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3 years ago

Which input value produces the same output value for the

Mathematics

1 answer:

Brrunno [24]3 years ago

4 0

Answer:

The input value that produces the same output value for the two functions on the graph is x = -2

It's important to know some concepts:

1. INPUT: Also called the domain of the function, it Is the set of all x-values for which the function is defined.

2. OUTPUT: Also called the range of the function, it is the set of all y-values for which the function is defined.

So we need to know which of the following inputs produces the same output value for the two functions on the graph

x=-3

x=-2

x=-1

x=3

By looking at the graph we can realize that the input value that produces the same output value for the two functions on the graph is the point of intersection of these graph, that is:

the point at x=-2

And the output value is the y-value:

y=1

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3 years ago

A rectangle is 6yards longer than it is wide. Find the dimensions of the rectangle if it’s area is 187 square yards

emmasim [6.3K]

Answer:

Width = 11 yards

Length = 17 yards

Step-by-step explanation:

First of all, the length of the rectangle is 6 yards longer than the width, this means, length = width + 6 yards. This dimensions can be represented on figure 1, where <em>w</em> is width, and <em>l</em>, for length.

We know the area of a rectangle is A = width x length

For our case 187 = w . (w + 6)

Using the Distributive Property for the multiplication we obtain

$187 = w^{2} +6w$

$w^{2} +6w-187 =0,$

Using the quadratic formula $w=\frac{-b\±\sqrt{b^{2}-4ac } }{2a}$ where a = 1, b = 6, c = - 187 and replacing into the formula, we will have:

$w=\frac{-6\±\sqrt{6^2-4(1)(-187)} }{2(1)}$

$w=\frac{-6\±\sqrt{36+748} }{2}=\frac{-6\±\sqrt{784} }{2}=\frac{-6\±28}{2}$

We have two options: $w=\frac{-6+28}{2}=\frac{22}{2}=11 yards$

$w=\frac{-6-28}{2}=\frac{-34}{2}=-17 yards$ But a distance (width) can not be negative so, this answer for w must be discarded.

The answer must be width = 11 yards.

To find the length $l =\frac{187}{11}=17 yards$

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Answer:

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