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3 years ago

(a-b)(a^2 + ab + b^2)

Mathematics

2 answers:

Nitella [24]3 years ago

6 0

Answer:

a^3-b^3

Step-by-step explanation:

(a−b)(a2+ab+b2)

=(a+−b)(a2+ab+b2)

=(a)(a2)+(a)(ab)+(a)(b2)+(−b)(a2)+(−b)(ab)+(−b)(b2)

=a3+a2b+ab2−a2b−ab2−b3

=a3−b3

kykrilka [37]3 years ago

3 0

Multiply through the parentheses:
a^3 + b(a^2)+ a(b^2) - b(a^2) - a(b^2) - b^3

Simply by combing like terms:
a^3 - b^3

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At the car dealership, they keep the ratio

Mashutka [201]

Answer

13 2/9

Step-by-step explanation:

8:3 is the ratio which means that you multiply that (8x3) is 24 - 11 because 2/9/ 2+9 = 11 and 24-11 is 13 so there is your answer

7 0

3 years ago

Let A be a set of numbers.

LUCKY_DIMON [66]

Answer:

a. closed under addition and multiplication

b. not closed under addition but closed under multiplication.

c. not closed under addition and multiplication

d. closed under addition and multiplication

e. not closed under addition but closed under multiplication

Step-by-step explanation:

Let A be a set of all integers divisible by 5.

Let $x,y$ ∈A such that $x=5m\,,\,y=5n$

Find $x+y,xy$

$x+y=5m+5n=5(m+n)$

So, $x+y$ is divisible by 5.

$xy=(5m)(5n)=25mn=5(5mn)$

So,

$xy$ is divisible by 5.

Therefore, A is closed under addition and multiplication.

Let A = { 2n +1 | n ∈ Z}

Let $x,y$ ∈A such that $x=2m+1\,,\,y=2n+1$ where m, n ∈ Z.

Find $x+y,xy$

$x+y=2m+1+2n+1=2m+2n+2=2(m+n+1)$

So,

$x+y$ ∉ A

$xy=(2m+1)(2n+1)=4mn+2m+2n+1=2(2mn+m+n)+1$

So,

$xy$ ∈ A

Therefore, A is not closed under addition but A is closed under multiplication.

$Let A=\{2,5,8,11,14,...\}$

Let $x=2,y=5$ but $x+y=2+5=7$ ∉A

Also,

$xy=2(5)=10$ ∉A

Therefore, A is not closed under addition and multiplication.

Let A = { 17n: n∈Z}

Let $x,y$ ∈ A such that $x=17n,y=17m$

Find x + y and xy

$x+y=17n+17m=17(n+m)$

$xy=(17m)(17n)=289mn=17(17mn)$

So,

$x+y,xy$ ∈ A

Therefore, A is closed under addition and multiplication.

Let A be the set of nonzero real numbers.

Let $x,y$ ∈ A such that $x=-1,y=1$

Find x + y

$x+y=-1+1=0$

So,

$x+y$ ∈ A

Also, if x and y are two nonzero real numbers then xy is also a non-zero real number.

Therefore, A is not closed under addition but A is closed under multiplication.

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3 years ago

Newton Street and Oakland Avenue intersect. If the diagonal distance across the intersection is 17 meters and Newton Street is 1

Margarita [4]

The Oakland Avenue is approximately what the time you think is it now though you have 120 days to

8 0

2 years ago

Calculate the area of the regular pentagon below: A regular pentagon with side length of 11.8 inches and dotted line from center

vlada-n [284]

Answer:

Area of regular pentagon is 238.95 square inches.

Step-by-step explanation:

Given a regular pentagon with side length of 11.8 inches and dotted line from center to middle of side of 8.1 inches.

we know a regular polygon divides into 5 congruent triangles.

Side of pentagon i.e base of one triangle is 11.8 inches.

Also, distance from center to middle of side which is height of triangle is 8.1 inches.

Area of 1 triangle= $\frac{1}{2}\times base\times height$

= $\frac{1}{2}\times 11.8\times 8.1$

= 47.79 sq inches.

Area of regular pentagon=area of 5 congruent triangles= $5\times 47.79$ =238.95 sq inches.

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3 years ago

What is the square root of 29 rounded to the nearest 10?

nydimaria [60]

5.40. It would be 5.38 but you round up to 5.40

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3 years ago

(a-b)(a^2 + ab + b^2)​

(a-b)(a^2 + ab + b^2)