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Shkiper50 [21]
3 years ago
6

Find the center of the circle that can be circumscribed about triangle EFG with E(2, 2), F(2, -2), and G(6,-2).

Mathematics
2 answers:
nadezda [96]3 years ago
6 0
Hello friend that would be the last option (3, 2)
it would be great if you gave me brainlest
babymother [125]3 years ago
3 0

Answer:

The centre of circle is (4,0)          

Step-by-step explanation:

Given points are,

E(2, 2), F(2, -2), and G(6,-2).

The center of the circle is the circumcenter of the triangle, the point where the perpendicular bisectors intersect.

To find out the circumcenter we have to solve any two equations of bisectors of sides triangle.

\text{Mid point of EF = }(\frac{2+2}{2},\frac{2-2}{2})= (2,0)

\text{Slope of EF = }\frac{y_2-y_1}{x_2-x_1}=\frac{-2-2}{2-2}=\frac{-4}{0}

Slope of the bisector is negative reciprocal of the given slope.

So, the slope of the perpendicular bisector = 0

Equation of EF with slope 0 and the coordinates (2,0) is,

(y - 0) = 0(x - 2)

y=0   →    (1)

Similarly, for EG

\text{Mid point of EG = }(\frac{2+6}{2},\frac{2-2}{2})= (4,0)

\text{Slope of EG = }\frac{y_2-y_1}{x_2-x_1}=\frac{-2-2}{6-2}=\frac{-4}{4}=-1

So, the slope of the perpendicular bisector = 1

Equation of EG with slope 1 and the coordinates (4,0) is,

(y - 0) =1(x - 4)

y=x-4   →    (2)

Solving equation (1) and (2),

0=x-4

x=4

So the circumcenter is (4,0)

Option 2 is correct.

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slamgirl [31]
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3 0
3 years ago
Find three consecutive interferes whose sum is 96
Ronch [10]

Answer:

31, 32, 33

Step-by-step explanation:

x + x + 1 +x + 2 = 96

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      -3    -3

3x = 93

/3     /3

x = 31

31 is the first number, so since they’re consecutive, the second two numbers are 32 and 33.

6 0
3 years ago
A circle has a circumference of 50.2450.2450, point, 24 units.<br> What is the radius of the circle?
beks73 [17]

Answer:

r = 8 units

Step-by-step explanation:

The circumference is calculated using C = 2\pi r. Substitute C = 50.24 units. Solve for the radius.

C = 2 \pi r\\50.24 = 2 \pi r\\25.12 = \pi r\\8 = r

7 0
3 years ago
Which of the following pairs represent a function ​
denis23 [38]

Option D: \{(-9,8),(-5,-8),(-7,8),(-6,-8)\} are the ordered pairs represents a function.

Explanation:

Given that the options of the set of ordered pairs.

We need to determine the ordered pairs that represents a function.

Option A: \{(-12,8),(-15,8),(-5,-8),(-12,-8)\}

A relation is said to be a function if each element of x is related to exactly one element in y.

From this set of ordered pairs, it is obvious that the element -12 of x is related to two different element in y.

Thus, the ordered pairs \{(-12,8),(-15,8),(-5,-8),(-12,-8)\} is not a function.

Hence, Option A is not the correct answer.

Option B: \{(8,-9),(-8,-5),(8,-7),(-8,-6)\}

From this set of ordered pairs, it is obvious that the elements -8 and 8 of x are related to two different element in y.

Thus, the ordered pairs \{(8,-9),(-8,-5),(8,-7),(-8,-6)\} is not a function.

Hence, Option B is not the correct answer.

Option C: \{(13,-3),(13,0),(13,-1),(13,-1)\}

From this set of ordered pairs, it is obvious that the element 13 of x is related to three different element in y.

Thus, the ordered pairs \{(13,-3),(13,0),(13,-1),(13,-1)\} is not a function.

Hence, Option C is not the correct answer.

Option D: \{(-9,8),(-5,-8),(-7,8),(-6,-8)\}

A relation is said to be a function if each element of x is related to exactly one element in y.

From this set of ordered pairs, it is obvious that the each element of x is related exactly one element in y.

Thus, the ordered pairs \{(-9,8),(-5,-8),(-7,8),(-6,-8)\} is a function.

Hence, Option D is the correct answer.

7 0
3 years ago
Convert pounds to ounces to<br> complete the table.
True [87]

1 : 16

2 : 32

4 : 64

6 : 96

12 : 192

You find these by multiplying the pounds by ounces

So, 2 pounds * 16 ounces = 32 ounces.

4 0
3 years ago
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