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4 years ago

The equation of a circle is (x - 3)2 + (y + 2)2 = 25. The point (8, -2) is on the circle.

Mathematics

2 answers:

katovenus [111]4 years ago

7 0

Answer:

2nd Option is correct.

Step-by-step explanation:

Given Equation of Circle,

( x - 3 )² + ( y + 2 )² = 25

Point on circle = ( 8 , -2 )

To find: The equation of the line that is tangent to the circle at given point.

By comparing equation of circle with standard equation of circle,

( x - h )² + ( y - k )² = r²

we get,

Coordinates of center = ( 3 , -2 )

Slope of the radius line from center to point ( 8 , -2 ) = $\frac{-2-(-2)}{8-3}=0$

Since, y-coordinate of radius line is same.

⇒ This line is parallel to x-axis.

We also knows that Radius and tangent are perpendicular to each other at point of contact.

⇒ Tangent is Parallel to y-axis and passes through ( 8 , -2 )

⇒ Equation of Tangent is x = 8

Therefore, 2nd Option is correct.

Svetlanka [38]4 years ago

4 0

Hello,

Answer A

y=8
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Mia found the area of a polygon The area is 32 square cm.

solniwko [45]

Answer:

Only the isosceles trapezoid has an area of 32 cm².

Step-by-step explanation:

Let's calculate the area of each polygon.

For the two triangles we have:

$A_{t} = \frac{bh}{2} = \frac{2 cm*4 cm}{2} = 4 cm^{2}$

This polygon does not have an area of 32 cm².

For the rectangle we have:

$A_{r} = bh = 6 cm*4 cm = 24 cm^{2}$

This polygon does not have an area of 32 cm².

For the rectangle trapezoid we have:

$A_{rt} = A_{t} + A_{r} = (4 + 24) cm^{2} = 28 cm^{2}$

So, this polygon does not have an area of 32 cm².

Finally, for the isosceles trapezoid:

$A_{it} = A_{t}*2 + A_{r} = (4*2 + 24) cm^{2} = 32 cm^{2}$

This polygon does have an area of 32 cm².

Therefore, only the isosceles trapezoid has an area of 32 cm².

I hope it helps you!

8 0

3 years ago

Which classification best describes the following system of equations? 3x+6y-12z=36, x+2y-4z=12, 4x+8-16z=48

Andrews [41]

(1) 3x+6y-12z=36
(2) x+2y-4z=12
(3) 4x+8y-16z=48

The first equation (1) is the second equation (2) multiplied by 3:
(2) x+2y-4z=12→3(x+2y-4z=12)→3x+6y-12z=36 (1)

The third equation (3) is the second equation (2) multiplied by 4:
(2) x+2y-4z=12→4(x+2y-4z=12)→4x+8y-16z=48 (3)

The equations are linearly dependent, Then the system of equations is dependent, and then consistent too.

5 0

4 years ago

What property is used to find a product

s344n2d4d5 [400]

The distributive property tells us how to solve equations in the form of a(b + c). The distributive property is sometimes called the distributive law of multiplication and division.
-join the gvcci gang

3 0

3 years ago

The function f(x) = 200(0.5)x/50 models the amount in pounds of a particular

victus00 [196]

Answer:

29 years

Step-by-step explanation:

Given the function $f(x)= 200(0.5)^{\frac{x}{50} }$ , where x stands for the number of years since the material was put into the vault, we can plug 140 into x to find the amount leftover.
Another way of doing this is to change the function to $f(x)=200(0.5^{\frac{1}{50} })^{x}$ which are equivalent functions, and then plug 140 into x. This function is helpful if you also needed to find the rate.
I'll use the 1st function because the question doesn't ask for the rate

$f(x)= 200(0.5)^\frac{140}{50}}$

From here I'll just use a calculator & get 28.7, or 29 years.

4 0

2 years ago

What is the solution to the system of equations?

Sergio039 [100]

The value for x is already given; x = -2

Substitute -2 in for x in the second equation.

y = 2/3(-2) + 3
y = -4/3 + 3
y = 5/3

The final answer is (-2, 5/3).

7 0

3 years ago