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3 years ago

Which ordered pairs is a solution to -5x + 3y > 12?

Mathematics

1 answer:

GaryK [48]3 years ago

5 0

9514 1404 393

Answer:

(-5, 5), (2, 8), (-6, 0)

Step-by-step explanation:

It is convenient to graph the solution, then plot the points to see which fall in the solution area.

The point (3, 9) falls on the boundary line, which is <em>not</em> part of the solution set.

The points that are solutions are ...

B(-5, 5)

E(2, 8)

F(-6, 0)

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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

There is a multiplication and division fact family with the numbers 2,4 and 8. Write the four fact family members

DanielleElmas [232]

Answer:

8-4=2

2 x 4=8

4 x 2=8

8-2=4

Step-by-step explanation:

6 0

3 years ago

There are 3 in. of snow on the ground when it begins to snow 0.5 in./h . Which linear equation represents the total depth of the

dexar [7]

There are 3 in. of snow on the ground when it begins to snow 0.5 in./h.

Initial depth of snow = 3 in.

it begins to snow 0.5 in./h. The constant rate of snow is 0.5. So slope = 0.5

Let x be the number of hours

y be the total depth of the snow

To frame linear equation we use y=mx+b

where m is the slope and b is the y intercept (initial depth of snow)

We know m=0.5 and b=3

Replace it in the equation

y = 0.5x + 3

The linear equation that represents the total depth of the snow(y), in inches, after x hours

is y= 0.5x + 3

7 0

3 years ago

Read 2 more answers

What is the area of this triangle?

olganol [36]

Answer:

the answer of the question is D

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3 years ago

At a baseball game, a vender sold a combined total of 236 sodas and hot dogs. The number of hot dogs sold was 50 less than the n

ELEN [110]

143 and 93

143 sodas 93 dogs

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3 years ago