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4 years ago

A circle is centered at the orgin and contains thr point (-4,-3) . What is the are of this circle?

Mathematics

1 answer:

Ray Of Light [21]4 years ago

4 0

Answer:

25π≈78.5 square units

Step-by-step explanation:

The equation for the area of a circle is

$A=\pi r^2$

We need to determine the radius of the circle. Since the circle is centered at the origin, and the point (-4,-3) is on the circle, we can use the Pythagorean theorem ( $a^2+b^2=c^2$ ) to calculate the radius of the circle.

$a^2+b^2=c^2$

$c=\sqrt{a^2+b^2}$

$c=\sqrt{4^2+3^2}=5$

Therefore, the radius of the circle is 5. Now we go back and plug it into the equation to find the area of the circle.

$A=\pi r^2=\pi (5)^2=25\pi$

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What is the solution to the system of equations? y = 2x – 3.5 x – 2y = –14 (–7, 3.5) (3.5, –7) (7, 10.5) (10.5, 7)

Mandarinka [93]

y = 2x-3.5 ----->1

x-2y=-14. ----->2

1 into 2

x-2(2x-3.5)=-14

x-4x+7=-14

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-3x=-21

x=-21/-3

x=7 --- -->3

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y = 2x-3.5

y=2(7)-3.5

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3 years ago

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Answer:

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3 years ago

Find the length of the third side. If necessary, round to the nearest tenth. 5 10

snow_lady [41]

Answer:

$\boxed {\boxed {\sf 8.7}}$

Step-by-step explanation:

We are asked to find the length of the third side in a triangle, given the other 2 sides.

Since this is a right triangle (note the small square in the corner of the triangle representing a 90 degree /right angle), we can use the Pythagorean Theorem.

$a^2 + b^2 =c^2$

In this theorem, a and b are the legs of the triangle and c is the hypotenuse.

We know that the unknown side (we can say it is a) and the side measuring 5 are the legs because they form the right angle. The side measuring 10 is the hypotenuse because it is opposite the right angle.

b= 5
c= 10

Substitute the values into the formula.

$a^2 + (5)^2 = (10)^2$

Solve the exponents.

(5)²= 5*5 = 25
(10)²= 10*10= 100

$a^2 + 25=100$

We are solving for a, so we must isolate the variable. 25 is being added to a. The inverse operation of addition is subtraction, so we subtract 25 from both sides.

$a^2 +25-25=100-25$

$a^2=100-25$

$a^2 = 75$

a is being squared. The inverse of a square is the square root, so we take the square root of both sides.

$\sqrt {a^2}= \sqrt{75}$

$a= \sqrt{75}$

$a= 8.660254038$

Round to the nearest tenth. The 6 in the hundredth place tells us to round the 6 up to a 7 in the tenth place.

$a \approx 8.7$

The length of the third side is approximately 8.7

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3 years ago

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Answer:

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