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3 years ago

How would you factor a^3 - b^3? Please leave detailed instructions. Thanks so much!

Mathematics

1 answer:

Sindrei [870]3 years ago

4 0

a³ - b³ = (a - b) (a² + ab + b²)

You can see why this works if you expand the right side as

a (a² + ab + b²) - b (a² + ab + b²)

(a³ + a²b + ab²) - (a²b + ab² + b³)

Both the a²b and ab² terms cancel, leaving you with a³ - b³.

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What is the reasoning?

solmaris [256]

Answer:

yes, i agree. the right angle is 90 and 90+90=180. The law of the congruent angle states that if one angle in a the plane is right then the other connected must be as well, making line L 180.

Step-by-step explanation:

i badly explained it however you should get the answer correct with that. i think... use your brain in addition to mine.

8 0

3 years ago

A binomial event has n = 60 trials. The probability of success for each trial is 0.20. Let x be the number of successes of the e

OLga [1]

Answer:

12 and 3.0984

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

$\mu_{x} = np$

The standard deviation of the binomial distribution is:

$\sigma_{x} = \sqrt{np(1-p)}$

In this problem, we have that:

$n = 60, p = 0.2$

$\mu_{x} = np = 60*0.2 = 12$

$\sigma_{x} = \sqrt{np(1-p)} = \sqrt{60*0.8*0.2} = 3.0984$

So the correct answer is:

12 and 3.0984

4 0

3 years ago

How do I find out if this is an infinite solution 4(x-2) + 7 = 4x - 1

damaskus [11]

Answer:

x = all real numbers, infinite solutions

Step-by-step explanation:

4(x-2) + 7 = 4x - 1

Distribute

4x -8+7 = 4x-1

Combine like terms

4x -1 = 4x-1

Subtract 4x from each side

4x-1 -4x = 4x-1-4x

-1 = -1

This is always true so there are infinite solutions for x

7 0

3 years ago

Which equation has x = -i and x = = 21v3 as two of its solutions?

Drupady [299]

Answer:

The equation in option A is correct.

Step-by-step explanation:

Given the equation

$\:y=x^4+13x^2+12$

Let us find the solution by setting y=0

$x^4+13x^2+12=0\:\:\:\:\:$

$\mathrm{Rewrite\:the\:equation\:with\:}u=x^2\mathrm{\:and\:}u^2=x^4$

$u^2+13u+12=0$

if $ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)$

$u+1=0\quad \mathrm{or}\quad \:u+12=0$

$u=-1,\:u=-12$

$\mathrm{Substitute\:back}\:u=x^2,\:\mathrm{solve\:for}\:x$

$x^2=-1,\:x^2=-12$

solving

$x^2=-1$

$\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

$x=\sqrt{-1},\:x=-\sqrt{-1}$

$x=i,\:x=-i$ ∵ $\:\sqrt{-1}=i$

solving

$x^2=-12$

$\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

$x=\sqrt{-12},\:x=-\sqrt{-12}$

$x=2\sqrt{3}i,\:x=-2\sqrt{3}i$

Hence, the solutions are:

$x=i,\:x=-i,\:x=2\sqrt{3}i,\:x=-2\sqrt{3}i$

Therefore, the equation in option A is correct.

6 0

3 years ago

Help me please and thank you

Sever21 [200]

Answer:

Step-by-step explanation:

Since CB is a tangent to the circle then ∠ ABC = 90°

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, thus

AC² = 5² + 8² = 25 + 64 = 89 ( take the square root of both sides )

AC = $\sqrt{89}$ → C

3 0

4 years ago