When two powers with the same base<br> are multiplied together, what is done<br> with the exponents?

a scaled drawing of a rectangular park is 5 inches wide and 7 inches long. the actual park is 210 yards long. what is the width

VMariaS [17]

Answer:

I think the width would be 150 yd

Step-by-step explanation:

just broke down the 210 yd we had already to inches found out how much it was scaled up and did the same on the other side

6 0

3 years ago

Read 2 more answers

Keith collected the names and ages of all of his classmates and organized them in the ordered pair (name, age).

erastova [34]

Answer:

It is both a relation and a function.

Step-by-step explanation:

Keith collected the names and ages of all of his classmates and organized them in the ordered pair (name, age).

Here, if we consider the name as the input and age is the output, then each and every different input there is a single output.

Because a single person can not have more than one age.

Therefore, it is both a relation and a function. (Answer)

7 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

⇒ $\frac{1}{−1 + \sqrt3i+2}$

or

⇒ $\frac{1}{1 + \sqrt3i}$

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

we get

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

or

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

or

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

or

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

Now,

considering the RHS

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

substituting the value of a and b, we get

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

or

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

or

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

or

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

now,

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

we get

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

or

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

or

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

or

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

or

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

or

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

or

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

or

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

Since, LHS = RHS

hence satisfied

3 0

3 years ago

Convert the following quantities to the indicated units. 57 miles per hour to meters per second

vichka [17]

Answer:

25.481

Step-by-step explanation:

divide by 2.237

8 0

3 years ago

A chair costs ₹ 452 and a table costs ₹ 1750. What will be cost of 15 chairs and 30 tables?

gavmur [86]

Answer:

1 chair cost=$452

so of 15 chairs=$452×15=$6780

1 table cost=$1750

so cost of 40 tables=$1750×30=$5250

Total cost=$6780+$5250=$12,030

Step-by-step explanation:

5 0

3 years ago

When two powers with the same base are multiplied together, what is done with the exponents?