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3 years ago

The product of a number and 50

2 answers:

4 0

"Product" means we are looking at a multiplication problem.

Can be written as:

A number (n) times 50

n x 50

The simplest (and most common way) to write it:

50n

natulia [17]3 years ago

3 0

Product means multiplcation
product of x and y means x times y or xy
like sum of x and y=x+y so

a number could be any number, we will represent it as x so
product of x and 50=x50 or 50x

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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

The smaller triangle was dilated to form the larger triangle. What is the value of x?

Nikolay [14]

We know that
scale factor=measure larger triangle/measure smaller triangle---->18/12
scale factor=1.5
so
measure larger triangle=scale factor*measure smaller triangle

for the leg in the smaller triangle equal to 5
measure larger triangle=1.5*5-----> 7.5

the answer is
7.5

8 0

3 years ago

Read 2 more answers

Is 2.55 a irrational, rational, integer, whole number or natural number?

satela [25.4K]

So, the first thing we need to know is what is what.

So, A natural number is a whole number

A whole number is an integer

and An integer is a rational number.

Now, since there is a terminating decimal (a decimal that does not go on forever) we know it is a rational number.

Since there is a decimal, it cannot be an integer, therefore

It is a rational number

4 0

2 years ago

Owen has a 15 ft ladder, the instructions say that the base of the ladder should be 6 ft from the wall. How high up the wall wil

pogonyaev

Answer:

height = 13.75 feet

Step-by-step explanation:

use the Pythagorean theorem

hypotenuse^2 =base^2 + height^2

15^2 = 6^2+height^2

225 = 36 + height^2

189 = height^2

height = 13.75 feet

6 0

3 years ago

The drama club is selling tickets to their play to raise money for the shows expenses. Each student ticket sells for $8 and each

vivado [14]

Answer:

32 adult tickets and 49 student tickets

Step-by-step explanation:

Step-by-step explanation: 32 x $11.50= $368 adult tickets 49 x $8=$392 student tickets

6 0

3 years ago