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anzhelika [568]
3 years ago
10

A circle is centered at the point (5, -4) and passes through the point (-3, 2).

Mathematics
1 answer:
zepelin [54]3 years ago
8 0

Answer:

(x-5)^2+(y+4)^2=100

Step-by-step explanation:

As we know the given points

Center = (5, -4)

and

Point on circle = (-3,2)

The distance between point on circle and center will give us the radius of circle

So,

The formula for distance is:

\sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1})^{2}}\\Taking\ center\ as\ point\ 1\ and\ the\ other\ point\ as\ point\ 2\\d=\sqrt{(-3-5)^{2}+(2-(-4))^{2}}\\d=\sqrt{(-8)^{2}+(2+4)^{2}}\\d=\sqrt{(-8)^{2}+(6)^{2}}\\\\d=\sqrt{64+36}\\d=\sqrt{100} \\ d=10\\So\ the\ radius\ is\ 10

The standard form of equation of circle is:

(x-h)^{2}+(y-k)^{2}=r^{2}

where h and k are the coordinates of the center. So putting in the value:

(x-5)^{2}+(y-(-4))^{2}=(10)^{2}\\(x-5)^{2}+(y+4)^{2}=100

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Answer:

B or C

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3 years ago
The measures of two supplementary angles are (2x – 8)° and (3x - 2)°. What is the measure of the
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Answer:

68°

Step-by-step explanation:

Here,

  • Two supplementary angles are (2x – 8)° and (3x - 2)°.

As we know that the sum of two supplementary angles are 180°. So,

→ (2x – 8)° + (3x – 2)° = 180°

→ 2x° – 8° + 3x° – 2° = 180°

→ 5x° – 10° = 180°

→ 5x° = 180° + 10°

→ 5x° = 190°

→ x = 190° ÷ 5°

→ <u>x</u><u> </u><u>=</u><u> </u><u>3</u><u>8</u><u>°</u>

Supplementary angles are,

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→ 2(38°) – 8

→ (76 – 8)°

→ 68°

  • 2nd angle = (3x – 2)°

→ 3(38°) – 2

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Therefore, the measure of the smaller angle is 68°.

4 0
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Martin finds a shirt on sale for 20% off at a department store. The original price was $20. Martin must also pay a 7.5% sales ta
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Answer: You will pay $13.52 for this shirt.

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Since the tax is 7.5%, you have to multiply 12.58 by 7.5% to find the amount of money paid as tax.

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12.58 x 0.075 = 0.9435

Since we are dealing with money we have to round to the nearest hundredth -- 0.9435 = 0.94

Then to find the final cost of the shirt, we have to add 12.58 and 0.94 to get  $13.52.

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So it would be:
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3 years ago
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