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Sidana [21]
3 years ago
12

HELP ME Using the following equation, complete the square and find the center and radius of the circle:

Mathematics
1 answer:
IrinaK [193]3 years ago
5 0

Answer: (-2,3), r=5\ \text{units}

Step-by-step explanation:

Given

the equation is x^2+y^2+4x-6y-12=0

completing the square

\Rightarrow (x^2+2\times 2\times x+4-4)+(y^2-2\times3\times y+9-9)-12=0\\\Rightarrow (x^2+2\times 2\times x+4)+(y^2-2\times3\times y+9)-12-4-9=0\\\Rightarrow (x+2)^2+(y-3)^2=25\\\Rightarrow (x+2)^2+(y-3)^2=5^2\\\Rightarrow (x-(-2))^2+(y-3)^2=5^2

Thus, the center of the circle is (-2,3) and radius is r=5\ \text{units}

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Solve the following inequality using both the graphical and algebraic approach: 0.5 x + 3 greater-than-or-equal-to 2 x minus 1.5
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Answer:

d. x les-than-or-equal-to 3 Graph B

Graph B expressed as follows; The graph on the coordinate plane, a line goes through (0, 3) and (4, 5). Another line goes through (1, 0.5), and (4, 6.5). The lines intersect at (3, 4.5)

Step-by-step explanation:

The given inequality is expressed as follows;

0.5·x + 3 ≥ 2·x - 1.5

Let y₁ = 0.5·x + 3, and y₂ = 2·x - 1.5, we get;

For x = -1, 0, 1, 2, 3, 4, 5, 6

y₁ = 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6

y₂ = -3.5, -1.5, 0.5, 2.5, 4.5, 6.5, 8.5, 10.5

From the given data, the lines intersect at (3, 4.5)

The graph on the coordinate plane, a line goes through (0, 3) and (4, 5). Another line goes through (1, 0.5), and (4, 6.5). The lines intersect at (3, 4.5)

Please find attached the required inequality created with MS Excel

Therefore, we have;

3 + 1.5 ≥ 2·x - 0.5·x

4.5 ≥ 1.5·x

∴ 3 ≥ x

x ≤ 3

Therefore, with (typographical) correction, the best option is x les-than-or-equal-to 3 Graph B

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two trains leave the station at the same time, one heading west and the other east. the westbound train travels at 80 miles per
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A vegetable garden and a surrounding path are shaped like a square that together are 12 ft wide. The path is 2 feet wide. The th
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Answer:

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