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pychu [463]
3 years ago
15

Mark all the Statements that are true:

Mathematics
1 answer:
Dmitry_Shevchenko [17]3 years ago
3 0

The graph represents the line x = 3.

Since there is more than one y-value for the one x-value provided, this graph is not a function.

The range is infinite, as there are no limits shown on the graph, and the slope is undefined.

The domain is only 3, since the only x-value on the graph is 3.

Based on this information, the statements that are true will be:

C. This graph is not a function because the value x = 3 is assigned to more than one y-value.

E. The equation of this line is x = 3.

(Note that D says the graph <em>is a function</em>. The graph isn't a function, as there is more than one y-value for x = 3.)

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Remember that the equation of a circle is:
(x - h)^{2} + (y - k)^{2} =  r^{2}
Where (h, k) is the center and r is the radius.
We need to get the equation into that form, and find k.

x^{2} - 6x +  y^{2} - 10y = 56

Complete the square. We must do this for x² - 6x and y² - 10y separately.

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Because we've added 9 on one side of the equation, we have to remember to do the same on the other side.

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Now factor x² - 6x + 9 to get (x - 3)² and do the same thing with y² - 10y.

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Divide -10 by 2 to get -5.
Square -5 to get 25.
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(x - 3)^{2}+ y^{2} - 10y + 25= 90

Factor y² - 10y + 25 to get (y - 5)²

(x - 3)^{2}+ (y - 5)^{2} = 90

Now our equation is in the correct form. We can easily see that h is 3 and k is 5. (not negative because the original equation has -h and -k so you must multiply -1 to it)

Since (h, k) represents the center, (3, 5) is the center and 5 is the y-coordinate of the center.
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