Find the circumcenter of the triangle ABC. A( - 4,3), B(5,7), C(-4,7).

Mathematics

1 answer:

lozanna [386]4 years ago

6 0

Answer:

Circumcenter O (0.5 , 5)

Step-by-step explanation:

Circumcenter O (x , y)

OA = OB = OC

OA² = (x + 4)² + (y - 3)²

OB² = (x - 5)² + (y - 7)²

OC² = ( x + 4)² + (y - 7)²

OA² = OC² : (x + 4)² + (y - 3)² = ( x + 4)² + (y - 7)²

(y - 3)² = (y - 7)² y² - 6y + 9 = y² -14y + 49

8y = 40

y = 5

OB² = OC² : (x - 5)² + (y - 7)² = ( x + 4)² + (y - 7)²

x² - 10x + 25 = x² + 8x + 16

18x = 9

x = 0.5

Circumcenter O (0.5 , 5)

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What polynomial has a graph that passes through the given points?

Evgen [1.6K]

The answer is B. y = x^3 + 4x^2 + 2x - 2

A line that passes through all given point is the correct choice. Now, substitute x and y in all of the choices:

B. y = x³ + 4x² + 2x - 2
Point 1: (-2, 2)
x = -2
y = 2
____
2 = (-2)³ + 4 *(-2)² + 2 * (-2) - 2
2 = -8 + 4 * 4 + (-4) - 2
2 = -8 + 16 - 4 - 2
2 = 2
_____

Point 2: (-1, -1)
x = -1
y = -1
____
-1 = (-1)³ + 4 *(-1)² + 2 * (-1) - 2
-1 = -1 + 4 * 1 + (-2) - 2
-1 = -1 + 4 - 2 - 2
-1 = -1
____

Point 3: (1, 5)
x = 1
y = 5
____
5 = (1)³ + 4 *(1)² + 2 * 1 - 2
5 = 1 + 4 * 1 + 2 - 2
5 = 1 + 4 + 2 - 2
5 = 5
____

Point 4: (3, 67)
x = 3
y = 67
____
67 = (3)³ + 4 *(3)² + 2 * (3) - 2
67 = 27 + 4 * 9 + 6 - 2
67 = 27 + 36 + 6 - 2
67 = 67

So, line B passes through all choices.

3 0

3 years ago

PLEASE HELPPPP!!!!!!!

Strike441 [17]

Answer:

Subtract 4 from each side

Step-by-step explanation:

x + 4 > -8

Subtract 4 from each side

x + 4-4 > -8-4

x>-12

6 0