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3 years ago

What is the solution to the system of

Mathematics

2 answers:

OverLord2011 [107]3 years ago

7 0

2x+2y=12.........&
6x-2y=20.........$

&+$: 8x=32
x=4

2*4+2y=12
y=4

Sonbull [250]3 years ago

3 0

Answer:

The solution, as an ordered pair, is (4, 2).

Step-by-step explanation:

2x + 2y = 12

6x - 2y = 20 Adding the 2 equations will eliminate y:

8x + 2y + (-2y) = 32

8x = 32

x = 4.

Substitute x = 4 in the first equation:

2(4) + 2y = 12

2y = 12 - 8

2y = 4

y = 2.

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3 years ago

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Determine the domain and range of (g ○ f)(x) if f of x is equal to 4 over the quantity x squared minus 4 end quantity and g(x) =

lara [203]

The domain and range of a function are the possible x and y values of the function.

The domain and the range of the function is: (a) $\mathbf{D:\{x \in R|x \ne -2,2\}}$ and $\mathbf{R:\{(-\infty,1) \cup (2,\infty)\}}$

The functions are given as:

$\mathbf{f(x) = \frac{4}{x^2 - 4}}$

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(g o f)(x) is calculated as:

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So, we have:

$\mathbf{(g\ o\ f)(x) = \frac{4}{x^2 - 4} + 2}$

Take LCM

$\mathbf{(g\ o\ f)(x) = \frac{4 + 2x^2 - 8}{x^2 - 4} }$

$\mathbf{(g\ o\ f)(x) = \frac{2x^2 - 4}{x^2 - 4} }$

Represent the denominator as follows, to calculate the domain

$\mathbf{x^2 - 4 \ne 0 }$

Add 4 to both sides

$\mathbf{x^2 \ne 4 }$

Take square roots of bot sides

$\mathbf{x \ne \±2 }$

Hence, the domain of the function is:

$\mathbf{D:\{x \in R|x \ne -2,2\}}$

On the graph of $\mathbf{(g\ o\ f)(x) = \frac{2x^2 - 4}{x^2 - 4} }$ (see attachment), the function does not have a value from y = 1 to 2.

Hence, the range is:

$\mathbf{R:\{(-\infty,1) \cup (2,\infty)\}}$

Read more about domain and range at:

brainly.com/question/1632425

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2 years ago

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marishachu [46]

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4 years ago

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Mariana [72]

Answer:

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