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2 years ago

FIND PRODUCT USING THIS AREA MODEL 300+70+8 AND WRITE THE EQUATION

Mathematics

1 answer:

Dmitrij [34]2 years ago

8 0

Answer:

378

Step-by-step explanation:

300

+-------

378

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What is the expansion of (3+x)^4

Vlad1618 [11]

Answer:

$\left(3+x\right)^4:\quad x^4+12x^3+54x^2+108x+81$

Step-by-step explanation:

Considering the expression

$\left(3+x\right)^4$

Lets determine the expansion of the expression

$\left(3+x\right)^4$

$\mathrm{Apply\:binomial\:theorem}:\quad \left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i$

$a=3,\:\:b=x$

$=\sum _{i=0}^4\binom{4}{i}\cdot \:3^{\left(4-i\right)}x^i$

Expanding summation

$\binom{n}{i}=\frac{n!}{i!\left(n-i\right)!}$

$i=0\quad :\quad \frac{4!}{0!\left(4-0\right)!}3^4x^0$

$i=1\quad :\quad \frac{4!}{1!\left(4-1\right)!}3^3x^1$

$i=2\quad :\quad \frac{4!}{2!\left(4-2\right)!}3^2x^2$

$i=3\quad :\quad \frac{4!}{3!\left(4-3\right)!}3^1x^3$

$i=4\quad :\quad \frac{4!}{4!\left(4-4\right)!}3^0x^4$

$=\frac{4!}{0!\left(4-0\right)!}\cdot \:3^4x^0+\frac{4!}{1!\left(4-1\right)!}\cdot \:3^3x^1+\frac{4!}{2!\left(4-2\right)!}\cdot \:3^2x^2+\frac{4!}{3!\left(4-3\right)!}\cdot \:3^1x^3+\frac{4!}{4!\left(4-4\right)!}\cdot \:3^0x^4$

$\frac{4!}{0!\left(4-0\right)!}\cdot \:\:3^4x^0:\:\:\:\:\:\:81$

$\frac{4!}{1!\left(4-1\right)!}\cdot \:3^3x^1:\quad 108x$

$\frac{4!}{2!\left(4-2\right)!}\cdot \:3^2x^2:\quad 54x^2$

$\frac{4!}{3!\left(4-3\right)!}\cdot \:3^1x^3:\quad 12x^3$

$\frac{4!}{4!\left(4-4\right)!}\cdot \:3^0x^4:\quad x^4$

so equation becomes

$=81+108x+54x^2+12x^3+x^4$

$=x^4+12x^3+54x^2+108x+81$

Therefore,

$\left(3+x\right)^4:\quad x^4+12x^3+54x^2+108x+81$

6 0

3 years ago

One-sixth the sum of eight and a number

Aleks04 [339]

Step-by-step explanation:

Let the number be x.

1 =8 + x

6×1=6×8+6×x

1=48+6x

1-48=6x

-47=6x

6. 6 x = -7 5

x is equal to minus seven whole number five divided by six.

7 0

3 years ago

Perimeter of a rectangle is 52 feet. If the length is 10 less than 2 times the width, what is the width?

ella [17]

Step-by-step explanation:

Let the width be x feet.

Therefore, length = 2x - 10

Perimeter of rectangle = 52

$2(2x - 10 + x) = 52 \\ 2(3x - 10) = 52 \\ \therefore \: 3x - 10 = \frac{52}{2} \\ \therefore \: 3x - 10 = 26\\ \therefore \: 3x = 26 + 10\\ \therefore \: 3x = 36 \\ \therefore \: x = \frac{36}{3} \\ \therefore \: x = 12 \\ \purple{ \boxed{\therefore \: width \: of \: rectangle = 12 \: feet }}$