

2 years ago

Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 6.9 per year. a. Find t

VLD [36.1K]

Answer:

a) 9.52% probability that, in a year, there will be 4 hurricanes.

b) 4.284 years are expected to have 4 hurricanes.

c) The value of 4 is very close to the expected value of 4.284, so the Poisson distribution works well here.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

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

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

6.9 per year.

This means that $\mu = 6.9$

a. Find the probability that, in a year, there will be 4 hurricanes.

This is P(X = 4).

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

$P(X = 4) = \frac{e^{-6.9}*(6.9)^{4}}{(4)!}$

$P(X = 4) = 0.0952$

9.52% probability that, in a year, there will be 4 hurricanes.

b. In a 45-year period, how many years are expected to have 4 hurricanes?

For each year, the probability is 0.0952.

Multiplying by 45

45*0.0952 = 4.284.

4.284 years are expected to have 4 hurricanes.

c. How does the result from part (b) compare to a recent period of 45 years in which 4 years had 4 hurricanes? Does the Poisson distribution work well here?

The value of 4 is very close to the expected value of 4.284, so the Poisson distribution works well here.

5 0

2 years ago

188 is 150% of what number?

Aleksandr-060686 [28]

1 Answer

Don't Memorise
Feb 16, 2016
The number
=
125.33
Explanation:
Let the number be denoted as
x
:
As per the question:
188
=
150
%
×
(
x
)
188
=
150
100
×
(
x
)
188
×
(
100
150
)
=
x
125.33
=
x

6 0

2 years ago

Read 2 more answers

The following lines are parallel.<br> 2x + 2y = 4 and y = -x + 5<br><br> True<br> False

insens350 [35]

The answer to your question is FALSE

6 0

3 years ago

If coordinate (3,1) is translated down 2 and left 4 what will the new coornidate be

iris [78.8K]

Answer:

(-1,-1)

Step-by-step explanation:

down 2 affects the y, so 1-2=-1

Left 4 affects the x, so 3-4=-1

4 0

3 years ago