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vredina [299]
3 years ago
12

A function, f, is defined by the set {(2,3), (4,7),(-1,5)}.

Mathematics
1 answer:
Kitty [74]3 years ago
3 0

Answer:

{(3,2), (7,4),(5,-1)}.

Step-by-step explanation:

To find the points reflected through y=x, you are really being asked to find the inverse relation. That means we are just swapping x and y per point; like (a,b) to (b,a).

So (2,3) when reflected through y=x becomes (3,2).

(4,7) when reflected through y=x becomes (7,4).

(-1,5) when reflected through y=x becomes (5,-1).

So the inverse relation is:

{(3,2), (7,4),(5,-1)}.

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Answer:

length of rectangle = 5

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Step-by-step explanation:

Since the length of the rectangle is "x", and the value of the area is given by the product of the length "x" times the width "10-x", indeed, the area "y" of the rectangle is given by the equation:

y=x\,(10-x)=10x-x^2

Now, they tell us that the area of the rectangle is such that coincides with the maximum (vertex) of the parabola this quadratic expression represents. So in order to find the dimensions of the rectangle and therefore its area, we find the x-coordinate for the vertex, and from it, the y-coordinate of the vertex, which is the rectangle's actual area.

Recall that the formula for the x of the vertex of a quadratic of the form :

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x_{vertex}=-\frac{b}{2\,a}

which in our case gives:

x_{vertex}=-\frac{b}{2\,a}\\x_{vertex}=-\frac{10}{2\,(-1)}\\x_{vertex}=5

Therefore, the length of the rectangle is 5, and its width (10-x) is also 5.

The area of the rectangle is therefore the product of these two values: 5 * 5 = 25

Which should coincide with the value we obtain when we replace x by 5 in the area formula:

y=10x-x^2\\y=50-(5)^2\\y=50-25\\y=25

8 0
3 years ago
The store is selling lemons at $0.39 each. Each lemon yields about 2 tablespoons of juice. How much will it cost to buy enough l
I am Lyosha [343]
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What is the range of the following set? 48, 47, 54, 55, 52, 48, 46, 53, 45
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Answer:

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