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3 years ago

Find the center of the circle: x2 + 2x - 3 + y2 = 5. A) (-1,0) B) (-2,3) C) (1,0) D) (2,-3)

Mathematics

1 answer:

yanalaym [24]3 years ago

8 0

A. (-1, 0) is the answer

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Answer both with STEPS

Amanda [17]

Answer:

7 )

x = $\frac{3\sqrt{2} }{2}$

$y= 3$

8 )

$x=6\sqrt{6}$

$y= 9\sqrt{2}$

Step-by-step explanation:

7 ) 8)

In Δ ABC In Δ XYZ

∠ C = 45° ∠ X = 60°

∠ A = 90° ∠ Y = 90°

$AC= \frac{3\sqrt{2} }{2}$ $XY= 3\sqrt{6}$

To Find :

x = ?

y = ?

Solution:

We Know

In Δ ABC

∠ C = 45°

∠ A = 90°

∴ ∠ B = 45° ......Angle sum property of a triangle i.e 180°

∴ Δ ABC is an Isosceles Triangle

∴ AC = AB = x = $\frac{3\sqrt{2} }{2}$

Now appplying Trignometry identity we get

$\sin C = \frac{\textrm{side opposite to angle C}}{Hypotenuse}\\\\\sin 45 = \frac{AC}{BC}\\\\\frac{1}{\sqrt{2} } =\frac{\frac{3\sqrt{2} }{2}}{y}\\\\y=\frac{3\times \sqrt{2}\times \sqrt{2} }{2}\\\\y= 3$

Now In Δ XYZ

∠ X = 60°

∠ Y = 90°

∴∠ Z = 30° . .....Angle sum property of a triangle i.e 180°

Now appplying Trignometry identity we get

$\tan X = \frac{\textrm{side opposite to angle X}}{\textrm{side adjacent to angle X}}$

$\tan 60 = \frac{YZ}{XY}\\\\\sqrt{3} =\frac{y}{3\sqrt{6} }\\ y= 3\sqrt{3} \sqrt{6} \\y= 9\sqrt{2}$

Now,

$\sin X = \frac{\textrm{side opposite to angle C}}{Hypotenuse}\\\\\\\sin 60 = \frac{YZ}{XZ}\\ \\\frac{\sqrt{3} }{2} =\frac{9\sqrt{2} }{x} \\\\x=\frac{18\sqrt{2} }{\sqrt{3} } \\\textrm{after fationalizing the denominator root 3 we get}\\\\x=6\sqrt{6}$

8 0

3 years ago

Determine the domain and the range of the graph.

dimulka [17.4K]

Answer:

Domain: (-∞,∞)

Range: -1

Step-by-step explanation:

Domain means the x-coordinates covered:

(-∞,∞)

Range means the y-coordinates covered:

Only -1 because there are no other existing y-coordinates.

5 0

3 years ago

A system of equations is graphed on a coordinate plane. Which coordinates are the best estimate of the solution to the system of

weqwewe [10]

A solution for a system of equations graph wise, is where they equations intersect or meet. check the picture below.

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3 years ago

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Determine if 7, 8, and 13 can be the lengths of the sides of a triangle. If yes, classify the triangle.

solniwko [45]

Should be A.... hope this helps

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2 years ago

The difference in the X-coordinates of two points is 3, and the difference in Y-coordinates of the two points is 6. What is the

pickupchik [31]

Answer: the slope is 2/1 or 2.

Step-by-step explanation:

The slope is the difference in the y coordinates divided by the difference in the x coordinates so you have to divide 6 by 3 since they have already given you the difference.

6/3 = 2

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3 years ago