Which points are on the graph .... HELP ASAP

Which of the following expressions is equivalent to a3 + b3?

lubasha [3.4K]

ANSWER
${a}^{3} + {b}^{3} = (a + b)( {a}^{2 } - ab + {b}^{2} )$

EXPLANATION

To find the expression that is equivalent to
${a}^{3} + {b}^{3}$
we must first expand
${(a + b)}^{3}$
Then we rearrange to find the required expression.

So let's get started.

${(a + b)}^{3} = (a + b) {(a + b)}^{2}$

We expand the parenthesis on the right hand side to get,

${(a + b)}^{3} = (a + b) ( {a}^{2} + 2ab + {b}^{2} )$

We expand again to obtain,

${(a + b)}^{3} = {a}^{3} + 3 {a}^{2}b + 3a {b}^{2} + {b}^{3}$

Let us group the cubed terms on the right hand side to get,

${(a + b)}^{3} = {a}^{3} + {b}^{3} + 3 {a}^{2}b + 3a {b}^{2}$

${(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab (a+ b)$

We make the cubed terms the subject,

${(a + b)}^{3} - 3ab (a+ b) = {a}^{3} + {b}^{3}$

We factor to get,

$(a + b)({(a + b)}^{2} - 3ab ) = {a}^{3} + {b}^{3}$

We expand the bracket on the left hand side to get,

$(a + b)( {a}^{2} + 2ab + {b}^{2} - 3ab ) = {a}^{3} + {b}^{3}$

We finally simplify to get,

$(a + b)( {a}^{2} - ab + {b}^{2} ) = {a}^{3} + {b}^{3}$

5 0

2 years ago

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The employees of a company were surveyed on questions regarding their educational background (college degree or no college degre

taurus [48]

Answer: D) 0.733.

Step-by-step explanation:

Let C denotes the number of employees having college degree and S denote the number of employees are single.

We are given ,

Total = 600 , n(C)=400 , n(S)=100 , n(C∩S)=60

Then,

$n(C\cup S)=n(C)+n(S)-n(C\cap S)\\\\=400+100-60=440$

Now, the probability that an employee of the company is single or has a college degree is

$P(C\cup S)=\dfrac{n(C\cup S)}{\text{Total}}\\\\=\dfrac{440}{600}=0.733333333\approx0.733$

Hence, the probability that an employee of the company is single or has a college degree is 0.733

8 0

3 years ago

If you traveled 5 miles in 10 minutes, how long will it take you to travel 1 mile

horrorfan [7]

Answer:

2 Minutes

Step-by-step explanation:

the first ratio is 5:10 since it is easier to work with big numbers let's start by multiplying it by 2 to get something

Now we have 10:20 we can divide this by 10 and get the ratio 1:2

1:2 equals 1 mile:2 minutes which is 1 mile in 2 minutes!

Have a nice day and I hope this helps!

8 0

2 years ago

If the trapezoid on the grid below is translated by using the rule (x,y)-> (x-4,y-3) what will be the coordinates of B’?

vesna_86 [32]

Answer:

B'(3, 5)

Step-by-step explanation:

Rule for the translation of a point (x, y) by 'h' units left and 'k' units upwards,

(x, y) → (x - h, y + k)

If h = 4 and k = 3,

$(x, y)\rightarrow(x-4,y+3)$

Following this rule coordinates of the image point of B will be,

B(7, 2) → B'(7 - 4, 2 + 3)

→ B'(3, 5)

Therefore, coordinates of the image point B' will be,

B'(3, 5)

6 0

2 years ago

A circle with radius r is inscribed into a right triangle. Find the perimeter of the triangle if the length of the hypotenuse is

tankabanditka [31]

Answer: 56

Step-by-step explanation:

4=(a+b-24)/2

32=a+b

32+24=56

5 0

3 years ago

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