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ASHA 777 [7]
3 years ago
7

Calculate the distance between these points in the coordinate plane.

Mathematics
1 answer:
Naily [24]3 years ago
4 0

Answer:

The distance between the two points = 7.81 units

Step-by-step explanation:

We are given two points and we are supposed to find the distance between the two points .

The general formula for distance between two points is

distance = \sqrt{(x_{1} -x_{2})^{2}+(y_{1}- y_{2})^{2}}

Here the points are (-2,4) and (4,-1).

Substituting these points in the above equation,

distance =  \sqrt{( -2 - 4)^{2}+(4 - -1)^{2}}

               = \sqrt{61}

               = 7.81 units

The distance between the two points = 7.81 units

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Step-by-step explanation:

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The spending limit on John’s credit card is given by the function f(x)=15,000+1.5x , where x is his monthly income. f^-1x . The
Katena32 [7]
<span>1.
"The spending limit on John’s credit card is given by the function f(x)=15,000+1.5x"

means that if the monthly income of John is $ 5,000 ,he can spend at most 

f(5,000)=15,000+1.5*5,000=15,000+ 7,500=22, 500 (dollars)

Or for example

if Johns monthly income is $8,000, then he can spend at most

 </span>f(8,000)=15,000+1.5*8,000=15,000+ 12,000=27,000 (dollars)<span>


2.
Now, assume that the maximum amount that John can spend is y.

Then, y=15,000+1.5x

we can express x, the monthly income, in terms of y by isolating x:

</span>y=15,000+1.5x
<span>
1.5x = y-15,000


</span>x= \frac{y-15,000}{1.5}
<span>
thus, in functional notation, x, the monthly income, is a function , say g, of variable y, the max amount:

</span>x=g(y)=\frac{y-15,000}{1.5}

since we generally use the letter x for the variable of a function, we write g again as:

g(x)=\frac{x-15,000}{1.5}
<span>
for example :

</span>g(50,000)=\frac{50,000-15,000}{1.5}= \frac{35,000}{1.5}= 23,333
<span>
tells us that if the maximum amount that John can spend is 50,000 $, then his monthly income is 23,333 $.

3.

If John's limit is $60,000, his monthly income is 

</span>g(60,000)=\frac{60,000-15,000}{1.5}= \frac{45,000}{1.5}=30,000<span>
 dollars.


Answer: $ 30,000

Remark: g is called the inverse function of f, since it undoes what f does.

instead of g(x), we could use the notation </span>f ^{-1}(x)<span>



</span>
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