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4 years ago

Appl Distributive property to 5(2d-3)

Mathematics

1 answer:

UkoKoshka [18]4 years ago

6 0

Answer:

10d - 15

Step-by-step explanation:

Take the 5 and multiply it by the numbers and variables inside the parentheses.

5(2d - 3)

(5 x 2d) + (5 x -3)

10d - 15

Once you do this you can take the parentheses away.

Hope this helps.

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(5a+6)+(7a+8) answer- now- please-

ddd [48]

Answer:

12a+14

you can just combine the numbers, hope this helped!

Step-by-step explanation:

4 0

3 years ago

Show that a = −1 + √3i and b = 2 satisfy 1/a+b=1/a + 1/b

Zarrin [17]

Answer:

LHS = $\frac{1 - \sqrt3i}{4}$ = RHS = $\frac{1 - \sqrt3i}{4}$

Step-by-step explanation:

Data provided in the question:

a = −1 + √3i and b = 2

to prove:

$\frac{1}{a+b}=\frac{1}{a} + \frac{1}{b}$

Considering the LHS

⇒ $\frac{1}{a+b}$

substituting the value of a and b, we get

⇒ $\frac{1}{−1 + \sqrt3i+2}$

⇒ $\frac{1}{1 + \sqrt3i}$

on multiplying and dividing by conjugate ( 1 - √3i )

we get

$\frac{1}{1 + \sqrt3i}\times\frac{1 - \sqrt3i}{1 - \sqrt3i}$

$\frac{1 - \sqrt3i}{(1^2 - (\sqrt3i)^2}$

$\frac{1 - \sqrt3i}{1 + 3}$ (as (√i)² = -1 )

$\frac{1 - \sqrt3i}{4}$

Now,

considering the RHS

$\frac{1}{a} + \frac{1}{b}$

substituting the value of a and b, we get

⇒ $\frac{1}{-1 + \sqrt3i} + \frac{1}{2}$

⇒ $\frac{2\times1 + ( -1 + \sqrt3i)\times1}{(-1 + \sqrt3i)\times2}$

⇒ $\frac{2 + ( -1 + \sqrt3i)}{(-1 + \sqrt3i)\times2}$

⇒ $\frac{1 + \sqrt3i}{(-1 + \sqrt3i)\times2}$

now,

on multiplying and dividing by conjugate ( -1 - √3i )

we get

$\frac{1 + \sqrt3i}{(−1 + \sqrt3i)\times2}\times\frac{-1 - \sqrt3i}{-1 - \sqrt3i}$

$\frac{1 + \sqrt3i}{(−1 + \sqrt3i)\times2}\times\frac{-1( 1 + \sqrt3i)}{-1 - \sqrt3i}$

$\frac{(1 + \sqrt3i}^2\times(-1){((-1)^2 - (\sqrt3i)^2)\times2}$

$\frac{(1^2 + (\sqrt3i)^2+2(1)(\sqrt3i)\times(-1)}{(1 + 3)\times2}$

$\frac{(1 - 3 + 2\sqrt3i)\times(-1)}{(4)\times2}$

$\frac{(-2 + 2\sqrt3i)\times(-1)}{(4)\times2}$

$\frac{-2( 1 - 2\sqrt3i)\times(-1)}{(4)\times2}$

$\frac{( 1 - 2\sqrt3i)}{(4)}$

Since, LHS = RHS

hence satisfied

3 0

3 years ago

What is the greatest possible whole number remainder if you divide any number by 41

sammy [17]

The greatest possible remainder is 40.

If it were 41, then the whole number of the quotient would increase by 1.

8 0

3 years ago

Can someone help me with 27 and 28?

netineya [11]

You have to do: { x^4 * 6x^2 }

(^ means to the power of)

(* means multiply)

Answer in picture

8 0

3 years ago

what do you call the middle value in the set of the data or quantities a mean b. median c.mode d.range

MakcuM [25]

Answer:

median is the middle value

mean is the average

mode is the one that occurs most

range is the highest number - lowest number

6 0

3 years ago