the counting pattern shown in my array has 180 windows. So you can count by 9's or 80's to get the total?

Consider the equality xy k. Write the following inverse proportion: y is inversely proportional to x. When y = 12, x=5.

skelet666 [1.2K]

Answer:

$y=\dfrac {60} {x}$ or $xy=60$ (depending on your teacher's format preference)

Step-by-step explanation:

<h3><u>Proportionality background</u></h3>

Proportionality is sometimes called "variation". (ex. " 'y' varies inversely as 'x' ")

There are two main types of proportionality/variation:

Direct
Inverse.

Every proportionality, regardless of whether it is direct or inverse, will have a constant of proportionality (I'm going to call it "k").

Below are several different examples of both types of proportionality, and how they might be stated in words:

$y=kx$ y is directly proportional to x
$y=kx^2$ y is directly proportional to x squared
$y=kx^3$ y is directly proportional to x cubed
$y=k\sqrt{x}}$ y is directly proportional to the square root of x
$y=\dfrac {k} {x}$ y is inversely proportional to x
$y=\dfrac {k} {x^2}$ y is inversely proportional to x squared

From these examples, we see that two things:

things that are <u>directly proportional</u> -- the thing is <u>multipli</u>ed to the constant of proportionality "k"
things that are <u>inversely proportional</u> -- the thing is <u>divide</u>d from the constant of proportionality "k".

<h3><u>Looking at our question</u></h3>

In our question, y is inversely proportional to x, so the equation we're looking at is the following $y=\dfrac {k} {x}$ .

It isn't yet clear what the constant of proportionality "k" is for this situation, but we are given enough information to solve for it: "When y=12, x=5."

We can substitute this known relationship pair, and find the "k" that relates this pair of numbers:

<h3><u>Solving for k, and finding the general equation</u></h3>

General Inverse variation equation...

$y=\dfrac {k} {x}$

Substituting known values...

$(12)=\dfrac {k} {(5)}$

Multiplying both sides by 5...

$(12)*5= \left ( \dfrac {k} {5} \right ) *5$

Simplifying/arithmetic...

$60=k$

So, for our situation, k=60. So the inverse proportionality relationship equation for this situation is $y=\dfrac {60} {x}$ .

The way your question is phrased, they may prefer the form: $xy=60$

7 0

2 years ago

Which product has 4 zeros after the digit 3? 0.03 times 10 with the power of 5. 0.3 times 10 with the power of 4 0.03 times 10 w

sweet [91]

Answer:

$0.3 * 10^5$

Step-by-step explanation:

0.3

^ You need to move the three before the decimal place and leave 4 empty digits (0) between

0.3

3.0

30.0

300.0

3000.0

30000.0

A total of 5 moves.

Each move is equivalent to x, the preceding value, times 10. x * 10

Repeated multiplication times the same factor equates to exponentiation, so for a total of 5 moves, it is notated as $10^5$ , giving you an expression of:

$0.3 * 10^5$

7 0

3 years ago

Which is the product of 4/5 x3/7

Keith_Richards [23]

Answer:

12/35

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

To the nearest 1000, there are 18,000 people at a festival . Write down the minimum possible number of people at the festival

Andreyy89

Answer:

17500

Step-by-step explanation:

17499 rounds down

17500 rounds up

8 0

3 years ago

13 At the beginning of 2009, Mr Veale bought a company.

katen-ka-za [31]

Answer:

£58,800

Step-by-step explanation:

The answer can be calculated using

FV=p(1+r/n)^nt

P=£50,000

r=2%=0.02

n=12

t=2009 to 2017=8 years

FV=p(1+r/n)^nt

=50,000(1+0.02/12)^12*8

=50,000(1+0.0017)^96

=50,000(1.0017)^96

=50,000(1.1771)

=58,855

FV=58,855

To the nearest £100=£58,800

7 0

3 years ago