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timofeeve [1]
3 years ago
13

Solve the systems of equation by graphing (Picture provided)

Mathematics
1 answer:
padilas [110]3 years ago
3 0

Answer:

The option d

Step-by-step explanation:

find the intersection with x and y

https://tex.z-dn.net/?f=x%3D0%0A

https://tex.z-dn.net/?f=0%2By%3D-9%20%5Clongrightarrow%20y%3D-9%0A

and https://tex.z-dn.net/?f=y%3D0%0A

https://tex.z-dn.net/?f=x%2B0%3D-9

we get the coordinates

https://tex.z-dn.net/?f=(0%2C-9)%2C%20(-9%2C0)

and the same process for another equation

https://tex.z-dn.net/?f=4*(0)%2By%3D-19%20%5Clongrightarrow%20y%3D-19%5C%5C%0A4*x%2B0%3D-19%20%5Clongrightarrow%20x%3D%5Cfrac%7B-19%7D%7B4%7D%20%5C%5C%5C%5C%0A(0%2C-19)%2C%20(%5Cfrac%7B-19%7D%7B4%7D%2C0)%20

and these coordinates are those expressed in the d graph

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The denominator of the first term is a difference of squares, such that

4<em>a</em> ² - <em>b</em> ² = (2<em>a</em>)² - <em>b</em> ² = (2<em>a</em> - <em>b</em>) (2<em>a</em> + <em>b</em>)

So you can write the fractions as

(4<em>a</em> ² + <em>b</em> ²)/((2<em>a</em> - <em>b</em>) (2<em>a</em> + <em>b</em>)) - (2<em>a</em> - <em>b</em>)/(2<em>a</em> + <em>b</em>)

Multiply through the second fraction by 2<em>a</em> - <em>b</em> to get a common denominator:

(4<em>a</em> ² + <em>b</em> ²)/((2<em>a</em> - <em>b</em>) (2<em>a</em> + <em>b</em>)) - (2<em>a</em> - <em>b</em>)²/((2<em>a</em> + <em>b</em>) (2<em>a</em> - <em>b</em>))

((4<em>a</em> ² + <em>b</em> ²) - (2<em>a</em> - <em>b</em>)²) / ((2<em>a</em> - <em>b</em>) (2<em>a</em> + <em>b</em>))

Expand the numerator:

(4<em>a</em> ² + <em>b</em> ²) - (2<em>a</em> - <em>b</em>)²

(4<em>a</em> ² + <em>b</em> ²) - (4<em>a</em> ² - 4<em>ab</em> + <em>b</em> ²)

4<em>ab</em>

<em />

So the original expression reduces to

4<em>ab</em> / ((2<em>a</em> - <em>b</em>) (2<em>a</em> + <em>b</em>))

or

4<em>ab</em> / (4<em>a</em> ² - <em>b</em> ²)

upon condensing the denominator again.

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Answer:

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Step-by-step explanation:

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Answer:

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That should evaluate to zero. Therefore: -27 - 9 + 30 + A = 0. Solve for A to get A = 6.

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