Place a check mark next to each equivalent expression

In our solar system, 6 of our 8 planets have moons. What percentage of the planets have moons?

bija089 [108]

75% of our planets have moons

8 0

4 years ago

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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

What is the greatest common factor of 18 and 90

Simora [160]

Hello,

The greatest common factor of 18 and 90 is 9 or 18.

Bye :)

3 0

3 years ago

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A rental car company offers a rental package for a mid-size car.

skelet666 [1.2K]

Answer:

$y=45x+40$

Step-by-step explanation:

Let

x -----> the number of days

y ----> the total cost in dollars,

we know that

The equation of a linear function in slope intercept form is equal to

$y=mx+b$

where

m is the slope o rate of the linear equation

b is the y-coordinate of the y-intercept

Remember that the y-intercept is the value of y when the value of x is equal to zero

In this problem we have

The slope is equal to the rental cost per day

so

$m=45\frac{\$}{day}$

When the number of days is equal to zero (x=0) the total cost is equal to $40 (administrative fee for the cleaning and maintenance of the car)

The y-intercept is the point (0,40)

so

$b=\$40$

substitute the values

$y=45x+40$

8 0

4 years ago

Find the measure of the missing angles.

seropon [69]

Okay with the vertical angles theorem we know that the angles across from each other are congruent so that immediately tells us g=92°.
then the straight line that h and 92° is on =180 so we can use that to solve for h. so 180-92=88. so h =88.
same rules apply to the lower intersection. k=91° and 91+m=180. so m=89°

6 0

3 years ago

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