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love history [14]
2 years ago
14

2) The product of 8 and a number is 104. What is the number? Write the equation

Mathematics
1 answer:
Vlad [161]2 years ago
4 0

Answer:

The equation is 8 x 13 = 104

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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:

  1. Direct
  2. 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
Factor as the product of two binomials x^2-2x+1
Ket [755]

Answer:(x + 1)^2

Step-by-step explanation:

4 0
2 years ago
What are some characteristics for simplest form  
givi [52]
Ex. 9 divided by 3=3 because 3x3=9
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PLEASE HELP <br>Answer: m = 3 <br>3 - y = x + 10​<br>Find the slope and y intercept
Kitty [74]

Answer:

slope is -1 and y intercept is -7.

Step-by-step explanation:

3- y = x+10

or, -y = x +10-3

or, -y = x+ 7

or, y = -x-7

comparing with y= mx +c, m= -1, c= -7

6 0
3 years ago
A caircular fountian has a circumference of 21 feet. Which expression can be used to find the diameter of the fountian in feet?​
KiRa [710]

Answer: 21 = 2\pi r

Step-by-step explanation:

To find the circumference of a circle, you can use 2\pi r. You can set this equal to 21 (feet). The equation to solve at this point would be 21=2\pi r.

5 0
2 years ago
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